Science.gov

Sample records for advanced numerical schemes

  1. Development of a numerical scheme to predict geomagnetic storms after intense solar events and geomagnetic activity 27 days in advance. Final report, 6 Aug 86-16 Nov 90

    SciTech Connect

    Akasofu, S.I.; Lee, L.H.

    1991-02-01

    The modern geomagnetic storm prediction scheme should be based on a numerical simulation method, rather than on a statistical result. Furthermore, the scheme should be able to predict the geomagnetic storm indices, such as the Dst and AE indices, as a function of time. By recognizing that geomagnetic storms are powered by the solar wind-magnetosphere generator and that its power is given in terms of the solar wind speed, the interplanetary magnetic field (IMF) magnitude and polar angle, the authors have made a major advance in predicting both flare-induced storms and recurrent storms. Furthermore, it is demonstrated that the prediction scheme can be calibrated using the interplanetary scintillation (IPS) observation, when the solar disturbance advances about half-way to the earth. It is shown, however, that we are still far from a reliable prediction scheme. The prediction of the IMF polar angle requires future advance in understanding characteristics of magnetic clouds.

  2. A numerical scheme for ionizing shock waves

    SciTech Connect

    Aslan, Necdet . E-mail: naslan@yeditepe.edu.tr; Mond, Michael

    2005-12-10

    A two-dimensional (2D) visual computer code to solve the steady state (SS) or transient shock problems including partially ionizing plasma is presented. Since the flows considered are hypersonic and the resulting temperatures are high, the plasma is partially ionized. Hence the plasma constituents are electrons, ions and neutral atoms. It is assumed that all the above species are in thermal equilibrium, namely, that they all have the same temperature. The ionization degree is calculated from Saha equation as a function of electron density and pressure by means of a nonlinear Newton type root finding algorithms. The code utilizes a wave model and numerical fluctuation distribution (FD) scheme that runs on structured or unstructured triangular meshes. This scheme is based on evaluating the mesh averaged fluctuations arising from a number of waves and distributing them to the nodes of these meshes in an upwind manner. The physical properties (directions, strengths, etc.) of these wave patterns are obtained by a new wave model: ION-A developed from the eigen-system of the flux Jacobian matrices. Since the equation of state (EOS) which is used to close up the conservation laws includes electronic effects, it is a nonlinear function and it must be inverted by iterations to determine the ionization degree as a function of density and temperature. For the time advancement, the scheme utilizes a multi-stage Runge-Kutta (RK) algorithm with time steps carefully evaluated from the maximum possible propagation speed in the solution domain. The code runs interactively with the user and allows to create different meshes to use different initial and boundary conditions and to see changes of desired physical quantities in the form of color and vector graphics. The details of the visual properties of the code has been published before (see [N. Aslan, A visual fluctuation splitting scheme for magneto-hydrodynamics with a new sonic fix and Euler limit, J. Comput. Phys. 197 (2004) 1

  3. Numerical Schemes for Rough Parabolic Equations

    SciTech Connect

    Deya, Aurelien

    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.

  4. Simple Numerical Schemes for the Korteweg-deVries Equation

    SciTech Connect

    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.

  5. PDE-based Morphology for Matrix Fields: Numerical Solution Schemes

    NASA Astrophysics Data System (ADS)

    Burgeth, Bernhard; Breuß, Michael; Didas, Stephan; Weickert, Joachim

    Tensor fields are important in digital imaging and computer vision. Hence there is a demand for morphological operations to perform e.g. shape analysis, segmentation or enhancement procedures. Recently, fundamental morphological concepts have been transferred to the setting of fields of symmetric positive definite matrices, which are symmetric rank two tensors. This has been achieved by a matrix-valued extension of the nonlinear morphological partial differential equations (PDEs) for dilation and erosion known for grey scale images. Having these two basic operations at our disposal, more advanced morphological operators such as top hats or morphological derivatives for matrix fields with symmetric, positive semidefinite matrices can be constructed. The approach realises a proper coupling of the matrix channels rather than treating them independently. However, from the algorithmic side the usual scalar morphological PDEs are transport equations that require special upwind-schemes or novel high-accuracy predictor-corrector approaches for their adequate numerical treatment. In this chapter we propose the non-trivial extension of these schemes to the matrix-valued setting by exploiting the special algebraic structure available for symmetric matrices. Furthermore we compare the performance and juxtapose the results of these novel matrix-valued high-resolution-type (HRT) numerical schemes by considering top hats and morphological derivatives applied to artificial and real world data sets.

  6. Numerical schemes for a model for nonlinear dispersive waves

    NASA Technical Reports Server (NTRS)

    Bona, J. L.; Pritchard, W. G.; Scott, L. R.

    1985-01-01

    A description is given of a number of numerical schemes to solve an evolution equation (Korteweg-deVries) that arises when modelling the propagation of water waves in a channel. The discussion also includes the results of numerical experiments made with each of the schemes. It is suggested, on the basis of these experiments, that one of the schemes may have (discrete) solitary-wave solutions.

  7. Numerical simulation of shock wave diffraction by TVD schemes

    NASA Technical Reports Server (NTRS)

    Young, Victor Y. C.; Yee, H. C.

    1987-01-01

    An upwind total variation diminishing (TVD) scheme and a predictor-corrector symmetric TVD scheme were used to numerically simulate the blast wave diffraction on a stationary object. The objective is to help design an optimum configuration so that lateral motion is minimized and at the same time vortex shedding and flow separation are reduced during a blast wave encounter. Results are presented for a generic configuration for both a coarse grid and a fine grid to illustrate the global and local diffraction flow fields. Numerical experiments for the shock wave reflection on a wedge are also included to validate the current approach. Numerical study indicated that these TVD schemes are more stable and produced higher shock resolution than classical shock capturing methods such as the explicit MacCormack scheme.

  8. Advances in numerical and applied mathematics

    NASA Technical Reports Server (NTRS)

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

    1986-01-01

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

  9. Numerical solution of a semilinear elliptic equation via difference scheme

    NASA Astrophysics Data System (ADS)

    Beigmohammadi, Elif Ozturk; Demirel, Esra

    2016-08-01

    We consider the Bitsadze-Samarskii type nonlocal boundary value problem { -d/2v (t ) d t2 +B v (t ) =h (t ,v (t ) ) ,0 scheme. The numerical results are computed by MATLAB.

  10. Numerical issues for coupling biological models with isopycnal mixing schemes

    NASA Astrophysics Data System (ADS)

    Gnanadesikan, Anand

    1999-01-01

    In regions of sloping isopycnals, isopycnal mixing acting in conjunction with biological cycling can produce patterns in the nutrient field which have negative values of tracer in light water and unrealistically large values of tracer in dense water. Under certain circumstances, these patterns can start to grow unstably. This paper discusses why such behavior occurs. Using a simple four-box model, it demonstrates that the instability appears when the isopycnal slopes exceed the grid aspect ratio ( Δz/ Δx). In contrast to other well known instabilities of the CFL type, this instability does not depend on the time step or time-stepping scheme. Instead it arises from a fundamental incompatibility between two requirements for isopycnal mixing schemes, namely that they should produce no net flux of passive tracer across an isopycnal and everywhere reduce tracer extrema. In order to guarantee no net flux of tracer across an isopycnal, some upgradient fluxes across certain parts of an isopycnal are required to balance downgradient fluxes across other parts of the isopycnal. However, these upgradient fluxes can cause local maxima in the nutrient field to become self-reinforcing. Although this is less of a problem in larger domains, there is still a strong tendency for isopycnal mixing to overconcentrate tracer in the dense water. The introduction of eddy-induced advection is shown to be capable of counteracting the upgradient fluxes of nutrient which cause problems, stabilizing the solution. The issue is not simply a numerical curiosity. When used in a GCM, different parameterizations of eddy mixing result in noticeably different distributions of nutrient and large differences in biological production. While much of this is attributable to differences in convection and circulation, the numerical errors described here may also play an important role in runs with isopycnal mixing alone.

  11. A numerical scheme for coastal morphodynamic modelling on unstructured grids

    NASA Astrophysics Data System (ADS)

    Guerin, Thomas; Bertin, Xavier; Dodet, Guillaume

    2016-08-01

    Over the last decade, modelling systems based on unstructured grids have been appearing increasingly attractive to investigate the dynamics of coastal zones. However, the resolution of the sediment continuity equation to simulate bed evolution is a complex problem which often leads to the development of numerical oscillations. To overcome this problem, addition of artificial diffusion or bathymetric filters are commonly employed methods, although these techniques can potentially over-smooth the bathymetry. This study aims to present a numerical scheme based on the Weighted Essentially Non-Oscillatory (WENO) formalism to solve the bed continuity equation on unstructured grids in a finite volume formulation. The new solution is compared against a classical method, which combines a basic node-centered finite volume method with artificial diffusion, for three idealized test cases. This comparison reveals that a higher accuracy is obtained with our new method while the addition of diffusion appears inappropriate mainly due to the arbitrary choice of the diffusion coefficient. Moreover, the increased computation time associated with the WENO-based method to solve the bed continuity equation is negligible when considering a fully-coupled simulation with tides and waves. Finally, the application of the new method to the pluri-monthly evolution of an idealized inlet subjected to tides and waves shows the development of realistic bed features (e.g. secondary flood channels, ebb-delta sandbars, or oblique sandbars at the adjacent beaches), that are smoothed or nonexistent when using additional diffusion.

  12. Variationally consistent discretization schemes and numerical algorithms for contact problems

    NASA Astrophysics Data System (ADS)

    Wohlmuth, Barbara

    We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal-dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration schemes. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of

  13. Lagrangian model of zooplankton dispersion: numerical schemes comparisons and parameter sensitivity tests

    NASA Astrophysics Data System (ADS)

    Qiu, Zhongfeng; Doglioli, Andrea M.; He, Yijun; Carlotti, Francois

    2011-03-01

    This paper presents two comparisons or tests for a Lagrangian model of zooplankton dispersion: numerical schemes and time steps. Firstly, we compared three numerical schemes using idealized circulations. Results show that the precisions of the advanced Adams-Bashfold-Moulton (ABM) method and the Runge-Kutta (RK) method were in the same order and both were much higher than that of the Euler method. Furthermore, the advanced ABM method is more efficient than the RK method in computational memory requirements and time consumption. We therefore chose the advanced ABM method as the Lagrangian particle-tracking algorithm. Secondly, we performed a sensitivity test for time steps, using outputs of the hydrodynamic model, Symphonie. Results show that the time step choices depend on the fluid response time that is related to the spatial resolution of velocity fields. The method introduced by Oliveira et al. in 2002 is suitable for choosing time steps of Lagrangian particle-tracking models, at least when only considering advection.

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

    NASA Technical Reports Server (NTRS)

    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.

  15. Advanced numerics for multi-dimensional fluid flow calculations

    SciTech Connect

    Vanka, S.P.

    1984-04-01

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

  16. Advanced numerics for multi-dimensional fluid flow calculations

    NASA Technical Reports Server (NTRS)

    Vanka, S. P.

    1984-01-01

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

  17. Numerical study of chemically reacting flows using an LU scheme

    NASA Technical Reports Server (NTRS)

    Shuen, Jian Shun; Yoon, Seokkwan

    1988-01-01

    A new computational fluid dynamic code has been developed for the study of mixing and chemical reactions in the flow fields of ramjets and scramjets. The code employs an implicit finite volume, lower-upper symmetric successive overrelaxation scheme for solving the complete two-dimensional Navier-Stokes equations and species transport equations in a fully-coupled and very efficient manner. The combustion processes are modeled by an 8-species, 14-step finite rate chemistry model whereas turbulence is simulated by a Baldwin-Lomax algebraic model. The validity of the code is demonstrated by comparing the numerical calculations with both experimental data and previous calculations of a cold flow helium injection into a straight channel and premixed hydrogen-air reacting flows in a ramped duct. The code is then used to calculate the mixing and chemical reactions of a hydrogen jet transversely injected into a supersonic airstream. Results are presented describing the flow field, the recirculation regions in front and behind the injector, and the chemical reactions.

  18. Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Sethian, James A.

    1997-01-01

    Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a virtual edge flipping technique, Lipschitz continuity of the numerical flux is restored on acute triangulations. Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These schemes possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the numerical Hamiltonian. Finally, a class of Petrov-Galerkin approximations are considered. These schemes are stabilized via a least-squares bilinear form. The Petrov-Galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy.

  19. An Advanced Leakage Scheme for Neutrino Treatment in Astrophysical Simulations

    NASA Astrophysics Data System (ADS)

    Perego, A.; Cabezón, R. M.; Käppeli, R.

    2016-04-01

    We present an Advanced Spectral Leakage (ASL) scheme to model neutrinos in the context of core-collapse supernovae (CCSNe) and compact binary mergers. Based on previous gray leakage schemes, the ASL scheme computes the neutrino cooling rates by interpolating local production and diffusion rates (relevant in optically thin and thick regimes, respectively) separately for discretized values of the neutrino energy. Neutrino trapped components are also modeled, based on equilibrium and timescale arguments. The better accuracy achieved by the spectral treatment allows a more reliable computation of neutrino heating rates in optically thin conditions. The scheme has been calibrated and tested against Boltzmann transport in the context of Newtonian spherically symmetric models of CCSNe. ASL shows a very good qualitative and a partial quantitative agreement for key quantities from collapse to a few hundreds of milliseconds after core bounce. We have proved the adaptability and flexibility of our ASL scheme, coupling it to an axisymmetric Eulerian and to a three-dimensional smoothed particle hydrodynamics code to simulate core collapse. Therefore, the neutrino treatment presented here is ideal for large parameter-space explorations, parametric studies, high-resolution tests, code developments, and long-term modeling of asymmetric configurations, where more detailed neutrino treatments are not available or are currently computationally too expensive.

  20. Comparison of SMAC, PISO, and iterative time-advancing schemes for unsteady flows

    NASA Technical Reports Server (NTRS)

    Kim, Sang-Wook; Benson, Thomas J.

    1991-01-01

    Calculations of unsteady flows using a simplified marker and cell (SMAC), a pressure implicit splitting of operators (PSIO), and an iterative time advancing scheme (ITA) are presented. A partial differential equation for incremental pressure is used in each time advancing scheme. Example flows considered are a polar cavity flow starting from rest and self-sustained oscillating flows over a circular and a square cylinder. For a large time step size, the SMAC and ITA are more strongly convergent and yield more accurate results than PSIO. The SMAC is the most efficient computationally. For a small time step size, the three time advancing schemes yield equally accurate Strouhal numbers. The capability of each time advancing scheme to accurately resolve unsteady flows is attributed to the use of new pressure correction algorithm that can strongly enforce the conservation of mass. The numerical results show that the low frequency of the vortex shedding is caused by the growth time of each vortex shed into the wake region.

  1. A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling.

    PubMed

    Boileau, Etienne; Nithiarasu, Perumal; Blanco, Pablo J; Müller, Lucas O; Fossan, Fredrik Eikeland; Hellevik, Leif Rune; Donders, Wouter P; Huberts, Wouter; Willemet, Marie; Alastruey, Jordi

    2015-10-01

    Haemodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1D numerical schemes has led to the development of alternative experimental setups and the use of three-dimensional numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1D scheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1D blood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensional numerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1D models and numerical schemes.

  2. Brush seal numerical simulation: Concepts and advances

    NASA Technical Reports Server (NTRS)

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

    1994-01-01

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

  3. Brush seal numerical simulation: Concepts and advances

    NASA Astrophysics Data System (ADS)

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

    1994-07-01

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

  4. Multi-dimensional high-order numerical schemes for Lagrangian hydrodynamics

    SciTech Connect

    Dai, William W; Woodward, Paul R

    2009-01-01

    An approximate solver for multi-dimensional Riemann problems at grid points of unstructured meshes, and a numerical scheme for multi-dimensional hydrodynamics have been developed in this paper. The solver is simple, and is developed only for the use in numerical schemes for hydrodynamics. The scheme is truely multi-dimensional, is second order accurate in both space and time, and satisfies conservation laws exactly for mass, momentum, and total energy. The scheme has been tested through numerical examples involving strong shocks. It has been shown that the scheme offers the principle advantages of high-order Codunov schemes; robust operation in the presence of very strong shocks and thin shock fronts.

  5. Eulerian-Lagrangian numerical scheme for simulating advection, dispersion, and transient storage in streams and a comparison of numerical methods

    USGS Publications Warehouse

    Cox, T.J.; Runkel, R.L.

    2008-01-01

    Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.

  6. Towards improved numerical schemes of turbulent lateral dispersion

    NASA Astrophysics Data System (ADS)

    Kämpf, Jochen; Cox, Darren

    2016-10-01

    This paper focuses on an alternative approach of lateral turbulent dispersion, proposed by Benoit Cushman-Roisin in 2008, that is based on a linear increase of the width of dispersing patches in a field of isotropic horizontal turbulence. In the open ocean, this Richardson-like dispersion regime is a well-observed feature on sub-mesoscale length scales from 10 to 100 km. In this work, we successfully validate and calibrate the new diffusion scheme using Lagrangian particles and Eulerian tracer in turbulent velocity fields simulated with the shallow-water equations. In discretized form, the new diffusion scheme exclusively relies on specification of a turbulent velocity scale that, unlike the turbulent diffusivity of Fickian approaches, is well defined through statistical properties of the turbulent flow.

  7. Positivity-preserving numerical schemes for multidimensional advection

    NASA Technical Reports Server (NTRS)

    Leonard, B. P.; Macvean, M. K.; Lock, A. P.

    1993-01-01

    This report describes the construction of an explicit, single time-step, conservative, finite-volume method for multidimensional advective flow, based on a uniformly third-order polynomial interpolation algorithm (UTOPIA). Particular attention is paid to the problem of flow-to-grid angle-dependent, anisotropic distortion typical of one-dimensional schemes used component-wise. The third-order multidimensional scheme automatically includes certain cross-difference terms that guarantee good isotropy (and stability). However, above first-order, polynomial-based advection schemes do not preserve positivity (the multidimensional analogue of monotonicity). For this reason, a multidimensional generalization of the first author's universal flux-limiter is sought. This is a very challenging problem. A simple flux-limiter can be found; but this introduces strong anisotropic distortion. A more sophisticated technique, limiting part of the flux and then restoring the isotropy-maintaining cross-terms afterwards, gives more satisfactory results. Test cases are confined to two dimensions; three-dimensional extensions are briefly discussed.

  8. On some numerical scheme of solving diffraction problem on open and closed screens

    SciTech Connect

    Ryzhakov, Gleb V.

    2015-03-10

    In the paper, the problem of diffraction on thin ideally conductive screens is reduced to vector hypersingular integral equation with integral treated in the sense of finite Hadamard value. An numerical scheme to solve the equation is introduced. The scheme is based on piecewise approximation of unknown function. The advantage of the scheme is that integral of singular part is reduced to contour integral which can be analytically calculated so numerical calculation are significantly accelerated. Several examples of resulting numerical experiments are given in comparison with known theoretical and experimental data.

  9. The numerical viscosity of entropy stable schemes for systems of conservation laws. I

    NASA Technical Reports Server (NTRS)

    Tadmor, Eitan

    1987-01-01

    Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison.To this end, conservative schemes which are also entropy-conservative are constructed. These entropy-conservative schemes enjoy second-order accuracy; moreover, they can be interpreted as piecewise-linear finite-element methods, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only they contain more viscosity than that present in the above-mentioned entropy-conservative ones.

  10. Earthquake ground motion prediction for real sedimentary basins: which numerical schemes are applicable?

    NASA Astrophysics Data System (ADS)

    Moczo, P.; Kristek, J.; Galis, M.; Pazak, P.

    2009-12-01

    Numerical prediction of earthquake ground motion in sedimentary basins and valleys often has to account for P-wave to S-wave speed ratios (Vp/Vs) as large as 5 and even larger, mainly in sediments below groundwater level. The ratio can attain values larger than 10 in unconsolidated sediments (e.g. in Ciudad de México). In a process of developing 3D optimally-accurate finite-difference schemes we encountered a serious problem with accuracy in media with large Vp/Vs ratio. This led us to investigate the very fundamental reasons for the inaccuracy. In order to identify the very basic inherent aspects of the numerical schemes responsible for their behavior with varying Vp/Vs ratio, we restricted to the most basic 2nd-order 2D numerical schemes on a uniform grid in a homogeneous medium. Although basic in the specified sense, the schemes comprise the decisive features for accuracy of wide class of numerical schemes. We investigated 6 numerical schemes: finite-difference_displacement_conventional grid (FD_D_CG) finite-element_Lobatto integration (FE_L) finite-element_Gauss integration (FE_G) finite-difference_displacement-stress_partly-staggered grid (FD_DS_PSG) finite-difference_displacement-stress_staggered grid (FD_DS_SG) finite-difference_velocity-stress_staggered grid (FD_VS_SG) We defined and calculated local errors of the schemes in amplitude and polarization. Because different schemes use different time steps, they need different numbers of time levels to calculate solution for a desired time window. Therefore, we normalized errors for a unit time. The normalization allowed for a direct comparison of errors of different schemes. Extensive numerical calculations for wide ranges of values of the Vp/Vs ratio, spatial sampling ratio, stability ratio, and entire range of directions of propagation with respect to the spatial grid led to interesting and surprising findings. Accuracy of FD_D_CG, FE_L and FE_G strongly depends on Vp/Vs ratio. The schemes are not

  11. SEAWAT 2000: modelling unstable flow and sensitivity to discretization levels and numerical schemes

    NASA Astrophysics Data System (ADS)

    Al-Maktoumi, A.; Lockington, D. A.; Volker, R. E.

    2007-09-01

    A systematic analysis shows how results from the finite difference code SEAWAT are sensitive to choice of grid dimension, time step, and numerical scheme for unstable flow problems. Guidelines to assist in selecting appropriate combinations of these factors are suggested. While the SEAWAT code has been tested for a wide range of problems, the sensitivity of results to spatial and temporal discretization levels and numerical schemes has not been studied in detail for unstable flow problems. Here, the Elder-Voss-Souza benchmark problem has been used to systematically explore the sensitivity of SEAWAT output to spatio-temporal resolution and numerical solver choice. A grid size of 0.38 and 0.60% of the total domain length and depth respectively is found to be fine enough to deliver results with acceptable accuracy for most of the numerical schemes when Courant number (Cr) is 0.1. All numerical solvers produced similar results for extremely fine meshes; however, some schemes converged faster than others. For instance, the 3rd-order total variation-diminishing method (TVD3) scheme converged at a much coarser mesh than the standard finite difference methods (SFDM) upstream weighting (UW) scheme. The sensitivity of the results to Cr number depends on the numerical scheme as expected.

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

    NASA Astrophysics Data System (ADS)

    Teodoro, M. F.

    2012-09-01

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

  13. Steady-State Analysis Model for Advanced Fuel Cycle Schemes.

    2008-03-17

    Version 00 SMAFS was developed as a part of the study, "Advanced Fuel Cycles and Waste Management", which was performed during 2003-2005 by an ad-hoc expert group under the Nuclear Development Committee in the OECD/NEA. The model was designed for an efficient conduct of nuclear fuel cycle scheme cost analyses. It is simple, transparent and offers users the capability to track down cost analysis results. All the fuel cycle schemes considered in the model aremore » represented in a graphic format and all values related to a fuel cycle step are shown in the graphic interface, i.e., there are no hidden values embedded in the calculations. All data on the fuel cycle schemes considered in the study including mass flows, waste generation, cost data, and other data such as activities, decay heat and neutron sources of spent fuel and high-level waste along time are included in the model and can be displayed. The user can easily modify values of mass flows and/or cost parameters and see corresponding changes in the results. The model calculates: front-end fuel cycle mass flows such as requirements of enrichment and conversion services and natural uranium; mass of waste based on the waste generation parameters and the mass flow; and all costs.« less

  14. Steady-state Analysis Model for Advanced Fuelcycle Schemes

    2006-05-12

    The model was developed as a part of the study, "Advanced Fuel Cycles and Waste Management", which was performed during 2003—2005 by an ad-hoc expert group under the Nuclear Development Committee in the OECD/NEA. The model was designed for an efficient conduct of nuclear fuel cycle scheme cost analyses. It is simple, transparent and offers users the capability to track down the cost analysis results. All the fuel cycle schemes considered in the model aremore » represented in a graphic format and all values related to a fuel cycle step are shown in the graphic interface, i.e., there are no hidden values embedded in the calculations. All data on the fuel cycle schemes considered in the study including mass flows, waste generation, cost data, and other data such as activities, decay heat and neutron sources of spent fuel and high—level waste along time are included in the model and can be displayed. The user can modify easily the values of mass flows and/or cost parameters and see the corresponding changes in the results. The model calculates: front—end fuel cycle mass flows such as requirements of enrichment and conversion services and natural uranium; mass of waste based on the waste generation parameters and the mass flow; and all costs. It performs Monte Carlo simulations with changing the values of all unit costs within their respective ranges (from lower to upper bounds).« less

  15. Linear Properties of Numerical Schemes for the Shallow Water Equations

    NASA Astrophysics Data System (ADS)

    Eldred, C.; Randall, D. A.

    2013-12-01

    The shallow water equations provide a useful analogue of fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. There has been extensive work exploring the linear properties (balanced states and propagating modes) of various schemes for the shallow water equations on uniform grids, but comparatively little work for non-uniform grids (especially in the case of finite difference and finite volume methods). With the simplifications associated with uniform grids, analytic results for the dispersion relationship and other linear properties can be obtained. However, such grids are not necessarily representative of the actual grids used in dynamical cores on the sphere. Using the Atmospheric Dynamical Core Testbed (ADCoT) built on top of Morphe, the linear properties of various popular finite-difference and finite-volume schemes are examined on both uniform and non-uniform grids (such as the cubed sphere, triangular geodesic and hexagonal-pentagonal geodesic grids).

  16. Adaptive Numerical Dissipative Control in High Order Schemes for Multi-D Non-Ideal MHD

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sjoegreen, B.

    2004-01-01

    The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free of numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multi-resolution wavelets (WAV) (for the above types of flow feature). These filter approaches also provide a natural and efficient way for the minimization of Div(B) numerical error. The filter scheme consists of spatially sixth order or higher non-dissipative spatial difference operators as the base scheme for the inviscid flux derivatives. If necessary, a small amount of high order linear dissipation is used to remove spurious high frequency oscillations. For example, an eighth-order centered linear dissipation (AD8) might be included in conjunction with a spatially sixth-order base scheme. The inviscid difference operator is applied twice for the viscous flux derivatives. After the completion of a full time step of the base scheme step, the solution is adaptively filtered by the product of a 'flow detector' and the 'nonlinear dissipative portion' of a high-resolution shock-capturing scheme. In addition, the scheme independent wavelet flow detector can be used in conjunction with spatially compact, spectral or spectral element type of base schemes. The ACM and wavelet filter schemes using the dissipative portion of a second-order shock-capturing scheme with sixth-order spatial central base scheme for both the inviscid and viscous MHD flux

  17. Finite-difference scheme for the numerical solution of the Schroedinger equation

    NASA Technical Reports Server (NTRS)

    Mickens, Ronald E.; Ramadhani, Issa

    1992-01-01

    A finite-difference scheme for numerical integration of the Schroedinger equation is constructed. Asymptotically (r goes to infinity), the method gives the exact solution correct to terms of order r exp -2.

  18. A Continuing Search for a Near-Perfect Numerical Flux Scheme. Part 1; [AUSM+

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing

    1994-01-01

    While enjoying demonstrated improvement in accuracy, efficiency, and robustness over existing schemes, the Advection Upstream Splitting Scheme (AUSM) was found to have some deficiencies in extreme cases. This recent progress towards improving the AUSM while retaining its advantageous features is described. The new scheme, termed AUSM+, features: unification of velocity and Mach number splitting; exact capture of a single stationary shock; and improvement in accuracy. A general construction of the AUSM+ scheme is layed out and then focus is on the analysis of the a scheme and its mathematical properties, heretofore unreported. Monotonicity and positivity are proved, and a CFL-like condition is given for first and second order schemes and for generalized curvilinear co-ordinates. Finally, results of numerical tests on many problems are given to confirm the capability and improvements on a variety of problems including those failed by prominent schemes.

  19. The Impacts of Numerical Schemes on Asymmetric Hurricane Intensification

    NASA Astrophysics Data System (ADS)

    Guimond, S.; Reisner, J. M.; Marras, S.; Giraldo, F.

    2015-12-01

    The fundamental pathways for tropical cyclone (TC) intensification are explored by considering axisymmetric and asymmetric impulsive thermal perturbations to balanced, TC-like vortices using the dynamic cores of three different numerical models. Attempts at reproducing the results of previous work, which used the community atmospheric model WRF (Nolan and Grasso 2003; NG03), revealed a discrepancy with the impacts of purely asymmetric thermal forcing. The current study finds that thermal asymmetries can have an important, largely positive role on the vortex intensification whereas NG03 and other studies find that asymmetric impacts are negligible. Analysis of the spectral energetics of each numerical model indicates that the vortex response to asymmetric thermal perturbations is significantly damped in WRF relative to the other numerical models. Spectral kinetic energy budgets show that this anomalous damping is due to the increased removal of kinetic energy from the convergence of the vertical pressure flux, which is related to the flux of inertia-gravity wave energy. The increased kinetic energy in the other two models is shown to originate around the scales of the heating and propagate upscale with time. For very large thermal amplitudes (~ 50 K and above), the anomalous removal of kinetic energy due to inertia-gravity wave activity is much smaller resulting in little differences between models. The results of this paper indicate that the numerical treatment of small-scale processes that project strongly onto inertia-gravity wave energy are responsible for these differences, with potentially important impacts for the understanding and prediction of TC intensification.

  20. The numerical viscosity of entropy stable schemes for systems of conservation laws

    NASA Technical Reports Server (NTRS)

    Tadmor, E.

    1985-01-01

    Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes, is quantified and related to their entropy stability by means of comparison. To this end, conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they admit a particular interpretation within the finite-element frameworks, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable if and only if they contain more viscosity than the mentioned above entropy conservative ones.

  1. Efficient energy stable numerical schemes for a phase field moving contact line model

    NASA Astrophysics Data System (ADS)

    Shen, Jie; Yang, Xiaofeng; Yu, Haijun

    2015-03-01

    In this paper, we present two efficient energy stable schemes to solve a phase field model incorporating moving contact line. The model is a coupled system that consists of incompressible Navier-Stokes equations with a generalized Navier boundary condition and Cahn-Hilliard equation in conserved form. In both schemes the projection method is used to deal with the Navier-Stokes equations and stabilization approach is used for the non-convex Ginzburg-Landau bulk potential. By some subtle explicit-implicit treatments, we obtain a linear coupled energy stable scheme for systems with dynamic contact line conditions and a linear decoupled energy stable scheme for systems with static contact line conditions. An efficient spectral-Galerkin spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes. Numerical results show that the proposed schemes are very efficient and accurate.

  2. Numerical Compression Schemes for Proteomics Mass Spectrometry Data*

    PubMed Central

    Teleman, Johan; Dowsey, Andrew W.; Gonzalez-Galarza, Faviel F.; Perkins, Simon; Pratt, Brian; Röst, Hannes L.; Malmström, Lars; Malmström, Johan; Jones, Andrew R.; Deutsch, Eric W.; Levander, Fredrik

    2014-01-01

    The open XML format mzML, used for representation of MS data, is pivotal for the development of platform-independent MS analysis software. Although conversion from vendor formats to mzML must take place on a platform on which the vendor libraries are available (i.e. Windows), once mzML files have been generated, they can be used on any platform. However, the mzML format has turned out to be less efficient than vendor formats. In many cases, the naïve mzML representation is fourfold or even up to 18-fold larger compared with the original vendor file. In disk I/O limited setups, a larger data file also leads to longer processing times, which is a problem given the data production rates of modern mass spectrometers. In an attempt to reduce this problem, we here present a family of numerical compression algorithms called MS-Numpress, intended for efficient compression of MS data. To facilitate ease of adoption, the algorithms target the binary data in the mzML standard, and support in main proteomics tools is already available. Using a test set of 10 representative MS data files we demonstrate typical file size decreases of 90% when combined with traditional compression, as well as read time decreases of up to 50%. It is envisaged that these improvements will be beneficial for data handling within the MS community. PMID:24677029

  3. Quantification of numerical diffusivity due to TVD schemes in the advection equation

    NASA Astrophysics Data System (ADS)

    Bidadi, Shreyas; Rani, Sarma L.

    2014-03-01

    In this study, the numerical diffusivity νnum inherent to the Roe-MUSCL scheme has been quantified for the scalar advection equation. The Roe-MUSCL scheme employed is a combination of: (1) the standard extension of the original Roe's formulation to the advection equation, and (2) van Leer's Monotone Upwind Scheme for Conservation Laws (MUSCL) technique that applies a linear variable reconstruction in a cell along with a scaled limiter function. An explicit expression is derived for the numerical diffusivity in terms of the limiter function, the distance between the cell centers on either side of a face, and the face-normal velocity. The numerical diffusivity formulation shows that a scaled limiter function is more appropriate for MUSCL in order to consistently recover the central-differenced flux at the maximum value of the limiter. The significance of the scaling factor is revealed when the Roe-MUSCL scheme, originally developed for 1-D scenarios, is applied to 2-D scalar advection problems. It is seen that without the scaling factor, the MUSCL scheme may not necessarily be monotonic in multi-dimensional scenarios. Numerical diffusivities of the minmod, superbee, van Leer and Barth-Jesperson TVD limiters were quantified for four problems: 1-D advection of a step function profile, and 2-D advection of step, sinusoidal, and double-step profiles. For all the cases, it is shown that the superbee scheme provides the lowest numerical diffusivity that is also most confined to the vicinity of the discontinuity. The minmod scheme is the most diffusive, as well as active in regions away from high gradients. As expected, the grid resolution study demonstrates that the magnitude and the spatial extent of the numerical diffusivity decrease with increasing resolution.

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

    NASA Astrophysics Data System (ADS)

    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.

  5. A practical numerical scheme for the ternary Cahn-Hilliard system with a logarithmic free energy

    NASA Astrophysics Data System (ADS)

    Jeong, Darae; Kim, Junseok

    2016-01-01

    We consider a practically stable finite difference method for the ternary Cahn-Hilliard system with a logarithmic free energy modeling the phase separation of a three-component mixture. The numerical scheme is based on a linear unconditionally gradient stable scheme by Eyre and is solved by an efficient and accurate multigrid method. The logarithmic function has a singularity at zero. To remove the singularity, we regularize the function near zero by using a quadratic polynomial approximation. We perform a convergence test, a linear stability analysis, and a robustness test of the ternary Cahn-Hilliard equation. We observe that our numerical solutions are convergent, consistent with the exact solutions of linear stability analysis, and stable with practically large enough time steps. Using the proposed numerical scheme, we also study the temporal evolution of morphology patterns during phase separation in one-, two-, and three-dimensional spaces.

  6. Analytical and numerical methods; advanced computer concepts

    SciTech Connect

    Lax, P D

    1991-03-01

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

  7. Advanced unrepeatered systems using novel Raman amplification schemes

    NASA Astrophysics Data System (ADS)

    Chang, Do-il; Pelouch, Wayne; Burtsev, Sergey; Perrier, Philippe; Fevrier, Herve

    2015-01-01

    Unrepeatered transmission systems provide a cost-effective solution to transmit high capacity channels in submarine networks to communicate between coastal population centers or in terrestrial networks to connect remote areas where service access is difficult. The main goal of unrepeatered systems has traditionally been to achieve the longest reach, however, increasing traffic demands now require unrepeatered systems to support both longer reach and higher transport capacity. As a result, transmission rate of unrepeatered systems has quickly moved from 10 Gb/s to 40 Gb/s or 100 Gb/s. This paper reviews the key basic technologies, with a specific focus on Raman amplification, required for long-reach, high-capacity unrepeatered optical transmission systems. We will discuss novel Raman amplification schemes, enhanced remote optically pumped amplifiers (ROPA), ultra-low loss / large effective area fibers, and coherent transmission with advanced modulation format and high FEC coding gain. We will also report recent experimental demonstrations that show how these technologies have been combined to achieve industry's leading capacity and reach transmission.

  8. An Analysis of Two Schemes to Numerically Solve the Stochastic Collection Growth Equation.

    NASA Astrophysics Data System (ADS)

    de Almeida, Fausto Carlos; Dennett, Roger D.

    1980-12-01

    Two schemes for the numerical solution of the stochastic collection growth equation for cloud drops are compared. Their numerical approaches are different. One (the Berry/Reinhardt method) emphasizes accuracy; the other (the Bleck method) emphasizes speed. Our analysis shows that for applications where the number of solutions (time steps) does not exceed 104 the accuracy-oriented scheme is faster. For larger, repetitive applications, such as a comprehensive cloud model, an objective analysis can be made on the merits of exchanging accuracy for computational time.

  9. A numerical method for solving the Vlasov-Poisson equation based on the conservative IDO scheme

    NASA Astrophysics Data System (ADS)

    Imadera, Kenji; Kishimoto, Yasuaki; Saito, Daisuke; Li, Jiquan; Utsumi, Takayuki

    2009-12-01

    We have applied the conservative form of the Interpolated Differential Operator (IDO-CF) scheme in order to solve the Vlasov-Poisson equation, which is one of the multi-moment schemes. Through numerical tests of the nonlinear Landau damping and two-stream instability, we compared the present scheme with other schemes such as the Spline and CIP ones. We mainly investigated the conservation property of the L1-norm, energy, entropy and phase space area for each scheme, and demonstrated that the IDO-CF scheme is capable of performing stable long time scale simulation while maintaining high accuracy. The scheme is based on an Eulerian approach, and it can thus be directly used for Fokker-Planck, high dimensional Vlasov-Poisson and also guiding-center drift simulations, aiming at particular problems of plasma physics. The benchmark tests for such simulations have shown that the IDO-CF scheme is superior in keeping the conservation properties without causing serious phase error.

  10. Numerical Simulation of Laser-Driven Rayleigh-Taylor Instability using TVD MUSCL Scheme

    NASA Astrophysics Data System (ADS)

    Nagatomo, Hideo; Ohnishi, Naofumo; Takeuchi, Hajime; Takabe, Hideaki; Mima, Kunioki

    1996-11-01

    For the inertial confinement fusion, it is important to simulate and predict the hydrodynamic instabilities. The numerical simulation of the laser-driven Rayleigh-Taylor instability was performed by using a newly developed numerical code which include the two temperature plasma effect and the equation of state. This code is robust and less dissipative because the scheme is based on flux vector splitting method. Furthermore, this method is coupled with high-order MUSCL TVD scheme which enable to capture the shock, the vortices and the contact discontinuity clearly. In the two temperature model, the relaxation of the ion and electron temperature is considered. Cowan ion equation and Thomas-Fermi fitting formula for electron are applied to the equation of state. The dependence on the equation of state will be discussed in this presentation. Also, some numerical results which are solved by the other numerical codes will be shown for the comparison.

  11. Advanced Numerical Model for Irradiated Concrete

    SciTech Connect

    Giorla, Alain B.

    2015-03-01

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

  12. Quantitative evaluation of numerical integration schemes for Lagrangian particle dispersion models

    NASA Astrophysics Data System (ADS)

    Ramli, Huda Mohd.; Esler, J. Gavin

    2016-07-01

    A rigorous methodology for the evaluation of integration schemes for Lagrangian particle dispersion models (LPDMs) is presented. A series of one-dimensional test problems are introduced, for which the Fokker-Planck equation is solved numerically using a finite-difference discretisation in physical space and a Hermite function expansion in velocity space. Numerical convergence errors in the Fokker-Planck equation solutions are shown to be much less than the statistical error associated with a practical-sized ensemble (N = 106) of LPDM solutions; hence, the former can be used to validate the latter. The test problems are then used to evaluate commonly used LPDM integration schemes. The results allow for optimal time-step selection for each scheme, given a required level of accuracy. The following recommendations are made for use in operational models. First, if computational constraints require the use of moderate to long time steps, it is more accurate to solve the random displacement model approximation to the LPDM rather than use existing schemes designed for long time steps. Second, useful gains in numerical accuracy can be obtained, at moderate additional computational cost, by using the relatively simple "small-noise" scheme of Honeycutt.

  13. A numerical study of ENO and TVD schemes for shock capturing

    NASA Technical Reports Server (NTRS)

    Chang, Shih-Hung; Liou, Meng-Sing

    1988-01-01

    The numerical performance of a second-order upwind-based total variation diminishing (TVD) scheme and that of a uniform second-order essentially non-oscillatory (ENO) scheme for shock capturing are compared. The TVD scheme used is a modified version of Liou, using the flux-difference splitting (FDS) of Roe and his superbee function as the limiter. The construction of the basic ENO scheme is based on Harten, Engquist, Osher, and Chakravarthy, and the 2-D extensions are obtained by using a Strang-type of fractional-step time-splitting method. Numerical results presented include both steady and unsteady, 1-D and 2-D calculations. All the chosen test problems have exact solutions so that numerical performance can be measured by comparing the computer results to them. For 1-D calculations, the standard shock-tube problems of Sod and Lax are chosen. A very strong shock-tube problem, with the initial density ratio of 400 to 1 and pressure ratio of 500 to 1, is also used to study the behavior of the two schemes. For 2-D calculations, the shock wave reflection problems are adopted for testing. The cases presented in this report include flows with Mach numbers of 2.9, 5.0, and 10.0.

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

    SciTech Connect

    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.

  15. Numerical calculation of tidal current with UTOPIA scheme for advection and application to Osaka Bay

    NASA Astrophysics Data System (ADS)

    Komoda, Jun; Matsuyama, Masaji

    UTOPIA scheme was applied to advection term for the numerical calculation of tide and tidal current to reproduce the strong tidal current realistically. Numerical model is constructed by boundary-fitted coordinate method vertically using Arakawa A grid in space. The new method is designed to suppress a numerical oscillation usually induced by Arakawa A grid. UTOPIA scheme was confirmed to be suitable to express a strong current around complicated topography. This model was applied to the tidal calculation for M2 constituent in Osaka Bay with two narrow straits, i.e., Akashi and Tomogashima straits. The tidal currents obtained in this model agree with them observed at monitoring stations, and the four eddies in the bay were also reproduced as the residual currents, i.e., tide induced transient eddy (TITE). The generation, growth and lifetime of the eddies also were investigated.

  16. A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation

    NASA Astrophysics Data System (ADS)

    Han, Daozhi; Wang, Xiaoming

    2015-06-01

    We propose a novel second order in time numerical scheme for Cahn-Hilliard-Navier-Stokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection for the Navier-Stokes equation. We show that the scheme is mass-conservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, we prove that the scheme is unconditionally uniquely solvable at each time step by exploring the monotonicity associated with the scheme. Thanks to the simple coupling of the scheme, we design an efficient Picard iteration procedure to further decouple the computation of Cahn-Hilliard equation and Navier-Stokes equation. We implement the scheme by the mixed finite element method. Ample numerical experiments are performed to validate the accuracy and efficiency of the numerical scheme.

  17. The numerical simulations of explosion and implosion in air: use of a modified Harten's TVD scheme

    NASA Astrophysics Data System (ADS)

    Liu, T. G.; Khoo, B. C.; Yeo, K. S.

    1999-10-01

    Numerical simulations of explosion and implosion in air are carried out with a modified Harten's TVD scheme. The new scheme has a high resolution for contact discontinuities in addition to maintaining the good features of Harten's TVD scheme. In the numerical experiment of spherical explosion in air, the second shock wave (which does not exist in the one-dimensional shock tube problem) and its subsequent implosion on the origin have been successfully captured. The positions of the main shock wave, the contact discontinuity and the second shock wave have shown satisfactory agreement with those predicted from previous analysis. The numerical results are also compared with those obtained experimentally. Finally, simulations of a cylindrical explosion and implosion in air are carried out. Results of the cylindrical implosion in air are compared with those of previous work, including the interaction of the reflected main shock wave with the contact discontinuity and the formation of a second shock wave. All these attest to the successful use of the modified Harten's TVD scheme for the simulations of shock waves arising from explosion and implosion. Copyright

  18. 3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"

    NASA Technical Reports Server (NTRS)

    Douglass, A.

    2005-01-01

    The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.

  19. 2D numerical simulation of the MEP energy-transport model with a finite difference scheme

    SciTech Connect

    Romano, V. . E-mail: romano@dmi.unict.it

    2007-02-10

    A finite difference scheme of Scharfetter-Gummel type is used to simulate a consistent energy-transport model for electron transport in semiconductors devices, free of any fitting parameters, formulated on the basis of the maximum entropy principle. Simulations of silicon n{sup +}-n-n{sup +} diodes, 2D-MESFET and 2D-MOSFET and comparisons with the results obtained by a direct simulation of the Boltzmann transport equation and with other energy-transport models, known in the literature, show the validity of the model and the robustness of the numerical scheme.

  20. A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations

    NASA Astrophysics Data System (ADS)

    Bernal, Francisco; Acebróon, Juan A.

    2016-09-01

    We review, implement, and compare numerical integration schemes for spatially bounded diffusions stopped at the boundary which possess a convergence rate of the discretization error with respect to the timestep $h$ higher than ${\\cal O}(\\sqrt{h})$. We address specific implementation issues of the most general-purpose of such schemes. They have been coded into a single Matlab program and compared, according to their accuracy and computational cost, on a wide range of problems in up to ${\\mathbb R}^{48}$. The paper is self-contained and the code will be made freely downloadable.

  1. Development of advanced control schemes for telerobot manipulators

    NASA Technical Reports Server (NTRS)

    Nguyen, Charles C.; Zhou, Zhen-Lei

    1991-01-01

    To study space applications of telerobotics, Goddard Space Flight Center (NASA) has recently built a testbed composed mainly of a pair of redundant slave arms having seven degrees of freedom and a master hand controller system. The mathematical developments required for the computerized simulation study and motion control of the slave arms are presented. The slave arm forward kinematic transformation is presented which is derived using the D-H notation and is then reduced to its most simplified form suitable for real-time control applications. The vector cross product method is then applied to obtain the slave arm Jacobian matrix. Using the developed forward kinematic transformation and quaternions representation of the slave arm end-effector orientation, computer simulation is conducted to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of the Jacobian pseudo-inverse for various sampling times. In addition, the equivalence between Cartesian velocities and quaternion is also verified using computer simulation. The motion control of the slave arm is examined. Three control schemes, the joint-space adaptive control scheme, the Cartesian adaptive control scheme, and the hybrid position/force control scheme are proposed for controlling the motion of the slave arm end-effector. Development of the Cartesian adaptive control scheme is presented and some preliminary results of the remaining control schemes are presented and discussed.

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

    NASA Astrophysics Data System (ADS)

    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.

  3. Efficient Schemes for Reducing Numerical Dispersion in ModelingMultiphase Transport through Porous and Fractured Media

    SciTech Connect

    Wu, Yu-Shu; Forsyth, Peter A.

    2006-04-13

    Numerical issues with modeling transport of chemicals or solute in realistic large-scale subsurface systems have been a serious concern, even with the continual progress made in both simulation algorithms and computer hardware in the past few decades. The problem remains and becomes even more difficult when dealing with chemical transport in a multiphase flow system using coarse, multidimensional regular or irregular grids, because of the known effects of numerical dispersion associated with moving plume fronts. We have investigated several total-variation-diminishing (TVD) or flux-limiter schemes by implementing and testing them in the T2R3D code, one of the TOUGH2 family of codes. The objectives of this paper are (1) to investigate the possibility of applying these TVD schemes, using multi-dimensional irregular unstructured grids, and (2) to help select more accurate spatial averaging methods for simulating chemical transport given a numerical grid or spatial discretization. We present an application example to show that such TVD schemes are able to effectively reduce numerical dispersion.

  4. Adaptive Numerical Dissipation Control in High Order Schemes for Multi-D Non-Ideal MHD

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sjoegreen, B.

    2005-01-01

    The required type and amount of numerical dissipation/filter to accurately resolve all relevant multiscales of complex MHD unsteady high-speed shock/shear/turbulence/combustion problems are not only physical problem dependent, but also vary from one flow region to another. In addition, proper and efficient control of the divergence of the magnetic field (Div(B)) numerical error for high order shock-capturing methods poses extra requirements for the considered type of CPU intensive computations. The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multiresolution wavelets (WAV) (for the above types of flow feature). These filters also provide a natural and efficient way for the minimization of Div(B) numerical error.

  5. Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows

    NASA Astrophysics Data System (ADS)

    Kotov, D. V.; Yee, H. C.; Wray, A. A.; Sjögreen, B.; Kritsuk, A. G.

    2016-02-01

    The Yee & Sjögreen adaptive numerical dissipation control in high order scheme (High Order Filter Methods for Wide Range of Compressible Flow Speeds, ICOSAHOM 09, 2009) is further improved for DNS and LES of shock-free turbulence and low speed turbulence with shocklets. There are vastly different requirements in the minimization of numerical dissipation for accurate turbulence simulations of different compressible flow types and flow speeds. Traditionally, the method of choice for shock-free turbulence and low speed turbulence are by spectral, high order central or high order compact schemes with high order linear filters. With a proper control of a local flow sensor, appropriate amount of numerical dissipation in high order shock-capturing schemes can have spectral-like accuracy for compressible low speed turbulent flows. The development of the method includes an adaptive flow sensor with automatic selection on the amount of numerical dissipation needed at each flow location for more accurate DNS and LES simulations with less tuning of parameters for flows with a wide range of flow speed regime during the time-accurate evolution, e.g., time varying random forcing. An automatic selection of the different flow sensors catered to the different flow types is constructed. A Mach curve and high-frequency oscillation indicators are used to reduce the tuning of parameters in controlling the amount of shock-capturing numerical dissipation to be employed for shock-free turbulence, low speed turbulence and turbulence with strong shocks. In Kotov et al. (High Order Numerical Methods for LES of Turbulent Flows with Shocks, ICCFD8, Chengdu, Sichuan, China, July 14-18, 2014) the LES of a turbulent flow with a strong shock by the Yee & Sjögreen scheme indicated a good agreement with the filtered DNS data. A work in progress for the application of the adaptive flow sensor for compressible turbulence with time-varying random forcing is forthcoming. The present study examines the

  6. Theoretical and numerical comparison of 3D numerical schemes for their accuracy with respect to P-wave to S-wave speed ratio

    NASA Astrophysics Data System (ADS)

    Moczo, P.; Kristek, J.; Galis, M.; Chaljub, E.; Chen, X.; Zhang, Z.

    2012-04-01

    Numerical modeling of earthquake ground motion in sedimentary basins and valleys often has to account for the P-wave to S-wave speed ratios (VP/VS) as large as five and even larger, mainly in sediments below groundwater level. The ratio can attain values larger than 10 - the unconsolidated lake sediments in Ciudad de México are a good example. At the same time, accuracy of the numerical schemes with respect to VP/VS has not been sufficiently analyzed. The numerical schemes are often applied without adequate check of the accuracy. We present theoretical analysis and numerical comparison of 18 3D numerical time-domain explicit schemes for modeling seismic motion for their accuracy with the varying VP/VS. The schemes are based on the finite-difference, spectral-element, finite-element and discontinuous-Galerkin methods. All schemes are presented in a unified form. Theoretical analysis compares accuracy of the schemes in terms of local errors in amplitude and vector difference. In addition to the analysis we compare numerically simulated seismograms with exact solutions for canonical configurations. We compare accuracy of the schemes in terms of the local errors, grid dispersion and full wavefield simulations with respect to the structure of the numerical schemes.

  7. Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows

    NASA Technical Reports Server (NTRS)

    Wilson, Robert V.; Demuren, Ayodeji O.; Carpenter, Mark

    1998-01-01

    A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization. The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure. It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes. The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems.

  8. Numerical investigation of BB-AMR scheme using entropy production as refinement criterion

    NASA Astrophysics Data System (ADS)

    Altazin, Thomas; Ersoy, Mehmet; Golay, Frédéric; Sous, Damien; Yushchenko, Lyudmyla

    2016-03-01

    In this work, a parallel finite volume scheme on unstructured meshes is applied to fluid flow for multidimensional hyperbolic system of conservation laws. It is based on a block-based adaptive mesh refinement strategy which allows quick meshing and easy parallelisation. As a continuation and as an extension of a previous work, the useful numerical density of entropy production is used as mesh refinement criterion combined with a local time-stepping method to preserve the computational time. Then, we numerically investigate its efficiency through several test cases with a confrontation with exact solution or experimental data.

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

    SciTech Connect

    Liu Di

    2008-10-01

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

  10. Advances in Numerical Boundary Conditions for Computational Aeroacoustics

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.

    1997-01-01

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

  11. Numerical Modeling of Deep Mantle Convection: Advection and Diffusion Schemes for Marker Methods

    NASA Astrophysics Data System (ADS)

    Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard

    2013-04-01

    Thermal and chemical evolution of Earth's deep mantle can be studied by modeling vigorous convection in a chemically heterogeneous fluid. Numerical modeling of such a system poses several computational challenges. Dominance of heat advection over the diffusive heat transport, and a negligible amount of chemical diffusion results in sharp gradients of thermal and chemical fields. The exponential dependence of the viscosity of mantle materials on temperature also leads to high gradients of the velocity field. The accuracy of many numerical advection schemes degrades quickly with increasing gradient of the solution, while the computational effort, in terms of the scheme complexity and required resolution, grows. Additional numerical challenges arise due to a large range of length-scales characteristic of a thermochemical convection system with highly variable viscosity. To examplify, the thickness of the stem of a rising thermal plume may be a few percent of the mantle thickness. An even thinner filament of an anomalous material that is entrained by that plume may consitute less than a tenth of a percent of the mantle thickness. We have developed a two-dimensional FEM code to model thermochemical convection in a hollow cylinder domain, with a depth- and temperature-dependent viscosity representative of the mantle (Steinberger and Calderwood, 2006). We use marker-in-cell method for advection of chemical and thermal fields. The main advantage of perfoming advection using markers is absence of numerical diffusion during the advection step, as opposed to the more diffusive field-methods. However, in the common implementation of the marker-methods, the solution of the momentum and energy equations takes place on a computational grid, and nodes do not generally coincide with the positions of the markers. Transferring velocity-, temperature-, and chemistry- information between nodes and markers introduces errors inherent to inter- and extrapolation. In the numerical scheme

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

    DOE PAGES

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

    2000-01-01

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

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

    SciTech Connect

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

    2000-03-23

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

  14. Toward a consistent framework for high order mesh refinement schemes in numerical relativity

    NASA Astrophysics Data System (ADS)

    Mongwane, Bishop

    2015-05-01

    It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. To this end, different modifications to the standard Berger-Oliger adaptive mesh refinement algorithm have been proposed. In this work we present a fourth order stable mesh refinement scheme with sub-cycling in time for numerical relativity. We do not use buffer zones to deal with refinement boundaries but explicitly specify boundary data for refined grids. We argue that the incompatibility of the standard mesh refinement algorithm with higher order Runge Kutta methods is a manifestation of order reduction phenomena, caused by inconsistent application of boundary data in the refined grids. Our scheme also addresses the problem of spurious reflections that are generated when propagating waves cross mesh refinement boundaries. We introduce a transition zone on refined levels within which the phase velocity of propagating modes is allowed to decelerate in order to smoothly match the phase velocity of coarser grids. We apply the method to test problems involving propagating waves and show a significant reduction in spurious reflections.

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

    SciTech Connect

    Fernández-Nieto, Enrique D.

    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.

  16. Topological invariants for interacting topological insulators. I. Efficient numerical evaluation scheme and implementations

    NASA Astrophysics Data System (ADS)

    He, Yuan-Yao; Wu, Han-Qing; Meng, Zi Yang; Lu, Zhong-Yi

    2016-05-01

    The aim of this series of two papers is to discuss topological invariants for interacting topological insulators (TIs). In the first paper (I), we provide a paradigm of efficient numerical evaluation scheme for topological invariants, in which we demystify the procedures and techniques employed in calculating Z2 invariant and spin Chern number via zero-frequency single-particle Green's function in quantum Monte Carlo (QMC) simulations. Here we introduce an interpolation process to overcome the ubiquitous finite-size effect, so that the calculated spin Chern number shows ideally quantized values. We also show that making use of symmetry properties of the underlying systems can greatly reduce the computational effort. To demonstrate the effectiveness of our numerical evaluation scheme, especially the interpolation process, for calculating topological invariants, we apply it on two independent two-dimensional models of interacting topological insulators. In the subsequent paper (II), we apply the scheme developed here to wider classes of models of interacting topological insulators, for which certain limitation of constructing topological invariant via single-particle Green's functions will be presented.

  17. The stability of numerical boundary treatments for compact high-order finite-difference schemes

    NASA Technical Reports Server (NTRS)

    Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul

    1991-01-01

    The stability characteristics of various compact fourth and sixth order spatial operators are assessed using the theory of Gustafsson, Kreiss and Sundstrom (G-K-S) for the semi-discrete Initial Boundary Value Problem (IBVP). These results are then generalized to the fully discrete case using a recently developed theory of Kreiss. In all cases, favorable comparisons are obtained between the G-K-S theory, eigenvalue determination, and numerical simulation. The conventional definition of stability is then sharpened to include only those spatial discretizations that are asymptotically stable. It is shown that many of the higher order schemes which are G-K-S stable are not asymptotically stable. A series of compact fourth and sixth order schemes, which are both asymptotically and G-K-S stable for the scalar case, are then developed.

  18. A new numerical scheme for computer simulation of multiple cracking in ceramic films during constrained sintering

    NASA Astrophysics Data System (ADS)

    Li, Fan; Pan, Jingzhe; Cocks, Alan

    2012-04-01

    Heterogeneities in a green film made from a powder compact is considered to be one of the major reasons for the generation of sintering cracks. Stresses are generated in a film due to the constraint of the substrate. Instabilities in the sintering process can occur at sites of these heterogeneities resulting in the generation of multiple cracks, which can propagate through the thickness of the film. The classical finite element method is fundamentally ill-suited to studying this multiple-cracking problem. This paper presents a simple and robust numerical method for the computer modelling of sintering and multiple cracking. The method is based on the so-called material point method, which was initially developed for large deformation problems in plasticity. A parallel computing algorithm is implemented and a simple scheme for modelling the initiation and propagation of multiple cracks is proposed. The numerical scheme is then validated by simulating a simple geometric problem for which an analytical solution can be obtained. Finally, the robust performance of the numerical method is demonstrated by modelling the sintering response of a film which contains different types of heterogeneities.

  19. Finite volume schemes optimized for low numerical dispersion and their aeroacoustic applications

    NASA Astrophysics Data System (ADS)

    Nance, Douglas Vinson

    1997-11-01

    The field of computational aeroacoustics is concerned with the calculation of acoustic fluctuations in an aerodynamic flow field. Moreover, it is desirable to resolve the spectral content and directivity of the aeroacoustic field with high accuracy. For the purposes of the designer, it is preferable to endow a computational fluid dynamics code with some capability for predicting aeroacoustic information. If the prediction algorithm can be written within the current flow solver's structure, the costly acquisition of a new code is not necessary. In an effort to provide designers with this option, a new finite volume methodology is developed in the present work. Three families of upwind, finite volume schemes are developed and demonstrated for a series of aeroacoustics problems. These new low dispersion finite volume schemes are designed to mitigate numerical dispersion and dissipation errors in the computational space while achieving high formal orders of accuracy. Variable extrapolation stands as the framework for these methods. In this case, the cell face variables are interpolated from cell nodes by using a procedure that optimizes the stencil representation of flow field properties in terms of sinusoidal waves. This procedure renders an accurate representation of these properties for a higher range of numerical wavenumbers. In addition, an unsteady, farfield boundary treatment is proposed. This low reflectivity farfield boundary treatment is designed as an integral part of the finite volume discretization procedure. This technique is very robust and causes only minimal reflection at the farfield boundary. The low dispersion finite volume schemes have been applied to a number of aeroacoustics problems. The numerical results are shown and compared either to exact solutions or to the results computed by other schemes. Good agreement with the exact solutions is evident. Results are also shown for the problem of laminar vortex- shedding from a circular cylinder. The

  20. A numerical study of a class of TVD schemes for compressible mixing layers

    NASA Technical Reports Server (NTRS)

    Sandham, N. D.; Yee, H. C.

    1989-01-01

    At high Mach numbers the two-dimensional time-developing mixing layer develops shock waves, positioned around large-scale vortical structures. A suitable numerical method has to be able to capture the inherent instability of the flow, leading to the roll-up of vortices, and also must be able to capture shock waves when they develop. Standard schemes for low speed turbulent flows, for example spectral methods, rely on resolution of all flow-features and cannot handle shock waves, which become too thin at any realistic Reynolds number. The performance of a class of second-order explicit total variation diminishing (TVD) schemes on a compressible mixing layer problem was studied. The basic idea is to capture the physics of the flow correctly, by resolving down to the smallest turbulent length scales, without resorting to turbulence or sub-grid scale modeling, and at the same time capture shock waves without spurious oscillations. The present study indicates that TVD schemes can capture the shocks accurately when they form, but (without resorting to a finer grid) have poor accuracy in computing the vortex growth. The solution accuracy depends on the choice of limiter. However a larger number of grid points are in general required to resolve the correct vortex growth. The low accuracy in computing time-dependent problems containing shock waves as well as vortical structures is partly due to the inherent shock-capturing property of all TVD schemes. In order to capture shock waves without spurious oscillations these schemes reduce to first-order near extrema and indirectly produce clipping phenomena, leading to inaccuracy in the computation of vortex growth. Accurate simulation of unsteady turbulent fluid flows with shock waves will require further development of efficient, uniformly higher than second-order accurate, shock-capturing methods.

  1. Application of an efficient hybrid scheme for aeroelastic analysis of advanced propellers

    NASA Technical Reports Server (NTRS)

    Srivastava, R.; Sankar, N. L.; Reddy, T. S. R.; Huff, D. L.

    1989-01-01

    An efficient 3-D hybrid scheme is applied for solving Euler equations to analyze advanced propellers. The scheme treats the spanwise direction semi-explicitly and the other two directions implicitly, without affecting the accuracy, as compared to a fully implicit scheme. This leads to a reduction in computer time and memory requirement. The calculated power coefficients for two advanced propellers, SR3 and SR7L, and various advanced ratios showed good correlation with experiment. Spanwise distribution of elemental power coefficient and steady pressure coefficient differences also showed good agreement with experiment. A study of the effect of structural flexibility on the performance of the advanced propellers showed that structural deformation due to centrifugal and aero loading should be included for better correlation.

  2. Preface to advances in numerical simulation of plasmas

    NASA Astrophysics Data System (ADS)

    Parker, Scott E.; Chacon, Luis

    2016-10-01

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

  3. Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Sethian, James A.

    2006-01-01

    Borrowing from techniques developed for conservation law equations, we have developed both monotone and higher order accurate numerical schemes which discretize the Hamilton-Jacobi and level set equations on triangulated domains. The use of unstructured meshes containing triangles (2D) and tetrahedra (3D) easily accommodates mesh adaptation to resolve disparate level set feature scales with a minimal number of solution unknowns. The minisymposium talk will discuss these algorithmic developments and present sample calculations using our adaptive triangulation algorithm applied to various moving interface problems such as etching, deposition, and curvature flow.

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

    NASA Astrophysics Data System (ADS)

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

    2003-04-01

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

  5. A hybrid numerical prediction scheme for solar radiation estimation in un-gauged catchments.

    NASA Astrophysics Data System (ADS)

    Shamim, M. A.; Bray, M.; Ishak, A. M.; Remesan, R.; Han, D.

    2009-09-01

    The importance of solar radiation on earth's surface is depicted in its wide range of applications in the fields of meteorology, agricultural sciences, engineering, hydrology, crop water requirements, climatic changes and energy assessment. It is quite random in nature as it has to go through different processes of assimilation and dispersion while on its way to earth. Compared to other meteorological parameters, solar radiation is quite infrequently measured, for example, the worldwide ratio of stations collecting solar radiation to those collecting temperature is 1:500 (Badescu, 2008). Researchers, therefore, have to rely on indirect techniques of estimation that include nonlinear models, artificial intelligence (e.g. neural networks), remote sensing and numerical weather predictions (NWP). This study proposes a hybrid numerical prediction scheme for solar radiation estimation in un-gauged catchments. It uses the PSU/NCAR's Mesoscale Modelling system (MM5) (Grell et al., 1995) to parameterise the cloud effect on extraterrestrial radiation by dividing the atmosphere into four layers of very high (6-12 km), high (3-6 km), medium (1.5-3) and low (0-1.5) altitudes from earth. It is believed that various cloud forms exist within each of these layers. An hourly time series of upper air pressure and relative humidity data sets corresponding to all of these layers is determined for the Brue catchment, southwest UK, using MM5. Cloud Index (CI) was then determined using (Yang and Koike, 2002): 1 p?bi [ (Rh - Rh )] ci =------- max 0.0,---------cri dp pbi - ptipti (1- Rhcri) where, pbi and pti represent the air pressure at the top and bottom of each layer and Rhcri is the critical value of relative humidity at which a certain cloud type is formed. Output from a global clear sky solar radiation model (MRM v-5) (Kambezidis and Psiloglu, 2008) is used along with meteorological datasets of temperature and precipitation and astronomical information. The analysis is aided by the

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

    NASA Astrophysics Data System (ADS)

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

    2005-04-01

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

  7. Multiscale/fractional step schemes for the numerical simulation of the rotating shallow water flows with complex periodic topography

    NASA Astrophysics Data System (ADS)

    Jauberteau, F.; Temam, R. M.; Tribbia, J.

    2014-08-01

    In this paper, we study several multiscale/fractional step schemes for the numerical solution of the rotating shallow water equations with complex topography. We consider the case of periodic boundary conditions (f-plane model). Spatial discretization is obtained using a Fourier spectral Galerkin method. For the schemes presented in this paper we consider two approaches. The first approach (multiscale schemes) is based on topography scale separation and the numerical time integration is function of the scales. The second approach is based on a splitting of the operators, and the time integration method is function of the operator considered (fractional step schemes). The numerical results obtained are compared with the explicit reference scheme (Leap-Frog scheme). With these multiscale/fractional step schemes the objective is to propose new schemes giving numerical results similar to those obtained using only one uniform fine grid N×N and a time step Δt, but with a CPU time near the CPU time needed when using only one coarse grid N1×N1, N1Δt.

  8. Orbital Advection by Interpolation: A Fast and Accurate Numerical Scheme for Super-Fast MHD Flows

    SciTech Connect

    Johnson, B M; Guan, X; Gammie, F

    2008-04-11

    In numerical models of thin astrophysical disks that use an Eulerian scheme, gas orbits supersonically through a fixed grid. As a result the timestep is sharply limited by the Courant condition. Also, because the mean flow speed with respect to the grid varies with position, the truncation error varies systematically with position. For hydrodynamic (unmagnetized) disks an algorithm called FARGO has been developed that advects the gas along its mean orbit using a separate interpolation substep. This relaxes the constraint imposed by the Courant condition, which now depends only on the peculiar velocity of the gas, and results in a truncation error that is more nearly independent of position. This paper describes a FARGO-like algorithm suitable for evolving magnetized disks. Our method is second order accurate on a smooth flow and preserves {del} {center_dot} B = 0 to machine precision. The main restriction is that B must be discretized on a staggered mesh. We give a detailed description of an implementation of the code and demonstrate that it produces the expected results on linear and nonlinear problems. We also point out how the scheme might be generalized to make the integration of other supersonic/super-fast flows more efficient. Although our scheme reduces the variation of truncation error with position, it does not eliminate it. We show that the residual position dependence leads to characteristic radial variations in the density over long integrations.

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

    NASA Astrophysics Data System (ADS)

    D'Ambrosio, Raffaele

    2016-06-01

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

  10. Comparing numerical integration schemes for time-continuous car-following models

    NASA Astrophysics Data System (ADS)

    Treiber, Martin; Kanagaraj, Venkatesan

    2015-02-01

    When simulating trajectories by integrating time-continuous car-following models, standard integration schemes such as the fourth-order Runge-Kutta method (RK4) are rarely used while the simple Euler method is popular among researchers. We compare four explicit methods both analytically and numerically: Euler's method, ballistic update, Heun's method (trapezoidal rule), and the standard RK4. As performance metrics, we plot the global discretization error as a function of the numerical complexity. We tested the methods on several time-continuous car-following models in several multi-vehicle simulation scenarios with and without discontinuities such as stops or a discontinuous behavior of an external leader. We find that the theoretical advantage of RK4 (consistency order 4) only plays a role if both the acceleration function of the model and the trajectory of the leader are sufficiently often differentiable. Otherwise, we obtain lower (and often fractional) consistency orders. Although, to our knowledge, Heun's method has never been used for integrating car-following models, it turns out to be the best scheme for many practical situations. The ballistic update always prevails over Euler's method although both are of first order.

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

    NASA Astrophysics Data System (ADS)

    Ku, S.; Hager, R.; Chang, C. S.; Kwon, J. M.; Parker, S. E.

    2016-06-01

    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.

  12. Advanced scheme for high-yield laser driven nuclear reactions

    NASA Astrophysics Data System (ADS)

    Margarone, D.; Picciotto, A.; Velyhan, A.; Krasa, J.; Kucharik, M.; Mangione, A.; Szydlowsky, A.; Malinowska, A.; Bertuccio, G.; Shi, Y.; Crivellari, M.; Ullschmied, J.; Bellutti, P.; Korn, G.

    2015-01-01

    The use of a low contrast nanosecond laser pulse with a relatively low intensity (3  ×  1016 W cm-2) allowed the enhancing of the yield of induced nuclear reactions in advanced solid targets. In particular the ‘ultraclean’ proton-boron fusion reaction, producing energetic alpha particles without neutron generation, was chosen. A spatially well-defined layer of boron dopants in a hydrogen-enriched silicon substrate was used as a target. A combination of the specific target composition and the laser pulse temporal shape allowed the enhancing of the yield of alpha particles up to 109 per steradian. This result can be ascribed to the interaction of the long-laser pre-pulse with the target and to the optimal target geometry and composition.

  13. Resource Allocation and Power Management Schemes in an LTE-Advanced Femtocell Network

    NASA Astrophysics Data System (ADS)

    Lee, Byung-Bog; Yu, Jae-Hak; Lee, In-Hwan; Pyo, Cheol-Sig; Kim, Se-Jin

    In this letter, we introduce two different resource allocation and Tx power management schemes, called resource control and fixed power (RCFP) and fixed resource and power control (FRPC), in an LTE-Advanced femtocell network. We analyze and compare the two schemes in terms of the system throughput for downlink and energy consumption of home evolved NodeB (HeNB) Tx power according to the number of HeNBs and home user equipment (HUE)'s user traffic density (C). The simulation results show that the FRPC scheme has better performance in terms of system throughput for macro user equipments (MUEs) and energy consumption in low C.

  14. Modeling of Convective-Stratiform Precipitation Processes: Sensitivity to Partitioning Methods and Numerical Advection Schemes

    NASA Technical Reports Server (NTRS)

    Lang, Steve; Tao, W.-K.; Simpson, J.; Ferrier, B.; Einaudi, Franco (Technical Monitor)

    2001-01-01

    Six different convective-stratiform separation techniques, including a new technique that utilizes the ratio of vertical and terminal velocities, are compared and evaluated using two-dimensional numerical simulations of a tropical [Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE)] and midlatitude continental [Preliminary Regional Experiment for STORM-Central (PRESTORM)] squall line. The simulations are made using two different numerical advection schemes: 4th order and positive definite advection. Comparisons are made in terms of rainfall, cloud coverage, mass fluxes, apparent heating and moistening, mean hydrometeor profiles, CFADs (Contoured Frequency with Altitude Diagrams), microphysics, and latent heating retrieval. Overall, it was found that the different separation techniques produced results that qualitatively agreed. However, the quantitative differences were significant. Observational comparisons were unable to conclusively evaluate the performance of the techniques. Latent heating retrieval was shown to be sensitive to the use of separation technique mainly due to the stratiform region for methods that found very little stratiform rain. The midlatitude PRESTORM simulation was found to be nearly invariant with respect to advection type for most quantities while for TOGA COARE fourth order advection produced numerous shallow convective cores and positive definite advection fewer cells that were both broader and deeper penetrating above the freezing level.

  15. Numerical Study for the Three-Dimensional Rayleigh Taylor Instability through the TVD/AC Scheme and Parallel Computation

    NASA Astrophysics Data System (ADS)

    Li, X. L.; Jin, B. X.; Glimm, J.

    1996-07-01

    The Rayleigh-Taylor instability is a gravity driven instability of a contact surface between fluids of different densities. The growth of this instability is sensitive to numerical or physical mass diffusion. For this reason, high resolution of the contact discontinuity is particularly important. In this paper, we address this problem using a second-order TVD finite difference scheme with artificial compression. We describe our numerical simulations of the 3D Rayleigh-Taylor instability using this scheme. The numerical solutions are compared to (a) the exact 2D solution in the linear regime and (b) numerical solutions using the TVD scheme and the front tracking method. The computational program is used to study the evolution of a single bubble and 3D bubble merger, i.e., the nonlinear evolution of a single mode and the process of nonlinear mode-mode interaction.

  16. Numerical simulation of three-dimensional transonic turbulent projectile aerodynamics by TVD schemes

    NASA Technical Reports Server (NTRS)

    Shiau, Nae-Haur; Hsu, Chen-Chi; Chyu, Wei-Jao

    1989-01-01

    The two-dimensional symmetric TVD scheme proposed by Yee has been extended to and investigated for three-dimensional thin-layer Navier-Stokes simulation of complex aerodynamic problems. An existing three-dimensional Navier-stokes code based on the beam and warming algorithm is modified to provide an option of using the TVD algorithm and the flow problem considered is a transonic turbulent flow past a projectile with sting at ten-degree angle of attack. Numerical experiments conducted for three flow cases, free-stream Mach numbers of 0.91, 0.96 and 1.20 show that the symmetric TVD algorithm can provide surface pressure distribution in excellent agreement with measured data; moreover, the rate of convergence to attain a steady state solution is about two times faster than the original beam and warming algorithm.

  17. Parallel solution of high-order numerical schemes for solving incompressible flows

    NASA Technical Reports Server (NTRS)

    Milner, Edward J.; Lin, Avi; Liou, May-Fun; Blech, Richard A.

    1993-01-01

    A new parallel numerical scheme for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained.

  18. A numerical scheme and some theoretical aspects for the cylindrically and spherically symmetric sine-Gordon equations

    NASA Astrophysics Data System (ADS)

    Nguyen, Lu Trong Khiem

    2016-07-01

    A finite difference formula based on the predictor-corrector technique is presented to integrate the cylindrically and spherically symmetric sine-Gordon equations numerically. Based on various numerical observations, one property of the waves of kink type is conjectured and used to explain their returning effect. Several numerical experiments are carried out and they are in excellent agreement with the existing results. In addition, the corresponding modulation solution for the two-dimensional ring-shaped kink is extended to that in three-dimension. Both numerical and theoretical aspects are utilized to verify the reliability of the proposed numerical scheme and thus the analytical modulation solutions.

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

    NASA Astrophysics Data System (ADS)

    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).

  20. An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

    NASA Technical Reports Server (NTRS)

    Jorgenson, Philip C. E.; Pletcher, Richard H.

    1994-01-01

    The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

  1. An improved snow cover scheme for high-resolution numerical weather prediction models.

    NASA Astrophysics Data System (ADS)

    Bellaire, S.; Sauter, T.; Rotach, M. W.

    2015-12-01

    Numerical weather prediction (NWP) is the core of any operational weather service. The horizontal and vertical resolution of numerical weather prediction models strongly increased during the last decades. However, numerical weather prediction in complex terrain is still challenging, because the underlying physics in the majority of subgrid-scale parameterizations have been developed for flat or idealized terrain. Weather prediction in alpine countries - such as Austria or Switzerland - is not only challenged by complex topography, furthermore, for a good part of the year the ground is snow covered influencing boundary layer processes such as turbulence and radiation. Currently, most NWP models predict the formation and evolution of the seasonal mountain snow cover in a simplified way, i.e. often a single layer model. We validated the performance of the currently implemented snow cover scheme of the COSMO model (Consortium for Small-scale Modelling) in terms of the snow surface temperature, a key parameter for the evolution of the snow cover, as well as snow height. Snow surface temperature and snow height from 120 alpine weather stations located across the Swiss Alps were compared to the corresponding COSMO output. Surface temperature was found to be overestimated especially during the night (up to 10 °C, RMSE = 6.0 °C). Snow height tends to be underestimated during the ablation phase, i.e. the COSMO model becomes snow-free too early. A new multi-layer snow module, which minimizes the energy balance equation with regard to snow surface temperature and then iteratively solves the heat equation has been implemented, predicting the daily cycle of the snow surface temperature accurately (RMSE = 1.8 °C). Furthermore, by implementing densification, melt-freeze processes and water transport snow height, especially during the ablation phase, was found to be in good agreement with the observations. Our suggested snow scheme shows promising potential not only for

  2. Gravitational waveforms from binary neutron star mergers with high-order weighted-essentially-nonoscillatory schemes in numerical relativity

    NASA Astrophysics Data System (ADS)

    Bernuzzi, Sebastiano; Dietrich, Tim

    2016-09-01

    The theoretical modeling of gravitational waveforms from binary neutron star mergers requires precise numerical relativity simulations. Assessing convergence of the numerical data and building the error budget is currently challenging due to the low accuracy of general-relativistic hydrodynamics schemes and to the grid resolutions that can be employed in (3 +1 )-dimensional simulations. In this work, we explore the use of high-order weighted-essentially-nonoscillatory (WENO) schemes in neutron star merger simulations and investigate the accuracy of the waveforms obtained with such methods. We find that high-order WENO schemes can be robustly employed for simulating the inspiral-merger phase and they significantly improve the assessment of the waveform's error budget with respect to finite-volume methods. High-order WENO schemes can be thus efficiently used for high-quality waveform production, and in future large-scale investigations of the binary parameter space.

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

    PubMed

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

    2015-10-01

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

  4. First order comparison of numerical calculation and two different turtle input schemes to represent a SLC defocusing magnet

    SciTech Connect

    Jaeger, J.

    1983-07-14

    Correcting the dispersion function in the SLC north arc it turned out that backleg-windings (BLW) acting horizontally as well as BLW acting vertically have to be used. In the latter case the question arose what is the best representation of a defocusing magnet with excited BLW acting in the vertical plane for the computer code TURTLE. Two different schemes, the 14.-scheme and the 20.-scheme were studied and the TURTLE output for one ray through such a magnet compared with the numerical solution of the equation of motion; only terms of first order have been taken into account.

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

    NASA Astrophysics Data System (ADS)

    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.

  6. Advanced numerical methods in mesh generation and mesh adaptation

    SciTech Connect

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

    2010-01-01

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

  7. A Second-order Divergence-constrained Multidimensional Numerical Scheme for Relativistic Two-fluid Electrodynamics

    NASA Astrophysics Data System (ADS)

    Amano, Takanobu

    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.

  8. Comparison of ice-phase microphysical parameterization schemes using numerical simulations of tropical convection

    NASA Technical Reports Server (NTRS)

    Mccumber, Michael; Tao, Wei-Kuo; Simpson, Joanne; Penc, Richard; Soong, Su-Tzai

    1991-01-01

    The performance of several ice parameterizations has been evaluated through a numerical cloud model. Ice effects using different schemes are contrasted with each other and with an ice-free control by incorporating them into the cloud model and by applying them to simulations of tropical squall systems. The latter are simulated in 2D so that a large domain can be used to incorporate a complete anvil. Nonsquall-type convective lines are simulated in 3D owing to their smaller horizontal scale. It is concluded that inclusion of ice microphysics in the cloud model enhanced the agreement of the simulated convection with some features of observed convection, including the proportion of surface rainfall in the anvil region and the intensity and structure of the radar brightband near the melting level in the anvil. In the experiments with bulk microphysics, three ice categories produced much better results than two ice categories, which in turn was better than no ice. For the tropical squall-type and nonsquall-type systems the optimal mix was ice, snow, and graupel.

  9. Analysis and Dynamically Consistent Numerical Schemes for the SIS Model and Related Reaction Diffusion Equation

    NASA Astrophysics Data System (ADS)

    Lubuma, J. M.-S.; Mureithi, E.; Terefe, Y. A.

    2011-11-01

    The classical SIS epidemiological model is extended in two directions: (a) The number of adequate contacts per infective in unit time is assumed to be a function of the total population in such a way that this number grows less rapidly as the total population increases; (b) A diffusion term is added to the SIS model and this leads to a reaction diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the model (a), with the disease-free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, traveling wave solutions are found for the model (b). Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous models are presented. In particular, for the model (a), a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided.

  10. Gas Evolution Dynamics in Godunov-Type Schemes and Analysis of Numerical Shock Instability

    NASA Technical Reports Server (NTRS)

    Xu, Kun

    1999-01-01

    In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers, e.g., the Flux Vector Splitting (FVS) and the Flux Difference Splitting (FDS) schemes. Since the FVS scheme and the Kinetic Flux Vector Splitting (KFVS) scheme have the same physical mechanism and similar flux function, based on the analysis of the discretized KFVS scheme the weakness and advantage of the FVS scheme are closely observed. The subtle dissipative mechanism of the Godunov method in the 2D case is also analyzed, and the physical reason for shock instability, i.e., carbuncle phenomena and odd-even decoupling, is presented.

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

    NASA Astrophysics Data System (ADS)

    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

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

    NASA Astrophysics Data System (ADS)

    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

  13. Ancient numerical daemons of conceptual hydrological modeling: 2. Impact of time stepping schemes on model analysis and prediction

    NASA Astrophysics Data System (ADS)

    Kavetski, Dmitri; Clark, Martyn P.

    2010-10-01

    Despite the widespread use of conceptual hydrological models in environmental research and operations, they remain frequently implemented using numerically unreliable methods. This paper considers the impact of the time stepping scheme on model analysis (sensitivity analysis, parameter optimization, and Markov chain Monte Carlo-based uncertainty estimation) and prediction. It builds on the companion paper (Clark and Kavetski, 2010), which focused on numerical accuracy, fidelity, and computational efficiency. Empirical and theoretical analysis of eight distinct time stepping schemes for six different hydrological models in 13 diverse basins demonstrates several critical conclusions. (1) Unreliable time stepping schemes, in particular, fixed-step explicit methods, suffer from troublesome numerical artifacts that severely deform the objective function of the model. These deformations are not rare isolated instances but can arise in any model structure, in any catchment, and under common hydroclimatic conditions. (2) Sensitivity analysis can be severely contaminated by numerical errors, often to the extent that it becomes dominated by the sensitivity of truncation errors rather than the model equations. (3) Robust time stepping schemes generally produce "better behaved" objective functions, free of spurious local optima, and with sufficient numerical continuity to permit parameter optimization using efficient quasi Newton methods. When implemented within a multistart framework, modern Newton-type optimizers are robust even when started far from the optima and provide valuable diagnostic insights not directly available from evolutionary global optimizers. (4) Unreliable time stepping schemes lead to inconsistent and biased inferences of the model parameters and internal states. (5) Even when interactions between hydrological parameters and numerical errors provide "the right result for the wrong reason" and the calibrated model performance appears adequate, unreliable

  14. An Improved Transformation and Optimized Sampling Scheme for the Numerical Evaluation of Singular and Near-Singular Potentials

    NASA Technical Reports Server (NTRS)

    Khayat, Michael A.; Wilton, Donald R.; Fink, Patrick W.

    2007-01-01

    Simple and efficient numerical procedures using singularity cancellation methods are presented for evaluating singular and near-singular potential integrals. Four different transformations are compared and the advantages of the Radial-angular transform are demonstrated. A method is then described for optimizing this integration scheme.

  15. A numerical scheme for modelling reacting flow with detailed chemistry and transport.

    SciTech Connect

    Knio, Omar M.; Najm, Habib N.; Paul, Phillip H.

    2003-09-01

    An efficient projection scheme is developed for the simulation of reacting flow with detailed kinetics and transport. The scheme is based on a zero-Mach-number formulation of the compressible conservation equations for an ideal gas mixture. It is a modified version of the stiff operator-split scheme developed by Knio, Najm & Wyckoff (1999, J. Comput. Phys. 154, 428). Similar to its predecessor, the new scheme relies on Strang splitting of the discrete evolution equations, where diffusion is integrated in two half steps that are symmetrically distributed around a single stiff step for the reaction source terms. The diffusive half-step is integrated using an explicit single-step, multistage, Runge-Kutta-Chebyshev (RKC) method, which replaces the explicit, multi-step, fractional sub-step approach used in the previous formulation. This modification maintains the overall second-order convergence properties of the scheme and enhances the efficiency of the computations by taking advantage of the extended real-stability region of the RKC scheme. Two additional efficiency-enhancements are also explored, based on an extrapolation procedure for the transport coefficients and on the use of approximate Jacobian data evaluated on a coarse mesh. By including these enhancement schemes, performance tests using 2D computations with a detailed C{sub 1}C{sub 2} methane-air mechanism and a detailed mixture-averaged transport model indicate that speedup factors of about 15 are achieved over the previous split-stiff scheme.

  16. Dynamic design, numerical solution and effective verification of acceleration-level obstacle-avoidance scheme for robot manipulators

    NASA Astrophysics Data System (ADS)

    Xiao, Lin; Zhang, Yunong

    2016-03-01

    For avoiding obstacles and joint physical constraints of robot manipulators, this paper proposes and investigates a novel obstacle avoidance scheme (termed the acceleration-level obstacle-avoidance scheme). The scheme is based on a new obstacle-avoidance criterion that is designed by using the gradient neural network approach for the first time. In addition, joint physical constraints such as joint-angle limits, joint-velocity limits and joint-acceleration limits are incorporated into such a scheme, which is further reformulated as a quadratic programming (QP). Two important 'bridge' theorems are established so that such a QP can be converted equivalently to a linear variational inequality and then equivalently to a piecewise-linear projection equation (PLPE). A numerical algorithm based on a PLPE is thus developed and applied for an online solution of the resultant QP. Four path-tracking tasks based on the PA10 robot in the presence of point and window-shaped obstacles demonstrate and verify the effectiveness and accuracy of the acceleration-level obstacle-avoidance scheme. Besides, the comparisons between the non-obstacle-avoidance and obstacle-avoidance results further validate the superiority of the proposed scheme.

  17. Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes

    NASA Technical Reports Server (NTRS)

    Marx, Yves P.

    1990-01-01

    An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.

  18. Numerical simulation by TVD schemes of complex shock reflections from airfoils at high angle of attack. [Total Variation Diminishing

    NASA Technical Reports Server (NTRS)

    Moon, Young J.; Yee, H. C.

    1987-01-01

    The shock-capturing capability of total variation diminishing (TVD) schemes is demonstrated for a more realistic complex shock-diffraction problem for which the experimental data are available. Second-order explicit upwind and symmetric TVD schemes are used to solve the time-dependent Euler equations of gas dynamics for the interaction of a blast wave with an airfoil at high angle-of-attack. The test cases considered are a time-dependent moving curved-shock wave and a contant moving planar-shock wave impinging at an angle-of-attack 30 deg on a NACA 0018 airfoil. Good agreement is obtained between isopycnic contours computed by the TVD schemes and those from experimental interferograms. No drastic difference in flow-field structure is found between the curved- and planar-shock wave cases, except for a difference in density level near the lower surface of the airfoil. Computation for cases with higher shock Mach numbers is also possible. Numerical experiments show that the symmetric TVD scheme is less sensitive to the boundary conditions treatment than the upwind scheme.

  19. A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

    NASA Technical Reports Server (NTRS)

    Weinan, E.; Shu, Chi-Wang

    1994-01-01

    High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth-order central differences through fast Fourier transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large scale features, such as the total circulation around the roll-up region, are adequately resolved.

  20. A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

    NASA Technical Reports Server (NTRS)

    Weinan, E.; Shu, Chi-Wang

    1992-01-01

    High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth order central differences through Fast Fourier Transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.

  1. A numerical classical flutter analysis of advanced propellers

    NASA Technical Reports Server (NTRS)

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

    1992-01-01

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

  2. Recent advances in two-phase flow numerics

    SciTech Connect

    Mahaffy, J.H.; Macian, R.

    1997-07-01

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

  3. Numerical Speed of Sound and its Application to Schemes for all Speeds

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing; Edwards, Jack R.

    1999-01-01

    The concept of "numerical speed of sound" is proposed in the construction of numerical flux. It is shown that this variable is responsible for the accurate resolution of' discontinuities, such as contacts and shocks. Moreover, this concept can he readily extended to deal with low speed and multiphase flows. As a results, the numerical dissipation for low speed flows is scaled with the local fluid speed, rather than the sound speed. Hence, the accuracy is enhanced the correct solution recovered, and the convergence rate improved. We also emphasize the role of mass flux and analyze the behavior of this flux. Study of mass flux is important because the numerical diffusivity introduced in it can be identified. In addition, it is the term common to all conservation equations. We show calculated results for a wide variety of flows to validate the effectiveness of using the numerical speed of sound concept in constructing the numerical flux. We especially aim at achieving these two goals: (1) improving accuracy and (2) gaining convergence rates for all speed ranges. We find that while the performance at high speed range is maintained, the flux now has the capability of performing well even with the low: speed flows. Thanks to the new numerical speed of sound, the convergence is even enhanced for the flows outside of the low speed range. To realize the usefulness of the proposed method in engineering problems, we have also performed calculations for complex 3D turbulent flows and the results are in excellent agreement with data.

  4. On one numerical scheme of the solution of a three-dimensional problem of diffraction of an electromagnetic wave on thin ideally conductive screens

    SciTech Connect

    Ryzhakov, G. V.

    2014-11-12

    In the paper, the problem of diffraction on thin ideally conductive screens is reduced to vector hypersingular integral equation with integral treated in the sense of finite Hadamard value. An numerical scheme to solve the equation is introduced. The scheme is based on piecewise approximation of unknown function. The advantage of the scheme is that integral of singular part is reduced to contour integral which can be analytically calculated so numerical calculation are significantly accelerated. Several examples of resulting numerical experiments are given in comparison with known theoretical and experimental data.

  5. Comparison of Numerical Schemes for a Realistic Computational Aeroacoustics Benchmark Problem

    NASA Technical Reports Server (NTRS)

    Hixon, R.; Wu, J.; Nallasamy, M.; Sawyer, S.; Dyson, R.

    2004-01-01

    In this work, a nonlinear structured-multiblock CAA solver, the NASA GRC BASS code, will be tested on a realistic CAA benchmark problem. The purpose of this test is to ascertain what effect the high-accuracy solution methods used in CAA have on a realistic test problem, where both the mean flow and the unsteady waves are simultaneously computed on a fully curvilinear grid from a commercial grid generator. The proposed test will compare the solutions obtained using several finite-difference methods on identical grids to determine whether high-accuracy schemes have advantages for this benchmark problem.

  6. Numerical study of unsteady shockwave reflections using an upwind TVD scheme

    NASA Technical Reports Server (NTRS)

    Hsu, Andrew T.; Liou, Meng-Sing

    1990-01-01

    An unsteady TVD Navier-Stokes solver was developed and applied to the problem of shock reflection on a circular cylinder. The obtained numerical results were compared with the Schlieren photos from an experimental study. These results show that the present computer code has the ability of capturing moving shocks.

  7. Recent advances in numerical analysis of structural eigenvalue problems

    NASA Technical Reports Server (NTRS)

    Gupta, K. K.

    1973-01-01

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

  8. Numerical simulation of Stokes flow around particles via a hybrid Finite Difference-Boundary Integral scheme

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Amitabh

    2013-11-01

    An efficient algorithm for simulating Stokes flow around particles is presented here, in which a second order Finite Difference method (FDM) is coupled to a Boundary Integral method (BIM). This method utilizes the strong points of FDM (i.e. localized stencil) and BIM (i.e. accurate representation of particle surface). Specifically, in each iteration, the flow field away from the particles is solved on a Cartesian FDM grid, while the traction on the particle surface (given the the velocity of the particle) is solved using BIM. The two schemes are coupled by matching the solution in an intermediate region between the particle and surrounding fluid. We validate this method by solving for flow around an array of cylinders, and find good agreement with Hasimoto's (J. Fluid Mech. 1959) analytical results.

  9. Numerical and experimental investigation into passive hydrogen recovery scheme using vacuum ejector

    NASA Astrophysics Data System (ADS)

    Hwang, Jenn-Jiang; Cho, Ching-Chang; Wu, Wei; Chiu, Ching-Huang; Chiu, Kuo-Ching; Lin, Chih-Hong

    2015-02-01

    The current work presents a numerical and experimental investigation into a passive ejector for recovering the anode off-gas in a proton exchange membrane fuel cell (PEMFC) system. The proposed ejector is consisted of a convergent-divergent channel and a suction channel, and it is connected with the anode outlet of PEMFC system for recovery the anode off-gas into the main gas supply. Numerical simulations based on a three-dimensional compressible steady-state k-ɛ turbulent model are performed to examine the effects of the inlet mass flow rate and nozzle throat diameter on the pressure, Mach number, temperature, suction channel mass flow rate, outlet channel mass flow rate, and suction channel entrainment ratio, respectively. The numerical results are confirmed by means of an experimental investigation. It is shown that supersonic flow conditions are induced in the ejector; resulting in the induction of a vacuum pressure in the suction channel and the subsequent recovery of the anode off-gas at the outlet of the main channel. In addition, it is shown that the mass flow rate in the suction channel increases with an increasing mass flow rate at the primary channel inlet. Finally, the results show that a higher entrainment ratio is obtained as the throat diameter of the nozzle in the ejector is reduced. Overall, the results presented in this study provide a useful source of reference for developing the ejector devices applied to fuel cell systems while simultaneously avoiding extra energy consumption.

  10. Numerical schemes for anomalous diffusion of single-phase fluids in porous media

    NASA Astrophysics Data System (ADS)

    Awotunde, Abeeb A.; Ghanam, Ryad A.; Al-Homidan, Suliman S.; Tatar, Nasser-eddine

    2016-10-01

    Simulation of fluid flow in porous media is an indispensable part of oil and gas reservoir management. Accurate prediction of reservoir performance and profitability of investment rely on our ability to model the flow behavior of reservoir fluids. Over the years, numerical reservoir simulation models have been based mainly on solutions to the normal diffusion of fluids in the porous reservoir. Recently, however, it has been documented that fluid flow in porous media does not always follow strictly the normal diffusion process. Small deviations from normal diffusion, called anomalous diffusion, have been reported in some experimental studies. Such deviations can be caused by different factors such as the viscous state of the fluid, the fractal nature of the porous media and the pressure pulse in the system. In this work, we present explicit and implicit numerical solutions to the anomalous diffusion of single-phase fluids in heterogeneous reservoirs. An analytical solution is used to validate the numerical solution to the simple homogeneous case. The conventional wellbore flow model is modified to account for anomalous behavior. Example applications are used to show the behavior of wellbore and wellblock pressures during the single-phase anomalous flow of fluids in the reservoirs considered.

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

    PubMed

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

    2016-09-01

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

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

    PubMed Central

    2016-01-01

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

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

    PubMed

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

    2016-09-01

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

  14. Solution of population balance equations in applications with fine particles: Mathematical modeling and numerical schemes

    NASA Astrophysics Data System (ADS)

    Nguyen, T. T.; Laurent, F.; Fox, R. O.; Massot, M.

    2016-11-01

    The accurate description and robust simulation, at relatively low cost, of global quantities (e.g. number density or volume fraction) as well as the size distribution of a population of fine particles in a carrier fluid is still a major challenge for many applications. For this purpose, two types of methods are investigated for solving the population balance equation with aggregation, continuous particle size change (growth and size reduction), and nucleation: the extended quadrature method of moments (EQMOM) based on the work of Yuan et al. [52] and a hybrid method (TSM) between the sectional and moment methods, considering two moments per section based on the work of Laurent et al. [30]. For both methods, the closure employs a continuous reconstruction of the number density function of the particles from its moments, thus allowing evaluation of all the unclosed terms in the moment equations, including the negative flux due to the disappearance of particles. Here, new robust and efficient algorithms are developed for this reconstruction step and two kinds of reconstruction are tested for each method. Moreover, robust and accurate numerical methods are developed, ensuring the realizability of the moments. The robustness is ensured with efficient and tractable algorithms despite the numerous couplings and various algebraic constraints thanks to a tailored overall strategy. EQMOM and TSM are compared to a sectional method for various simple but relevant test cases, showing their ability to describe accurately the fine-particle population with a much lower number of variables. These results demonstrate the efficiency of the modeling and numerical choices, and their potential for the simulation of real-world applications.

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

    NASA Technical Reports Server (NTRS)

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

    1995-01-01

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

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

    SciTech Connect

    Toumi, I.; Caruge, D.

    1997-07-01

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

  17. Effect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical scheme.

    PubMed

    Owolabi, Kolade M; Patidar, Kailash C

    2016-01-01

    In this paper, we consider the numerical simulations of an extended nonlinear form of Kierstead-Slobodkin reaction-transport system in one and two dimensions. We employ the popular fourth-order exponential time differencing Runge-Kutta (ETDRK4) schemes proposed by Cox and Matthew (J Comput Phys 176:430-455, 2002), that was modified by Kassam and Trefethen (SIAM J Sci Comput 26:1214-1233, 2005), for the time integration of spatially discretized partial differential equations. We demonstrate the supremacy of ETDRK4 over the existing exponential time differencing integrators that are of standard approaches and provide timings and error comparison. Numerical results obtained in this paper have granted further insight to the question 'What is the minimal size of the spatial domain so that the population persists?' posed by Kierstead and Slobodkin (J Mar Res 12:141-147, 1953), with a conclusive remark that the population size increases with the size of the domain. In attempt to examine the biological wave phenomena of the solutions, we present the numerical results in both one- and two-dimensional space, which have interesting ecological implications. Initial data and parameter values were chosen to mimic some existing patterns.

  18. A Numerical Scheme for Special Relativistic Radiation Magnetohydrodynamics Based on Solving the Time-dependent Radiative Transfer Equation

    NASA Astrophysics Data System (ADS)

    Ohsuga, Ken; Takahashi, Hiroyuki R.

    2016-02-01

    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.

  19. High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving

    NASA Astrophysics Data System (ADS)

    Qiu, Junchao; Zhang, Lin; Li, Diyang; Liu, Xingcheng

    2016-06-01

    Chaotic sequences can be applied to realize multiple user access and improve the system security for a visible light communication (VLC) system. However, since the map patterns of chaotic sequences are usually well known, eavesdroppers can possibly derive the key parameters of chaotic sequences and subsequently retrieve the information. We design an advanced encryption standard (AES) interleaving aided multiple user access scheme to enhance the security of a chaotic code division multiple access-based visible light communication (C-CDMA-VLC) system. We propose to spread the information with chaotic sequences, and then the spread information is interleaved by an AES algorithm and transmitted over VLC channels. Since the computation complexity of performing inverse operations to deinterleave the information is high, the eavesdroppers in a high speed VLC system cannot retrieve the information in real time; thus, the system security will be enhanced. Moreover, we build a mathematical model for the AES-aided VLC system and derive the theoretical information leakage to analyze the system security. The simulations are performed over VLC channels, and the results demonstrate the effectiveness and high security of our presented AES interleaving aided chaotic CDMA-VLC system.

  20. PROBABILISTIC SIMULATION OF SUBSURFACE FLUID FLOW: A STUDY USING A NUMERICAL SCHEME

    SciTech Connect

    Buscheck, Timothy Eric

    1980-03-01

    There has been an increasing interest in probabilistic modeling of hydrogeologic systems. The classical approach to groundwater modeling has been deterministic in nature, where individual layers and formations are assumed to be uniformly homogeneous. Even in the case of complex heterogeneous systems, the heterogeneities describe the differences in parameter values between various layers, but not within any individual layer. In a deterministic model a single-number is assigned to each hydrogeologic parameter, given a particular scale of interest. However, physically there is no such entity as a truly uniform and homogeneous unit. Single-number representations or deterministic predictions are subject to uncertainties. The approach used in this work models such uncertainties with probabilistic parameters. The resulting statistical distributions of output variables are analyzed. A numerical algorithm, based on axiomatic principles of probability theory, performs arithmetic operations between probability distributions. Two subroutines are developed from the algorithm and incorporated into the computer program TERZAGI, which solves groundwater flow problems in saturated, multi-dimensional systems. The probabilistic computer program is given the name, PROGRES. The algorithm has been applied to study the following problems: one-dimensional flow through homogeneous media, steady-state and transient flow conditions, one-dimensional flow through heterogeneous media, steady-state and transient flow conditions, and two-dimensional steady-stte flow through heterogeneous media. The results are compared with those available in the literature.

  1. Immersed boundary Eulerian-Lagrangian 3D simulation of pyroclastic density currents: numerical scheme and experimental validation

    NASA Astrophysics Data System (ADS)

    Doronzo, Domenico Maria; de Tullio, Marco; Pascazio, Giuseppe; Dellino, Pierfrancesco

    2010-05-01

    Pyroclastic density currents are ground hugging, hot, gas-particle flows representing the most hazardous events of explosive volcanism. Their impact on structures is a function of dynamic pressure, which expresses the lateral load that such currents exert over buildings. In this paper we show how analog experiments can be matched with numerical simulations for capturing the essential physics of the multiphase flow. We used an immersed boundary scheme for the mesh generation, which helped in reconstructing the steep velocity and particle concentration gradients near the ground surface. Results show that the calculated values of dynamic pressure agree reasonably with the experimental measurements. These outcomes encourage future application of our method for the assessment of the impact of pyroclastic density currents at the natural scale.

  2. Development of comprehensive numerical schemes for predicting evaporating gas-droplets flow processes of a liquid-fueled combustor

    NASA Technical Reports Server (NTRS)

    Chen, C. P.

    1990-01-01

    An existing Computational Fluid Dynamics code for simulating complex turbulent flows inside a liquid rocket combustion chamber was validated and further developed. The Advanced Rocket Injector/Combustor Code (ARICC) is simplified and validated against benchmark flow situations for laminar and turbulent flows. The numerical method used in ARICC Code is re-examined for incompressible flow calculations. For turbulent flows, both the subgrid and the two equation k-epsilon turbulence models are studied. Cases tested include idealized Burger's equation in complex geometries and boundaries, a laminar pipe flow, a high Reynolds number turbulent flow, and a confined coaxial jet with recirculations. The accuracy of the algorithm is examined by comparing the numerical results with the analytical solutions as well as experimented data with different grid sizes.

  3. Investigation of magnetic field generation by non-Gaussian, non-Markovian velocity fluctuations using meshless, Lagrangian numerical schemes

    NASA Astrophysics Data System (ADS)

    Sanchez, Raul; Newman, David

    2014-10-01

    Turbulent velocity fields can generate perturbations of the electric current and magnetic field that, under certain conditions, may generate an average, large-scale magnetic field. Such generation is important to understand the behavior of stars, planetary and laboratory plasmas. This generation is traditionally studied by assuming near-Gaussian, random velocity fluctuations. This simplification allows to exprese the effective electromotive force in Faraday's law in terms of a piece proportional to the large-scale magnetic field itself (the α-term) and another proportional to its curl (the β term) assuming certain symmetry conditions are met. Physically, the α-term is a measure of the mean helicity of the flow and drives the dynamo process. In a previous contribution, we examined theoretically what consequences would follow from assuming instead Levy-distributed, Lagrangianly-correlated velocity fields, that have been recently identified as of relevance in regimes of near-marginal turbulence or in the presence of a strong, stable sheared flow. Here, we will discuss and extend these results numerically by implementing the kinematic dynamo equation using a Lagrangian, meshless numerical method inspired by the SPH schemes frequently used in hydrodynamics.

  4. Numerical Simulation of the Slider Air Bearing Problem of Hard Disk Drives by Two Multidimensional Upwind Residual Distribution Schemes over Unstructured Triangular Meshes

    NASA Astrophysics Data System (ADS)

    Wu, Lin; Bogy, D. B.

    2001-09-01

    In this paper we present two multigrid numerical schemes over unstructured triangular meshes that solve the slider air bearing problem of hard disk drives. For each fixed slider attitude, the air bearing pressure is obtained by solving the generalized Reynolds equation. The convection part of the equation is modeled in one scheme by the PSI multidimensional upwind residual distribution approach and in the other scheme by the SUPG finite element approach cast in residual distribution form. In both schemes, a linear Galerkin method is used to discretize the diffusion terms. In addition, a non-nested multigrid iteration technique is used to speed up the convergence rate. Finally, the balanced steady state flying attitude of the slider subject to pre-applied suspension force and torques is obtained by a Quasi-Newton iteration method (Broyden's method), and the results of the numerical solutions are compared to each other and to experimental data.

  5. Evaluation of Injection Efficiency of Carbon Dioxide Using an Integrated Injection Well and Geologic Formation Numerical Simulation Scheme

    NASA Astrophysics Data System (ADS)

    Kihm, J.; Park, S.; Kim, J.; SNU CO2 GEO-SEQ TEAM

    2011-12-01

    A series of integrated injection well and geologic formation numerical simulations was performed to evaluate the injection efficiency of carbon dioxide using a multiphase thermo-hydrological numerical model. The numerical simulation results show that groundwater flow, carbon dioxide flow, and heat transport in both injection well and sandstone formation can be simultaneously analyzed, and thus the injection efficiency (i.e., injection rate and injectivity) of carbon dioxide can be quantitatively evaluated using the integrated injection well and geologic formation numerical simulation scheme. The injection rate and injectivity of carbon dioxide increase rapidly during the early period of time (about 10 days) and then increase slightly up to about 2.07 kg/s (equivalent to 0.065 Mton/year) and about 2.84 × 10-7 kg/s/Pa, respectively, until 10 years for the base case. The sensitivity test results show that the injection pressure and temperature of carbon dioxide at the wellhead have significant impacts on its injection rate and injectivity. The vertical profile of the fluid pressure in the injection well becomes almost a hydrostatical equilibrium state within 1 month for all the cases. The vertical profile of the fluid temperature in the injection well becomes a monotonously increasing profile with the depth due to isenthalpic or adiabatic compression within 6 months for all the cases. The injection rate of carbon dioxide increases linearly with the fluid pressure difference between the well bottom and the sandstone formation far from the injection well. In contrast, the injectivity of carbon dioxide varies unsystematically with the fluid pressure difference. On the other hand, the reciprocal of the kinematic viscosity of carbon dioxide at the well bottom has an excellent linear relationship with the injectivity of carbon dioxide. It indicates that the above-mentioned variation of the injectivity of carbon dioxide can be corrected using this linear relationship. The

  6. Technical note: Improving the AWAT filter with interpolation schemes for advanced processing of high resolution data

    NASA Astrophysics Data System (ADS)

    Peters, Andre; Nehls, Thomas; Wessolek, Gerd

    2016-06-01

    Weighing lysimeters with appropriate data filtering yield the most precise and unbiased information for precipitation (P) and evapotranspiration (ET). A recently introduced filter scheme for such data is the AWAT (Adaptive Window and Adaptive Threshold) filter (Peters et al., 2014). The filter applies an adaptive threshold to separate significant from insignificant mass changes, guaranteeing that P and ET are not overestimated, and uses a step interpolation between the significant mass changes. In this contribution we show that the step interpolation scheme, which reflects the resolution of the measuring system, can lead to unrealistic prediction of P and ET, especially if they are required in high temporal resolution. We introduce linear and spline interpolation schemes to overcome these problems. To guarantee that medium to strong precipitation events abruptly following low or zero fluxes are not smoothed in an unfavourable way, a simple heuristic selection criterion is used, which attributes such precipitations to the step interpolation. The three interpolation schemes (step, linear and spline) are tested and compared using a data set from a grass-reference lysimeter with 1 min resolution, ranging from 1 January to 5 August 2014. The selected output resolutions for P and ET prediction are 1 day, 1 h and 10 min. As expected, the step scheme yielded reasonable flux rates only for a resolution of 1 day, whereas the other two schemes are well able to yield reasonable results for any resolution. The spline scheme returned slightly better results than the linear scheme concerning the differences between filtered values and raw data. Moreover, this scheme allows continuous differentiability of filtered data so that any output resolution for the fluxes is sound. Since computational burden is not problematic for any of the interpolation schemes, we suggest always using the spline scheme.

  7. Analytical and numerical schemes for a derivative with filtering property and no singular kernel with applications to diffusion

    NASA Astrophysics Data System (ADS)

    Doungmo Goufo, Emile Franc; Atangana, Abdon

    2016-08-01

    There have been numbers of conflicting and confusing situations, but also uniformity, in the application of the two most popular fractional derivatives, namely the classic Riemann-Liouville and Caputo fractional derivatives. The range of these issues is wide, including the initialization with the Caputo derivative and its observed difficulties compared to the Riemann-Liouville initialization conditions. In this paper, being aware of these issues and reacting to the newly introduced Caputo-Fabrizio fractional derivative (CFFD) without singular kernel, we introduce a new definition of fractional derivative called the new Riemann-Liouville fractional derivative (NRLFD) without singular kernel. The filtering property of the NRLFD is pointed out by showing it as the derivative of a convolution and contrary to the CFFD, it matches with the function when the order is zero. We also explore various scientific situations that may be conflicting and confusing in the applicability of both new derivatives. In particular, we show that both definitions still have some basic similarities, like not obeying the traditional chain rule. Furthermore, we provide the explicit formula for the Laplace transform of the NRLFD and we prove that, contrary to the CFFD, the NRLFD requires non-constant initial conditions and does not require the function f to be continuous or differentiable. Some simulations for the NRLFD are presented for different values of the derivative order. In the second part of this work, numerical approximations for the first- and second-order NRLFD are developped followed by a concrete application to diffusion. The stability of the numerical scheme is proved and numerical simulations are performed for different values of the derivative order α. They exhibit similar behavior for closed values of α.

  8. Self-consistent field theory and numerical scheme for calculating the phase diagram of wormlike diblock copolymers.

    PubMed

    Jiang, Ying; Chen, Jeff Z Y

    2013-10-01

    This paper concerns establishing a theoretical basis and numerical scheme for studying the phase behavior of AB diblock copolymers made of wormlike chains. The general idea of a self-consistent field theory is the combination of the mean-field approach together with a statistical weight that describes the configurational properties of a polymer chain. In recent years, this approach has been extensively used for structural prediction of block copolymers, based on the Gaussian-model description of a polymer chain. The wormlike-chain model has played an important role in the description of polymer systems, covering the semiflexible-to-rod crossover of the polymer properties and the highly stretching regime, which the Gaussian-chain model has difficulties to describe. Although the idea of developing a self-consistent field theory for wormlike chains could be traced back to early development in polymer physics, the solution of such a theory has been limited due to technical difficulties. In particular, a challenge has been to develop a numerical algorithm enabling the calculation of the phase diagram containing three-dimensional structures for wormlike AB diblock copolymers. This paper describes a computational algorithm that combines a number of numerical tricks, which can be used for such a calculation. A phase diagram covering major parameter areas was constructed for the wormlike-chain system and reported by us, where the ratio between the total length and the persistence length of a constituent polymer is suggested as another tuning parameter for the microphase-separated structures; all detailed technical issues are carefully addressed in the current paper. PMID:24229202

  9. Self-consistent field theory and numerical scheme for calculating the phase diagram of wormlike diblock copolymers

    NASA Astrophysics Data System (ADS)

    Jiang, Ying; Chen, Jeff Z. Y.

    2013-10-01

    This paper concerns establishing a theoretical basis and numerical scheme for studying the phase behavior of AB diblock copolymers made of wormlike chains. The general idea of a self-consistent field theory is the combination of the mean-field approach together with a statistical weight that describes the configurational properties of a polymer chain. In recent years, this approach has been extensively used for structural prediction of block copolymers, based on the Gaussian-model description of a polymer chain. The wormlike-chain model has played an important role in the description of polymer systems, covering the semiflexible-to-rod crossover of the polymer properties and the highly stretching regime, which the Gaussian-chain model has difficulties to describe. Although the idea of developing a self-consistent field theory for wormlike chains could be traced back to early development in polymer physics, the solution of such a theory has been limited due to technical difficulties. In particular, a challenge has been to develop a numerical algorithm enabling the calculation of the phase diagram containing three-dimensional structures for wormlike AB diblock copolymers. This paper describes a computational algorithm that combines a number of numerical tricks, which can be used for such a calculation. A phase diagram covering major parameter areas was constructed for the wormlike-chain system and reported by us, where the ratio between the total length and the persistence length of a constituent polymer is suggested as another tuning parameter for the microphase-separated structures; all detailed technical issues are carefully addressed in the current paper.

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

    NASA Astrophysics Data System (ADS)

    Katsaounis, T. D.

    2005-02-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1992-01-01

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

  12. A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2de

    NASA Technical Reports Server (NTRS)

    Lopez Ortega, Alejandro; Mikellides, Ioannis G.

    2014-01-01

    We present a new algorithm in the Hall2De code to simulate the ion hydrodynamics in the acceleration channel and near plume regions of Hall-effect thrusters. This implementation constitutes an upgrade of the capabilities built in the Hall2De code. The equations of mass conservation and momentum for unmagnetized ions are solved using a conservative, finite-volume, cell-centered scheme on a magnetic-field-aligned grid. Major computational savings are achieved by making use of an implicit predictor/multi-corrector algorithm for time evolution. Inaccuracies in the prediction of the motion of low-energy ions in the near plume in hydrodynamics approaches are addressed by implementing a multi-fluid algorithm that tracks ions of different energies separately. A wide range of comparisons with measurements are performed to validate the new ion algorithms. Several numerical experiments with the location and value of the anomalous collision frequency are also presented. Differences in the plasma properties in the near-plume between the single fluid and multi-fluid approaches are discussed. We complete our validation by comparing predicted erosion rates at the channel walls of the thruster with measurements. Erosion rates predicted by the plasma properties obtained from simulations replicate accurately measured rates of erosion within the uncertainty range of the sputtering models employed.

  13. Simulation of ammonium and chromium transport in porous media using coupling scheme of a numerical algorithm and a stochastic algorithm.

    PubMed

    Palanichamy, Jegathambal; Schüttrumpf, Holger; Köngeter, Jürgen; Becker, Torsten; Palani, Sundarambal

    2009-01-01

    The migration of the species of chromium and ammonium in groundwater and their effective remediation depend on the various hydro-geological characteristics of the system. The computational modeling of the reactive transport problems is one of the most preferred tools for field engineers in groundwater studies to make decision in pollution abatement. The analytical models are less modular in nature with low computational demand where the modification is difficult during the formulation of different reactive systems. Numerical models provide more detailed information with high computational demand. Coupling of linear partial differential Equations (PDE) for the transport step with a non-linear system of ordinary differential equations (ODE) for the reactive step is the usual mode of solving a kinetically controlled reactive transport equation. This assumption is not appropriate for a system with low concentration of species such as chromium. Such reaction systems can be simulated using a stochastic algorithm. In this paper, a finite difference scheme coupled with a stochastic algorithm for the simulation of the transport of ammonium and chromium in subsurface media has been detailed.

  14. Numerical framework and performance of the new multiple-phase cloud microphysics scheme in RegCM4.5: precipitation, cloud microphysics, and cloud radiative effects

    NASA Astrophysics Data System (ADS)

    Nogherotto, Rita; Tompkins, Adrian Mark; Giuliani, Graziano; Coppola, Erika; Giorgi, Filippo

    2016-07-01

    We implement and evaluate a new parameterization scheme for stratiform cloud microphysics and precipitation within regional climate model RegCM4. This new parameterization is based on a multiple-phase one-moment cloud microphysics scheme built upon the implicit numerical framework recently developed and implemented in the ECMWF operational forecasting model. The parameterization solves five prognostic equations for water vapour, cloud liquid water, rain, cloud ice, and snow mixing ratios. Compared to the pre-existing scheme, it allows a proper treatment of mixed-phase clouds and a more physically realistic representation of cloud microphysics and precipitation. Various fields from a 10-year long integration of RegCM4 run in tropical band mode with the new scheme are compared with their counterparts using the previous cloud scheme and are evaluated against satellite observations. In addition, an assessment using the Cloud Feedback Model Intercomparison Project (CFMIP) Observational Simulator Package (COSP) for a 1-year sub-period provides additional information for evaluating the cloud optical properties against satellite data. The new microphysics parameterization yields an improved simulation of cloud fields, and in particular it removes the overestimation of upper level cloud characteristics of the previous scheme, increasing the agreement with observations and leading to an amelioration of a long-standing problem in the RegCM system. The vertical cloud profile produced by the new scheme leads to a considerably improvement of the representation of the longwave and shortwave components of the cloud radiative forcing.

  15. Developing a TPCK-SRL Assessment Scheme for Conceptually Advancing Technology in Education

    ERIC Educational Resources Information Center

    Kohen, Zehavit; Kramarski, Bracha

    2012-01-01

    The present study aimed to: (a) develop a conceptual TPCK-SRL scheme for assessing teachers' integration of self-regulated learning (SRL) considerations while infusing technology into a TPCK classroom context (blending K = knowledge about T = technology, P = pedagogy, and C = content), which reflects all three knowledge components' dynamic…

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

    PubMed Central

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

    2013-01-01

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

  17. Physical control oriented model of large scale refrigerators to synthesize advanced control schemes. Design, validation, and first control results

    SciTech Connect

    Bonne, François; Bonnay, Patrick

    2014-01-29

    In this paper, a physical method to obtain control-oriented dynamical models of large scale cryogenic refrigerators is proposed, in order to synthesize model-based advanced control schemes. These schemes aim to replace classical user experience designed approaches usually based on many independent PI controllers. This is particularly useful in the case where cryoplants are submitted to large pulsed thermal loads, expected to take place in the cryogenic cooling systems of future fusion reactors such as the International Thermonuclear Experimental Reactor (ITER) or the Japan Torus-60 Super Advanced Fusion Experiment (JT-60SA). Advanced control schemes lead to a better perturbation immunity and rejection, to offer a safer utilization of cryoplants. The paper gives details on how basic components used in the field of large scale helium refrigeration (especially those present on the 400W @1.8K helium test facility at CEA-Grenoble) are modeled and assembled to obtain the complete dynamic description of controllable subsystems of the refrigerator (controllable subsystems are namely the Joule-Thompson Cycle, the Brayton Cycle, the Liquid Nitrogen Precooling Unit and the Warm Compression Station). The complete 400W @1.8K (in the 400W @4.4K configuration) helium test facility model is then validated against experimental data and the optimal control of both the Joule-Thompson valve and the turbine valve is proposed, to stabilize the plant under highly variable thermals loads. This work is partially supported through the European Fusion Development Agreement (EFDA) Goal Oriented Training Program, task agreement WP10-GOT-GIRO.

  18. Physical control oriented model of large scale refrigerators to synthesize advanced control schemes. Design, validation, and first control results

    NASA Astrophysics Data System (ADS)

    Bonne, François; Alamir, Mazen; Bonnay, Patrick

    2014-01-01

    In this paper, a physical method to obtain control-oriented dynamical models of large scale cryogenic refrigerators is proposed, in order to synthesize model-based advanced control schemes. These schemes aim to replace classical user experience designed approaches usually based on many independent PI controllers. This is particularly useful in the case where cryoplants are submitted to large pulsed thermal loads, expected to take place in the cryogenic cooling systems of future fusion reactors such as the International Thermonuclear Experimental Reactor (ITER) or the Japan Torus-60 Super Advanced Fusion Experiment (JT-60SA). Advanced control schemes lead to a better perturbation immunity and rejection, to offer a safer utilization of cryoplants. The paper gives details on how basic components used in the field of large scale helium refrigeration (especially those present on the 400W @1.8K helium test facility at CEA-Grenoble) are modeled and assembled to obtain the complete dynamic description of controllable subsystems of the refrigerator (controllable subsystems are namely the Joule-Thompson Cycle, the Brayton Cycle, the Liquid Nitrogen Precooling Unit and the Warm Compression Station). The complete 400W @1.8K (in the 400W @4.4K configuration) helium test facility model is then validated against experimental data and the optimal control of both the Joule-Thompson valve and the turbine valve is proposed, to stabilize the plant under highly variable thermals loads. This work is partially supported through the European Fusion Development Agreement (EFDA) Goal Oriented Training Program, task agreement WP10-GOT-GIRO.

  19. Particle exhaust schemes in the DIII-D advanced divertor configuration

    SciTech Connect

    Menon, M.M.; Mioduszewski, P.K.

    1989-01-01

    For density control in long-pulse operation, the open divertor on the DIII-D tokamak will be equipped with a baffled chamber and a pumping system. The throat of the baffle chamber is sized to provide optimal pumping for the typical plasma equilibrium configuration. Severe limitations on the toroidal conductance of this baffle chamber require the use of in-vessel pumping to achieve the desired particle exhaust of about 25 Torr{center dot}l/s. Two separate pumping schemes are considered: an array of titanium getter modules based on the design developed by the Tore Supra team and a cryocondensation pump. The merits and demerits of each scheme are analyzed, and the design considerations introduced by the tokamak environment are brought out. 3 refs., 5 figs.

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

    NASA Astrophysics Data System (ADS)

    Saanouni, K.

    2013-05-01

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

  1. Numerical simulation of precipitation formation in the case orographically induced convective cloud: Comparison of the results of bin and bulk microphysical schemes

    NASA Astrophysics Data System (ADS)

    Sarkadi, N.; Geresdi, I.; Thompson, G.

    2016-11-01

    In this study, results of bulk and bin microphysical schemes are compared in the case of idealized simulations of pre-frontal orographic clouds with enhanced embedded convection. The description graupel formation by intensive riming of snowflakes was improved compared to prior versions of each scheme. Two methods of graupel melting coincident with collisions with water drops were considered: (1) all simulated melting and collected water drops increase the amount of melted water on the surface of graupel particles with no shedding permitted; (2) also no shedding permitted due to melting, but the collision with the water drops can induce shedding from the surface of the graupel particles. The results of the numerical experiments show: (i) The bin schemes generate graupel particles more efficiently by riming than the bulk scheme does; the intense riming of snowflakes was the most dominant process for the graupel formation. (ii) The collision-induced shedding significantly affects the evolution of the size distribution of graupel particles and water drops below the melting level. (iii) The three microphysical schemes gave similar values for the domain integrated surface precipitation, but the patterns reveal meaningful differences. (iv) Sensitivity tests using the bulk scheme show that the depth of the melting layer is sensitive to the description of the terminal velocity of the melting snow. (v) Comparisons against Convair-580 flight measurements suggest that the bin schemes simulate well the evolution of the pristine ice particles and liquid drops, while some inaccuracy can occur in the description of snowflakes riming. (vi) The bin scheme with collision-induced shedding reproduced well the quantitative characteristics of the observed bright band.

  2. Computational Benefits Using an Advanced Concatenation Scheme Based on Reduced Order Models for RF Structures

    NASA Astrophysics Data System (ADS)

    Heller, Johann; Flisgen, Thomas; van Rienen, Ursula

    The computation of electromagnetic fields and parameters derived thereof for lossless radio frequency (RF) structures filled with isotropic media is an important task for the design and operation of particle accelerators. Unfortunately, these computations are often highly demanding with regard to computational effort. The entire computational demand of the problem can be reduced using decomposition schemes in order to solve the field problems on standard workstations. This paper presents one of the first detailed comparisons between the recently proposed state-space concatenation approach (SSC) and a direct computation for an accelerator cavity with coupler-elements that break the rotational symmetry.

  3. Sequencing by hybridization with the generic 6-mer oligonucleotide microarray : an advanced scheme for data processing.

    SciTech Connect

    Chechetkin, V. R.; Turygin, A. Y.; Proudnikov, D. Y.; Prokopenko, D. V.; Kirillov, E. V.; Mirzabekov, A. D.; Biochip Technology Center; Russian Academy of Sciences

    2000-08-01

    DNA sequencing by hybridization was carried out with a microarray of all 4{sup 6} = 4,096 hexadeoxyribonucleotides (the generic microchip). The oligonucleotides immobilized in 100 x 100 x 20-{mu}m polyacrylamide gel pads of the generic microchip were hybridized with fluorescently labeled ssDNA, providing perfect and mismatched duplexes. Melting curves were measured in parallel for all microchip duplexes with a fluorescence microscope equipped with CCD camera. This allowed us to discriminate the perfect duplexes formed by the oligonucleotides, which are complementary to the target DNA. The DNA sequence was reconstructed by overlapping the complementary oligonucleotide probes. We developed a data processing scheme to heighten the discrimination of perfect duplexes from mismatched ones. The procedure was united with a reconstruction of the DNA sequence. The scheme includes the proper definition of a discriminant signal, preprocessing, and the variational principle for the sequence indicator function. The effectiveness of the procedure was confirmed by sequencing, proofreading, and nucleotide polymorphism (mutation) analysis of 13 DNA fragments from 31 to 70 nucleotides long.

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

    NASA Technical Reports Server (NTRS)

    Winowich, Nicholas S.

    1991-01-01

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

  5. Theoretical analysis of advanced schemes for free electron laser with a large {mu}{sub c}

    SciTech Connect

    Zhulin, V.I.; Zanadvorov, N.P.

    1995-12-31

    The possibility to operate with a short pulse FEL (electron pulse length a {sigma} {approx_equal} 1mm) in far infrared region (with the radiation wavelength 10{mu}m {le}{lambda}{le}300{mu}m) gives rise to many new applications. The parameter {mu}{sub c} = N{lambda}/{sigma}, which characterises the interaction time between the electron and radiation pulses in the undulator with N periods, becomes rather large ({mu}{sub c}{approximately}10) even for {lambda}{approximately}100{mu}m. An increase in {lambda} leads to the reduction in output power owing to an increase in both the diffraction losses and {mu}{sub c}. We consider two options capable to improve the situation in the FEL with planar undulator geometry: I. Reduction of the diffraction losses by use of circular or rectangular hollow waveguides in the cavity. II. Effective reduction of {mu}{sub c} factor by increasing the FEL-interaction time by means of the optical klystron undulator scheme. We demonstrate that; I. Introduction of a waveguide into the cavity causes additional difficulties. In both circular and rectangular cases the waveguide dispersion leads to the undesirable variation of radiation pulse shape. For the circular case the effect of depolarization becomes important and leads to the additional losses (up to 30%) due to the violation of the axial symmetry and linear polarization. II. The optical klystron scheme consisting of several separated undulators, can indeed increase the FEL-interaction time. The right choice of electron bunch delay between these undulators gives the possibility to couple several successive electron pulses with one radiation pulse during one passage through the cavity. This results in considerable increase in FEL-interaction time and corresponding increase in gain.

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

    DOE PAGES

    François, Marianne M.

    2015-05-28

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

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

    SciTech Connect

    François, Marianne M.

    2015-05-28

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

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

    SciTech Connect

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

    2014-05-15

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

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

    NASA Technical Reports Server (NTRS)

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

    1984-01-01

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

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

    NASA Astrophysics Data System (ADS)

    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.

  11. Numerical simulation of a dust event in northeastern Germany with a new dust emission scheme in COSMO-ART

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The dust emission scheme of Shao (2004) has been implemented into the regional atmospheric model COSMO-ART and has been applied to a severe dust event in northeastern Germany on 8th April 2011. The model sensitivity to soil moisture and vegetation cover has been studied. Soil moisture has been found...

  12. An energy and potential enstrophy conserving numerical scheme for the multi-layer shallow water equations with complete Coriolis force

    NASA Astrophysics Data System (ADS)

    Stewart, Andrew L.; Dellar, Paul J.

    2016-05-01

    We present an energy- and potential enstrophy-conserving scheme for the non-traditional shallow water equations that include the complete Coriolis force and topography. These integral conservation properties follow from material conservation of potential vorticity in the continuous shallow water equations. The latter property cannot be preserved by a discretisation on a fixed Eulerian grid, but exact conservation of a discrete energy and a discrete potential enstrophy seems to be an effective substitute that prevents any distortion of the forward and inverse cascades in quasi-two dimensional turbulence through spurious sources and sinks of energy and potential enstrophy, and also increases the robustness of the scheme against nonlinear instabilities. We exploit the existing Arakawa-Lamb scheme for the traditional shallow water equations, reformulated by Salmon as a discretisation of the Hamiltonian and Poisson bracket for this system. The non-rotating, traditional, and our non-traditional shallow water equations all share the same continuous Hamiltonian structure and Poisson bracket, provided one distinguishes between the particle velocity and the canonical momentum per unit mass. We have determined a suitable discretisation of the non-traditional canonical momentum, which includes additional coupling between the layer thickness and velocity fields, and modified the discrete kinetic energy to suppress an internal symmetric computational instability that otherwise arises for multiple layers. The resulting scheme exhibits the expected second-order convergence under spatial grid refinement. We also show that the drifts in the discrete total energy and potential enstrophy due to temporal truncation error may be reduced to machine precision under suitable refinement of the timestep using the third-order Adams-Bashforth or fourth-order Runge-Kutta integration schemes.

  13. The HiPER project for inertial confinement fusion and some experimental results on advanced ignition schemes

    NASA Astrophysics Data System (ADS)

    Batani, D.; Koenig, M.; Baton, S.; Perez, F.; Gizzi, L. A.; Koester, P.; Labate, L.; Honrubia, J.; Antonelli, L.; Morace, A.; Volpe, L.; Santos, J.; Schurtz, G.; Hulin, S.; Ribeyre, X.; Fourment, C.; Nicolai, P.; Vauzour, B.; Gremillet, L.; Nazarov, W.; Pasley, J.; Richetta, M.; Lancaster, K.; Spindloe, Ch; Tolley, M.; Neely, D.; Kozlová, M.; Nejdl, J.; Rus, B.; Wolowski, J.; Badziak, J.; Dorchies, F.

    2011-12-01

    This paper presents the goals and some of the results of experiments conducted within the Working Package 10 (Fusion Experimental Programme) of the HiPER Project. These experiments concern the study of the physics connected to 'advanced ignition schemes', i.e. the fast ignition and the shock ignition approaches to inertial fusion. Such schemes are aimed at achieving a higher gain, as compared with the classical approach which is used in NIF, as required for future reactors, and make fusion possible with smaller facilities. In particular, a series of experiments related to fast ignition were performed at the RAL (UK) and LULI (France) Laboratories and studied the propagation of fast electrons (created by a short-pulse ultra-high-intensity beam) in compressed matter, created either by cylindrical implosions or by compression of planar targets by (planar) laser-driven shock waves. A more recent experiment was performed at PALS and investigated the laser-plasma coupling in the 1016 W cm-2 intensity regime of interest for shock ignition.

  14. An optimal scheme for numerical evaluation of Eshelby tensors and its implementation in a MATLAB package for simulating the motion of viscous ellipsoids in slow flows

    NASA Astrophysics Data System (ADS)

    Qu, Mengmeng; Jiang, Dazhi; Lu, Lucy X.

    2016-11-01

    To address the multiscale deformation and fabric development in Earth's ductile lithosphere, micromechanics-based self-consistent homogenization is commonly used to obtain macroscale rheological properties from properties of constituent elements. The homogenization is heavily based on the solution of an Eshelby viscous inclusion in a linear viscous medium and the extension of the solution to nonlinear viscous materials. The homogenization requires repeated numerical evaluation of Eshelby tensors for constituent elements and becomes ever more computationally challenging as the elements are deformed to more elongate or flattened shapes. In this paper, we develop an optimal scheme for evaluating Eshelby tensors, using a combination of a product Gaussian quadrature and the Lebedev quadrature. We first establish, through numerical experiments, an empirical relationship between the inclusion shape and the computational time it takes to evaluate its Eshelby tensors. We then use the relationship to develop an optimal scheme for selecting the most efficient quadrature to obtain the Eshelby tensors. The optimal scheme is applicable to general homogenizations. In this paper, it is implemented in a MATLAB package for investigating the evolution of solitary rigid or deformable inclusions and the development of shape preferred orientations in multi-inclusion systems during deformation. The MATLAB package, upgrading an earlier effort written in MathCad, can be downloaded online.

  15. Investigation of numerical viscosities and dissipation rates of second-order TVD-MUSCL schemes for implicit large-eddy simulation

    NASA Astrophysics Data System (ADS)

    Bidadi, Shreyas; Rani, Sarma L.

    2015-01-01

    Monotonically integrated large-eddy simulation (MILES) approach utilizes the dissipation inherent to shock-capturing schemes to emulate the role played by explicit subgrid-scale eddy diffusivity at the high-wavenumber end of the turbulent energy spectrum. In the current study, a novel formulation is presented for quantifying the numerical viscosity inherent to Roe-based second-order TVD-MUSCL schemes for the Euler equations. Using this formulation, the effects of numerical viscosity and dissipation rate on implicit large-eddy simulations of turbulent flows are investigated. At first, the three-dimensional (3-D) finite-volume extension of the original Roe's flux, including Roe's Jacobian matrix, is presented. The fluxes are then extended to second-order using van Leer's MUSCL extrapolation technique. Starting from the 3-D Roe-MUSCL flux, an expression is derived for the numerical viscosity as a function of flux limiter and characteristic speed for each conserved variable, distance between adjacent cell centers, and a scaling parameter. Motivated by Thornber et al. [16] study, the high numerical viscosity inherent to TVD-MUSCL schemes is mitigated using a z-factor that depends on local Mach number. The TVD limiters, along with the z-factor, were initially applied to the 1-D shock-tube and 2-D inviscid supersonic wedge flows. Spatial profiles of numerical viscosities are plotted, which provide insights into the role of these limiters in controlling the dissipative nature of Roe's flux while maintaining monotonicity and stability in regions of high gradients. Subsequently, a detailed investigation was performed of decaying homogeneous isotropic turbulence with varying degrees of compressibility. Spectra of numerical viscosity and dissipation rate are presented, which clearly demonstrate the effectiveness of the z-factor both in narrowing the wavenumber range in which dissipation occurs, and in shifting the location of dissipation peak closer to the cut-off wavenumber

  16. Advanced scheme for high-yield laser driven proton-boron fusion reaction

    NASA Astrophysics Data System (ADS)

    Margarone, D.; Picciotto, A.; Velyhan, A.; Krasa, J.; Kucharik, M.; Morrissey, M.; Mangione, A.; Szydlowsky, A.; Malinowska, A.; Bertuccio, G.; Shi, Y.; Crivellari, M.; Ullschmied, J.; Bellutti, P.; Korn, G.

    2015-02-01

    A low contrast nanosecond laser pulse with relatively low intensity (3 × 1016 W cm-2) was used to enhance the yield of induced nuclear reactions in advanced solid targets. In particular the "ultraclean" proton-boron fusion reaction, producing energetic alpha-particles without neutron generation, was chosen. A spatially well-defined layer of boron dopants in a hydrogen-enriched silicon substrate was used as target. The combination of the specific target geometry and the laser pulse temporal shape allowed enhancing the yield of alpha-particles up to 109 per steradian, i.e 100 times higher than previous experimental achievements. Moreover the alpha particle stream presented a clearly peaked angular and energy distribution, which make this secondary source attractive for potential applications. This result can be ascribed to the interaction of the long laser pre-pulse with the target and to the optimal target geometry and composition.

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

    ERIC Educational Resources Information Center

    Hitt, Fernando; Morasse, Christian

    2009-01-01

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

  18. Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows

    NASA Astrophysics Data System (ADS)

    Kulikov, Igor; Vorobyov, Eduard

    2016-07-01

    An approach for constructing a low-dissipation numerical method is described. The method is based on a combination of the operator-splitting method, Godunov method, and piecewise-parabolic method on the local stencil. Numerical method was tested on a standard suite of hydrodynamic test problems. In addition, the performance of the method is demonstrated on a global test problem showing the development of a spiral structure in a gravitationally unstable gaseous galactic disk.

  19. Explicit robust schemes for implementation of a class of principal value-based constitutive models: Symbolic and numeric implementation

    NASA Technical Reports Server (NTRS)

    Arnold, S. M.; Saleeb, A. F.; Tan, H. Q.; Zhang, Y.

    1993-01-01

    The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, special purpose functions (running under MACSYMA) are developed for the symbolic derivation, evaluation, and automatic FORTRAN code generation of explicit expressions for the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid over the entire deformation range, since the singularities resulting from repeated principal-stretch values have been theoretically removed. The required computational algorithms are outlined, and the resulting FORTRAN computer code is presented.

  20. Improved scheme for parametrization of convection in the Met Office's Numerical Atmospheric-dispersion Modelling Environment (NAME)

    NASA Astrophysics Data System (ADS)

    Meneguz, Elena; Thomson, David; Witham, Claire; Kusmierczyk-Michulec, Jolanta

    2015-04-01

    NAME is a Lagrangian atmospheric dispersion model used by the Met Office to predict the dispersion of both natural and man-made contaminants in the atmosphere, e.g. volcanic ash, radioactive particles and chemical species. Atmospheric convection is responsible for transport and mixing of air resulting in a large exchange of heat and energy above the boundary layer. Although convection can transport material through the whole troposphere, convective clouds have a small horizontal length scale (of the order of few kilometres). Therefore, for large-scale transport the horizontal scale on which the convection exists is below the global NWP resolution used as input to NAME and convection must be parametrized. Prior to the work presented here, the enhanced vertical mixing generated by non-resolved convection was reproduced by randomly redistributing Lagrangian particles between the cloud base and cloud top with probability equal to 1/25th of the NWP predicted convective cloud fraction. Such a scheme is essentially diffusive and it does not make optimal use of all the information provided by the driving meteorological model. To make up for these shortcomings and make the parametrization more physically based, the convection scheme has been recently revised. The resulting version, presented in this paper, is now based on the balance equation between upward, entrainment and detrainment fluxes. In particular, upward mass fluxes are calculated with empirical formulas derived from Cloud Resolving Models and using the NWP convective precipitation diagnostic as closure. The fluxes are used to estimate how many particles entrain, move upward and detrain. Lastly, the scheme is completed by applying a compensating subsidence flux. The performance of the updated convection scheme is benchmarked against available observational data of passive tracers. In particular, radioxenon is a noble gas that can undergo significant long range transport: this study makes use of observations of

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

    SciTech Connect

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

    2007-07-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-10-01

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

  3. Direct Numerical Simulation of Transitional and Turbulent Flow Over a Heated Flat Plate Using Finite-Difference Schemes

    NASA Technical Reports Server (NTRS)

    Madavan, Nateri K.

    1995-01-01

    The work in this report was conducted at NASA Ames Research Center during the period from August 1993 to January 1995 deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a heated flat plate in the presence of relatively high freestream turbulence was performed. The geometry and flow conditions were chosen to match earlier experiments. The development of the momentum and thermal boundary layers was documented. Velocity and temperature profiles, as well as distributions of skin friction, surface heat transfer rate, Reynolds shear stress, and turbulent heat flux were shown to compare well with experiment. The numerical method used here can be applied to complex geometries in a straightforward manner.

  4. Direct numerical simulation of transitional and turbulent flow over a heated flat plate using finite-difference schemes

    NASA Technical Reports Server (NTRS)

    Madavan, Nateri K.

    1995-01-01

    This report deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a heated flat plate in the presence of relatively high freestream turbulence was performed. The geometry and flow conditions were chosen to match earlier experiments. The development of the momentum and thermal boundary layers was documented. Velocity and temperature profiles, as well as distributions of skin friction, surface heat transfer rate, Reynolds shear stress, and turbulent heat flux, were shown to compare well with experiment. The results indicate that the essential features of the transition process have been captured. The numerical method used here can be applied to complex geometries in a straightforward manner.

  5. The numerical investigation of spreading process of two viscoelastic droplets impact problem by using an improved SPH scheme

    NASA Astrophysics Data System (ADS)

    Jiang, Tao; Lu, Lin-Guang; Lu, Wei-Gang

    2014-05-01

    In this paper, the spreading process of two XPP model droplets impacting on a plate in sequence at low Reynolds number is numerically simulated by using an improved smoothed particle hydrodynamics (I-SPH) method. The I-SPH method is a coupled approach which uses the traditional SPH (TSPH) method near the boundary domain and uses a kernel-gradient-corrected SPH method in the interior of fluid flow for the reason of remedying the accuracy and stability of TSPH. Meanwhile, an artificial stress term and a periodic density re-initialization technique are presented to eliminate the tensile instability and restrain pressure oscillation, respectively. A new boundary treatment is also adopted. The ability and merit of proposed I-SPH method combined with other techniques are first illustrated by simulating three typical examples. Subsequently, the deformation phenomena of two viscoelastic droplets impacting and spreading on a plate in sequence are numerically investigated. Particularly, the influences of the falling time interval, Weissenberg number and other rheological parameters on the deformation process are studied respectively. All numerical results agree well with the available data.

  6. A new design of the LAPS land surface scheme for use over and through heterogeneous and non-heterogeneous surfaces: Numerical simulations and tests

    NASA Astrophysics Data System (ADS)

    Mihailovic, Dragutin T.; Lazic, Jelena; Leśny, Jacek; Olejnik, Janusz; Lalic, Branislava; Kapor, Darko; Cirisan, Ana

    2010-05-01

    Numerical simulations and tests with the recently redesigned land-air parameterization scheme (LAPS) are presented. In all experiments, supported either by one-point micrometeorological, 1D or 3D simulations, the attention has been directed to: (1) comparison of simulation outputs, expressing the energy transfer over and through heterogeneous and non-heterogeneous surfaces, versus observations and (2) analysis of uncertainties occurring in the solution of the energy balance equation at the land-air interface. To check the proposed method for aggregation of albedo, "propagating hole" sensitivity tests with LAPS over a sandstone rock grid cell have been performed with the forcing meteorological data for July 17, 1999 in Baxter site, Philadelphia (USA). Micrometeorological and biophysical measurements from the surface experiments conducted over crops and apple orchard in Serbia, Poland, Austria and France were used to test the operation of LAPS in calculating surface fluxes and canopy environment temperatures within and above plant covers of different densities. In addition, sensitivity tests with single canopy covers over the Central Europe region and comparison against the observations taken from SYNOP data using 3D simulations were made. Validation of LAPS performances over a solid surface has been done by comparison of 2 m air temperature observations against 5-day simulations over the Sahara Desert rocky ground using 3D model. To examine how realistically the LAPS simulates surface processes over a heterogeneous surface, we compared the air temperature measured at 2 m and that predicted by the 1D model with the LAPS as the surface scheme. Finally, the scheme behaviour over urban surface was tested by runs over different parts of a hypothetical urban area. The corresponding 1D simulations were carried out with an imposed meteorological dataset collected during HAPEX-MOBILHY experiment at Caumont (France). The quantities predicted by the LAPS compare well with the

  7. Blood flow velocity estimation from x-ray densitometric data: an efficient numerical scheme for the inverse advection problem

    NASA Astrophysics Data System (ADS)

    Sarry, L.; Peng, Y. J.; Boire, J. Y.

    2002-01-01

    In previously published studies, blood flow velocity from x-ray biplane angiography was measured by solving an inverse advection problem, relating velocity to bolus densities summed across sections. Both spatial and temporal velocity variations were recovered through a computationally expensive parameter estimation algorithm. Here we prove the existence and uniqueness of the solution on three sub-domains of the plane defined by the axial position along the vessel and the time of the angiographic sequence. A fast direct scheme was designed in conjunction with a regularization step stemming from the volume flow conservation law applied on consecutive segments. Its accuracy and immunity towards noise were tested on both simulated and real densitometric data. The relative error between the estimated and expected velocities was less than 5% for more than 90% of the points of the spatiotemporal plane with simulated densities normalized to 1.0 and a Gaussian additive noise of standard deviation 0.01. For densities reconstructed from a biplane angiographic sequence, increase in velocity is used as a functional index for the stenosis ratio and to characterize the sharing of flow at bifurcation.

  8. Numerical simulations of bubble-induced star formation in dwarf irregular galaxies with a novel stellar feedback scheme

    NASA Astrophysics Data System (ADS)

    Kawata, Daisuke; Gibson, Brad K.; Barnes, David J.; Grand, Robert J. J.; Rahimi, Awat

    2014-02-01

    To study the star formation and feedback mechanism, we simulate the evolution of an isolated dwarf irregular galaxy (dIrr) in a fixed dark matter halo, similar in size to Wolf-Lundmark-Melotte, using a new stellar feedback scheme. We use the new version of our original N-body/smoothed particle chemodynamics code, GCD+, which adopts improved hydrodynamics, metal diffusion between the gas particles and new modelling of star formation and stellar wind and supernovae feedback. Comparing the simulations with and without stellar feedback effects, we demonstrate that the collisions of bubbles produced by strong feedback can induce star formation in a more widely spread area. We also demonstrate that the metallicity in star-forming regions is kept low due to the mixing of the metal-rich bubbles and the metal-poor interstellar medium. Our simulations also suggest that the bubble-induced star formation leads to many counter-rotating stars. The bubble-induced star formation could be a dominant mechanism to maintain star formation in dIrrs, which is different from larger spiral galaxies where the non-axisymmetric structures, such as spiral arms, are a main driver of star formation.

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

    NASA Astrophysics Data System (ADS)

    Alliss, R.

    2014-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Yoshida, Hiroyuki; Takase, Kazuyuki

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

  11. A finite-difference, frequency-domain numerical scheme for the solution of the linearized unsteady Euler equations

    NASA Technical Reports Server (NTRS)

    Scott, James R.; Atassi, Hafiz M.

    1991-01-01

    A numerical method is developed for solving periodic, three-dimensional, vortical flows around lifting airfoils in subsonic flow. The first-order method, that is presented, fully accounts for the distortion effects of the nonuniform mean flow on the convected upstream vortical disturbances. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Using an elliptic coordinate transformation, the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the Mach number and reduced frequency. Extensive comparisons are made with known solutions to unsteady vortical flow problems, and it is seen that the agreement is generally very good for reduced frequencies ranging from 0 up to 4.

  12. Coarse- and fine-grid numerical behavior of MRT/TRT lattice-Boltzmann schemes in regular and random sphere packings

    NASA Astrophysics Data System (ADS)

    Khirevich, Siarhei; Ginzburg, Irina; Tallarek, Ulrich

    2015-01-01

    We analyze the intrinsic impact of free-tunable combinations of the relaxation rates controlling viscosity-independent accuracy of the multiple-relaxation-times (MRT) lattice-Boltzmann models. Preserving all MRT degrees of freedom, we formulate the parametrization conditions which enable the MRT schemes to provide viscosity-independent truncation errors for steady state solutions, and support them with the second- and third-order accurate ("linear" and "parabolic", respectively) boundary schemes. The parabolic schemes demonstrate the advanced accuracy with weak dependency on the relaxation rates, as confirmed by the simulations with the D3Q15 model in three regular arrays (SC, BCC, FCC) of touching spheres. Yet, the low-order, bounce-back boundary rule remains appealing for pore-scale simulations where the precise distance to the boundaries is undetermined. However, the effective accuracy of the bounce-back crucially depends on the free-tunable combinations of the relaxation rates. We find that the combinations of the kinematic viscosity rate with the available "ghost" antisymmetric collision mode rates mainly impact the accuracy of the bounce-back scheme. As the first step, we reduce them to the one combination (presented by so-called "magic" parameter Λ in the frame of the two-relaxation-times (TRT) model), and study its impact on the accuracy of the drag force/permeability computations with the D3Q19 velocity set in two different, dense, random packings of 8000 spheres each. We also run the simulations in the regular (BCC and FCC) packings of the same porosity for the broad range of the discretization resolutions, ranging from 5 to 750 lattice nodes per sphere diameter. A special attention is given to the discretization procedure resulting in significantly reduced scatter of the data obtained at low resolutions. The results reveal the identical Λ-dependency versus the discretization resolution in all four packings, regular and random. While very small

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

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  14. Implementation of Black Sea numerical model based on NEMO and 3DVAR data assimilation scheme for operational forecasting

    NASA Astrophysics Data System (ADS)

    Ciliberti, Stefania Angela; Peneva, Elisaveta; Storto, Andrea; Rostislav, Kandilarov; Lecci, Rita; Yang, Chunxue; Coppini, Giovanni; Masina, Simona; Pinardi, Nadia

    2016-04-01

    This study describes a new model implementation for the Black Sea, which uses data assimilation, towards operational forecasting, based on NEMO (Nucleus for European Modelling of the Ocean, Madec et al., 2012). The Black Sea domain is resolved with 1/27°×1/36° horizontal resolution (~3 km) and 31 z-levels with partial steps based on the GEBCO bathymetry data (Grayek et al., 2010). The model is forced by momentum, water and heat fluxes interactively computed by bulk formulae using high resolution atmospheric forcing provided by the European Centre for Medium-Range Forecast (ECMWF). The initial condition is calculated from long-term climatological temperature and salinity 3D fields. Precipitation field over the basin has been computed from the climatological GPCP rainfall monthly data (Adler et al., 2003; Huffman et al., 2009), while the evaporation is derived from the latent heat flux. The climatological monthly mean runoff of the major rivers in the Black Sea is computed using the hydrological dataset provided by SESAME project (Ludvig et al., 2009). The exchange with Mediterranean Sea through the Bosporus Straits is represented by a surface boundary condition taking into account the barotropic transport calculated to balance the fresh water fluxes on monthly bases (Stanev and Beckers, 1999, Peneva et al., 2001). A multi-annual run 2011-2015 has been completed in order to describe the main characteristics of the Black Sea circulation dynamics and thermohaline structure and the numerical results have been validated using in-situ (ARGO) and satellite (SST, SLA) data. The Black Sea model represents also the core of the new Black Sea Forecasting System, implemented at CMCC operationally since January 2016, which produces at daily frequency 10-day forecasts, 3-days analyses and 1-day simulation. Once a week, the system is run 15-day in the past in analysis mode to compute the new optimal initial condition for the forecast cycle. The assimilation is performed by a

  15. Numerical study of the two-species Vlasov-Ampère system: Energy-conserving schemes and the current-driven ion-acoustic instability

    NASA Astrophysics Data System (ADS)

    Cheng, Yingda; Christlieb, Andrew J.; Zhong, Xinghui

    2015-05-01

    In this paper, we propose energy-conserving Eulerian solvers for the two-species Vlasov-Ampère (VA) system and apply the methods to simulate current-driven ion-acoustic instability. The two-species VA systems are of practical importance in applications, and they conserve many physical quantities including the particle number of each species and the total energy that is comprised of kinetic energy for both species and the electric energy. The main goal of this paper is to generalize our previous work for the single-species VA system [9] and Vlasov-Maxwell (VM) system [8] to the two-species case. The methodologies proposed involve careful design of temporal discretization and the use of the discontinuous Galerkin (DG) spatial discretizations. We show that the energy-conserving time discretizations for single-species equations [9,8] can also work for the two-species case if extended properly. Compared to other high order schemes, we emphasize that our schemes can preserve the total particle number and total energy on the fully discrete level regardless of mesh size, making them very attractive for long time simulations. We benchmark our algorithms on a test example to check the one-species limit, and the current-driven ion-acoustic instability. To simulate the current-driven ion-acoustic instability, a slight modification for the implicit method is necessary to fully decouple the split equations. This is achieved by a Gauss-Seidel type iteration technique. Numerical results verified the conservation and performance of our methods. Finally, we remark that the schemes in this paper can be readily extended to applications when the models take more general form, such as the multi-species VM equations.

  16. Development and validation of burnup dependent computational schemes for the analysis of assemblies with advanced lattice codes

    NASA Astrophysics Data System (ADS)

    Ramamoorthy, Karthikeyan

    The main aim of this research is the development and validation of computational schemes for advanced lattice codes. The advanced lattice code which forms the primary part of this research is "DRAGON Version4". The code has unique features like self shielding calculation with capabilities to represent distributed and mutual resonance shielding effects, leakage models with space-dependent isotropic or anisotropic streaming effect, availability of the method of characteristics (MOC), burnup calculation with reaction-detailed energy production etc. Qualified reactor physics codes are essential for the study of all existing and envisaged designs of nuclear reactors. Any new design would require a thorough analysis of all the safety parameters and burnup dependent behaviour. Any reactor physics calculation requires the estimation of neutron fluxes in various regions of the problem domain. The calculation goes through several levels before the desired solution is obtained. Each level of the lattice calculation has its own significance and any compromise at any step will lead to poor final result. The various levels include choice of nuclear data library and energy group boundaries into which the multigroup library is cast; self shielding of nuclear data depending on the heterogeneous geometry and composition; tracking of geometry, keeping error in volume and surface to an acceptable minimum; generation of regionwise and groupwise collision probabilities or MOC-related information and their subsequent normalization thereof, solution of transport equation using the previously generated groupwise information and obtaining the fluxes and reaction rates in various regions of the lattice; depletion of fuel and of other materials based on normalization with constant power or constant flux. Of the above mentioned levels, the present research will mainly focus on two aspects, namely self shielding and depletion. The behaviour of the system is determined by composition of resonant

  17. Pollutant transport by shallow water equations on unstructured meshes: Hyperbolization of the model and numerical solution via a novel flux splitting scheme

    NASA Astrophysics Data System (ADS)

    Vanzo, Davide; Siviglia, Annunziato; Toro, Eleuterio F.

    2016-09-01

    The purpose of this paper is twofold. First, using the Cattaneo's relaxation approach, we reformulate the system of governing equations for the pollutant transport by shallow water flows over non-flat topography and anisotropic diffusion as hyperbolic balance laws with stiff source terms. The proposed relaxation system circumvents the infinite wave speed paradox which is inherent in standard advection-diffusion models. This turns out to give a larger stability range for the choice of the time step. Second, following a flux splitting approach, we derive a novel numerical method to discretise the resulting problem. In particular, we propose a new flux splitting and study the associated two systems of differential equations, called the "hydrodynamic" and the "relaxed diffusive" system, respectively. For the presented splitting we analyse the resulting two systems of differential equations and propose two discretisation schemes of the Godunov-type. These schemes are simple to implement, robust, accurate and fast when compared with existing methods. The resulting method is implemented on unstructured meshes and is systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems including non-flat topography and wetting and drying problems. Formal second order accuracy is assessed through convergence rates studies.

  18. Development of comprehensive numerical schemes for predicting evaporating gas-droplets flow processes of a liquid-fueled combustor. Semiannual report, 15 June 1988-30 November 1988

    SciTech Connect

    Chen, C.P.

    1990-01-01

    An existing Computational Fluid Dynamics code for simulating complex turbulent flows inside a liquid rocket combustion chamber was validated and further developed. The Advanced Rocket Injector/Combustor Code (ARICC) is simplified and validated against benchmark flow situations for laminar and turbulent flows. The numerical method used in ARICC Code is re-examined for incompressible flow calculations. For turbulent flows, both the subgrid and the two equation k-epsilon turbulence models are studied. Cases tested include idealized Burger's equation in complex geometries and boundaries, a laminar pipe flow, a high Reynolds number turbulent flow, and a confined coaxial jet with recirculations. The accuracy of the algorithm is examined by comparing the numerical results with the analytical solutions as well as experimented data with different grid sizes.

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

    NASA Astrophysics Data System (ADS)

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

    2015-04-01

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

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

    SciTech Connect

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

    2014-12-15

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-12-01

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

  2. Progress in the study of magnetic dynamo generation processes by non-Gaussian, non-Markovian velocity fluctuations using meshless, Lagrangian numerical schemes

    NASA Astrophysics Data System (ADS)

    Sanchez, Raul; Reynolds-Barredo, J. Miguel; Newman, David E.

    2015-11-01

    The generation of magnetic dynamos by turbulent velocity fields is traditionally studied, at the simplest level, by assuming near-Gaussian, random velocity fluctuations. This allows to express the effective electromotive force in terms of a piece proportional to the large-scale magnetic field (the α-term) and another proportional to its curl (the β term), once certain symmetry conditions are assumed. Physically, the α-term is a measure of the mean helicity of the flow and drives the dynamo. Previously, we examined theoretically the consequences of assuming instead Levy-distributed, Lagrangianly-correlated velocity fields, which have been recently identified as relevant in regimes of near-marginal turbulence (superdiffusion) or in the presence of strong, stable sheared flows (subdiffusion). Here, we report on recent numerical progress on the study of these processes by implementing the kinematic dynamo equation using a meshless numerical method inspired by the SPH schemes frequently used in hydrodynamics. The results suggest that subdiffusive flows may importantly enhance the dynamo generation, even in the absence of mean helicity, which might be meaningful for the understanding of dynamo generation in situations where sheared, zonal flows are present.

  3. An advanced temporal credential-based security scheme with mutual authentication and key agreement for wireless sensor networks.

    PubMed

    Li, Chun-Ta; Weng, Chi-Yao; Lee, Cheng-Chi

    2013-01-01

    Wireless sensor networks (WSNs) can be quickly and randomly deployed in any harsh and unattended environment and only authorized users are allowed to access reliable sensor nodes in WSNs with the aid of gateways (GWNs). Secure authentication models among the users, the sensor nodes and GWN are important research issues for ensuring communication security and data privacy in WSNs. In 2013, Xue et al. proposed a temporal-credential-based mutual authentication and key agreement scheme for WSNs. However, in this paper, we point out that Xue et al.'s scheme cannot resist stolen-verifier, insider, off-line password guessing, smart card lost problem and many logged-in users' attacks and these security weaknesses make the scheme inapplicable to practical WSN applications. To tackle these problems, we suggest a simple countermeasure to prevent proposed attacks while the other merits of Xue et al.'s authentication scheme are left unchanged. PMID:23887085

  4. An Advanced Temporal Credential-Based Security Scheme with Mutual Authentication and Key Agreement for Wireless Sensor Networks

    PubMed Central

    Li, Chun-Ta; Weng, Chi-Yao; Lee, Cheng-Chi

    2013-01-01

    Wireless sensor networks (WSNs) can be quickly and randomly deployed in any harsh and unattended environment and only authorized users are allowed to access reliable sensor nodes in WSNs with the aid of gateways (GWNs). Secure authentication models among the users, the sensor nodes and GWN are important research issues for ensuring communication security and data privacy in WSNs. In 2013, Xue et al. proposed a temporal-credential-based mutual authentication and key agreement scheme for WSNs. However, in this paper, we point out that Xue et al.'s scheme cannot resist stolen-verifier, insider, off-line password guessing, smart card lost problem and many logged-in users' attacks and these security weaknesses make the scheme inapplicable to practical WSN applications. To tackle these problems, we suggest a simple countermeasure to prevent proposed attacks while the other merits of Xue et al.'s authentication scheme are left unchanged. PMID:23887085

  5. An advanced temporal credential-based security scheme with mutual authentication and key agreement for wireless sensor networks.

    PubMed

    Li, Chun-Ta; Weng, Chi-Yao; Lee, Cheng-Chi

    2013-07-24

    Wireless sensor networks (WSNs) can be quickly and randomly deployed in any harsh and unattended environment and only authorized users are allowed to access reliable sensor nodes in WSNs with the aid of gateways (GWNs). Secure authentication models among the users, the sensor nodes and GWN are important research issues for ensuring communication security and data privacy in WSNs. In 2013, Xue et al. proposed a temporal-credential-based mutual authentication and key agreement scheme for WSNs. However, in this paper, we point out that Xue et al.'s scheme cannot resist stolen-verifier, insider, off-line password guessing, smart card lost problem and many logged-in users' attacks and these security weaknesses make the scheme inapplicable to practical WSN applications. To tackle these problems, we suggest a simple countermeasure to prevent proposed attacks while the other merits of Xue et al.'s authentication scheme are left unchanged.

  6. Development and validation of burnup dependent computational schemes for the analysis of assemblies with advanced lattice codes

    NASA Astrophysics Data System (ADS)

    Ramamoorthy, Karthikeyan

    The main aim of this research is the development and validation of computational schemes for advanced lattice codes. The advanced lattice code which forms the primary part of this research is "DRAGON Version4". The code has unique features like self shielding calculation with capabilities to represent distributed and mutual resonance shielding effects, leakage models with space-dependent isotropic or anisotropic streaming effect, availability of the method of characteristics (MOC), burnup calculation with reaction-detailed energy production etc. Qualified reactor physics codes are essential for the study of all existing and envisaged designs of nuclear reactors. Any new design would require a thorough analysis of all the safety parameters and burnup dependent behaviour. Any reactor physics calculation requires the estimation of neutron fluxes in various regions of the problem domain. The calculation goes through several levels before the desired solution is obtained. Each level of the lattice calculation has its own significance and any compromise at any step will lead to poor final result. The various levels include choice of nuclear data library and energy group boundaries into which the multigroup library is cast; self shielding of nuclear data depending on the heterogeneous geometry and composition; tracking of geometry, keeping error in volume and surface to an acceptable minimum; generation of regionwise and groupwise collision probabilities or MOC-related information and their subsequent normalization thereof, solution of transport equation using the previously generated groupwise information and obtaining the fluxes and reaction rates in various regions of the lattice; depletion of fuel and of other materials based on normalization with constant power or constant flux. Of the above mentioned levels, the present research will mainly focus on two aspects, namely self shielding and depletion. The behaviour of the system is determined by composition of resonant

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

    NASA Astrophysics Data System (ADS)

    Nimmatoori, Praneeth

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

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

    PubMed

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

    2012-01-01

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

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

    ERIC Educational Resources Information Center

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

    2014-01-01

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

  10. Numerous Numerals.

    ERIC Educational Resources Information Center

    Henle, James M.

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

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

    NASA Astrophysics Data System (ADS)

    Holladay, J. D.; Wang, Y.

    2015-05-01

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

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

    ERIC Educational Resources Information Center

    Skowronski, Steven D.; Tatum, Kenneth

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

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

    SciTech Connect

    Rame, M.

    1990-01-01

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

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

    NASA Technical Reports Server (NTRS)

    Nystrom, P. A.; Farassat, F.

    1980-01-01

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

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

    SciTech Connect

    Holladay, Jamelyn D.; Wang, Yong

    2015-05-01

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

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

    SciTech Connect

    Mazzolani, Federico M.

    2008-07-08

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

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

    SciTech Connect

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

    2014-03-01

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

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

    PubMed

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

    2014-12-01

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

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

    PubMed

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

    2014-12-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1996-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2011-03-01

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

  3. Numerical simulation and intercomparison of boundary layer structure with different PBL schemes in WRF using experimental observations at a tropical site

    NASA Astrophysics Data System (ADS)

    Hariprasad, K. B. R. R.; Srinivas, C. V.; Singh, A. Bagavath; Vijaya Bhaskara Rao, S.; Baskaran, R.; Venkatraman, B.

    2014-08-01

    In this study the performance of seven PBL parameterizations in the Weather Research and Forecast (WRF-ARW) mesoscale model was tested at the tropical site Kalpakkam. Meteorological observations collected during an intense observation campaign for wind field modeling called Round Robin Exercise (RRE) were used for comparison. High resolution simulations were conducted for a warm summer condition on 22-24 September 2010. The observations included GPS Sonde vertical profiles, surface level data from meteorological towers and turbulent fluxes from sonic anemometers. Sensitivity experiments with seven PBL schemes [Mellor-Yamada-Janjic (MYJ), Mellor-Yamada-Nakanishi-Niino (MYNN), Quasi Normal Scale Elimination (QNSE), Yonsei University (YSU), Asymmetric Convective Model (ACM2), Bougeault-Lacarrére (BL), Bretherton-Park (UW)] indicated that while all the schemes similarly produced the stable boundary layer characteristics there were large differences in the convective daytime PBL. It has been found that while ACM2 and QNSE produced highly unstable and deep convective layers, the UW produced relatively shallow mixed layer and all other schemes (YSU, MYNN, MYJ, BL) produced intermediately deep convective layers. All the schemes well produced the vertical wind directional shear within the PBL. A wide variation in the eddy diffusivities was simulated by different PBL schemes in convective daytime condition. ACM2 and UW produced excessive diffusivities which led to relatively weaker winds, warmer and dryer mixed layers with these schemes. Overall the schemes MYNN and YSU simulated the various PBL quantities in better agreement with observations. The differences in the simulated PBL structures could be partly due to various surface layer formulations that produced variation in friction velocity and heat fluxes in each case.

  4. Numerical Modelling of Subduction Plate Interface, Technical Advances for Outstanding Questions

    NASA Astrophysics Data System (ADS)

    Le Pourhiet, L.; Ruh, J.; Pranger, C. C.; Zheng, L.; van Dinther, Y.; May, D.; Gerya, T.; Burov, E. B.

    2015-12-01

    and fluids pathways together with adaptative time stepping schemes permitting to switch from static long term-tectonic approach to seismic cycle modelling within the same frame work and discuss how the results of these forward models can be used to better assess coupling at the subduction zone interface from geodetic, seismologic and geologic record.

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

    NASA Astrophysics Data System (ADS)

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

    2011-12-01

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

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

    PubMed Central

    Bisetti, Fabrizio; Attili, Antonio; Pitsch, Heinz

    2014-01-01

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

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

    PubMed

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

    2015-04-01

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

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

    PubMed

    Bisetti, Fabrizio; Attili, Antonio; Pitsch, Heinz

    2014-08-13

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

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

    PubMed

    Bisetti, Fabrizio; Attili, Antonio; Pitsch, Heinz

    2014-08-13

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

  10. Relaxation schemes for Chebyshev spectral multigrid methods

    NASA Technical Reports Server (NTRS)

    Kang, Yimin; Fulton, Scott R.

    1993-01-01

    Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The first scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an efficient and relatively simple approach for solving two-dimensional spectral equations. Numerical examples and comparisons with other methods are given.

  11. A Correction Scheme for Thermal Conductivity Measurement Using the Comparative Cut-bar Technique Based on a 3D Numerical Simulation

    SciTech Connect

    Douglas W. Marshall; Changhu Xing; Charles Folsom; Colby Jensen; Heng Ban

    2014-05-01

    As an important factor affecting the accuracy of the thermal conductivity measurement, systematic (bias) error in the guarded comparative axial heat flow (cut-bar) method was mostly neglected by previous researches. This bias is due primarily to the thermal conductivity mismatch between sample and meter bars (reference), which is common for a sample of unknown thermal conductivity. A correction scheme, based on a finite element simulation of the measurement system, was proposed to reduce the magnitude of the overall measurement uncertainty. This scheme was experimentally validated by applying corrections on four types of sample measurements in which the specimen thermal conductivity is much smaller, slightly smaller, equal and much larger than that of the meter bar. As an alternative to the optimum guarding technique proposed before, the correction scheme can be used to minimize uncertainty contribution from the measurement system with non-optimal guarding conditions. It is especially necessary for large thermal conductivity mismatches between sample and meter bars.

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

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2013-12-01

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

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

    SciTech Connect

    Halavanau, A.; Piot, P.

    2015-06-01

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

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

    NASA Astrophysics Data System (ADS)

    Blum, Volker

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

  16. Analysis and design of numerical schemes for gas dynamics 1: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence

    NASA Technical Reports Server (NTRS)

    Jameson, Antony

    1994-01-01

    The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for one-dimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multi-dimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.

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

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

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

  18. Validating the turbulence parameterization schemes of a numerical model using eddy dissipation rate and turbulent kinetic energy measurements in terrain-disrupted airflow

    NASA Astrophysics Data System (ADS)

    Chan, P. W.

    2010-10-01

    A number of turbulence parameterization schemes are available in the latest version (6.0) of the Regional Atmospheric Modelling System (RAMS). Chan in Meteorol Atmos Phys 103:145-157, (2009), studied the performance of these schemes by simulating the eddy dissipation rate (EDR) distribution in the vicinity of the Hong Kong International Airport (HKIA) and comparing with the EDR measurements of remote-sensing instruments at the airport. For the e-l (turbulent kinetic energy - mixing length) scheme considered in that study, the asymptotic mixing length was assumed to be a constant. This assumption is changed in the present paper, a variable asymptotic mixing length is chosen and simulations of EDR fields are repeated for terrain-disrupted airflow in the vicinity of HKIA. It is found that, with a variable asymptotic mixing length, the performance of the e-l scheme is greatly improved. With suitable choice of the empirical constants in the turbulence closure, the accuracy of the EDR profile (in comparison with LIDAR and wind profiler measurements) is found to be comparable with that predicted by the Deardorff scheme. A study on the sensitivity of the simulation results to these empirical constants has also been performed. Moreover, as a follow-up of the previous study of Chan in Meteorol Atmos Phys 103:145-157, (2009), case studies have been conducted on the following issues of the model simulation of turbulence for aviation application: (a) the effect of vertical gridding on the simulation results, (b) possibility of false alarm (such as over-forecasting of EDR value) in light turbulence cases, and (c) the performance in the simulation of other turbulence intensity metric for aviation purpose, e.g. TKE.

  19. Re-evaluation of an Optimized Second Order Backward Difference (BDF2OPT) Scheme for Unsteady Flow Applications

    NASA Technical Reports Server (NTRS)

    Vatsa, Veer N.; Carpenter, Mark H.; Lockard, David P.

    2009-01-01

    Recent experience in the application of an optimized, second-order, backward-difference (BDF2OPT) temporal scheme is reported. The primary focus of the work is on obtaining accurate solutions of the unsteady Reynolds-averaged Navier-Stokes equations over long periods of time for aerodynamic problems of interest. The baseline flow solver under consideration uses a particular BDF2OPT temporal scheme with a dual-time-stepping algorithm for advancing the flow solutions in time. Numerical difficulties are encountered with this scheme when the flow code is run for a large number of time steps, a behavior not seen with the standard second-order, backward-difference, temporal scheme. Based on a stability analysis, slight modifications to the BDF2OPT scheme are suggested. The performance and accuracy of this modified scheme is assessed by comparing the computational results with other numerical schemes and experimental data.

  20. High resolution schemes for hyperbolic conservation laws

    NASA Technical Reports Server (NTRS)

    Harten, A.

    1983-01-01

    A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurate scheme to an appropriately modified flux function. The so-derived second order accurate schemes achieve high resolution while preserving the robustness of the original nonoscillatory first order accurate scheme. Numerical experiments are presented to demonstrate the performance of these new schemes.

  1. Upwind schemes and bifurcating solutions in real gas computations

    NASA Technical Reports Server (NTRS)

    Suresh, Ambady; Liou, Meng-Sing

    1992-01-01

    The area of high speed flow is seeing a renewed interest due to advanced propulsion concepts such as the National Aerospace Plane (NASP), Space Shuttle, and future civil transport concepts. Upwind schemes to solve such flows have become increasingly popular in the last decade due to their excellent shock capturing properties. In the first part of this paper the authors present the extension of the Osher scheme to equilibrium and non-equilibrium gases. For simplicity, the source terms are treated explicitly. Computations based on the above scheme are presented to demonstrate the feasibility, accuracy and efficiency of the proposed scheme. One of the test problems is a Chapman-Jouguet detonation problem for which numerical solutions have been known to bifurcate into spurious weak detonation solutions on coarse grids. Results indicate that the numerical solution obtained depends both on the upwinding scheme used and the limiter employed to obtain second order accuracy. For example, the Osher scheme gives the correct CJ solution when the super-bee limiter is used, but gives the spurious solution when the Van Leer limiter is used. With the Roe scheme the spurious solution is obtained for all limiters.

  2. Saturation-free numerical scheme for computing the flow past a lattice of airfoils and the determination of separation points in a viscous fluid

    NASA Astrophysics Data System (ADS)

    Petrov, A. G.

    2011-07-01

    A numerical method for computing the potential flow past a lattice of airfoils is described. The problem is reduced to a linear integrodifferential equation on the lattice contour, which is then approximated by a linear system of equations with the help of specially derived quadrature formulas. The quadrature formulas exhibit exponential convergence in the number of points on an airfoil and have a simple analytical form. Due to its fast convergence and high accuracy, the method can be used to directly optimize the airfoils as based on any given integral characteristics. The shear stress distribution and the separation points are determined from the velocity distribution at the airfoil boundary calculated by solving the boundary layer equations. The method proposed is free of laborious grid generation procedures and does not involve difficulties associated with numerical viscosity at high Reynolds numbers.

  3. A numerical study of the 2- and 3-dimensional unsteady Navier-Stokes equations in velocity-vorticity variables using compact difference schemes

    NASA Technical Reports Server (NTRS)

    Gatski, T. B.; Grosch, C. E.

    1984-01-01

    A compact finite-difference approximation to the unsteady Navier-Stokes equations in velocity-vorticity variables is used to numerically simulate a number of flows. These include two-dimensional laminar flow of a vortex evolving over a flat plate with an embedded cavity, the unsteady flow over an elliptic cylinder, and aspects of the transient dynamics of the flow over a rearward facing step. The methodology required to extend the two-dimensional formulation to three-dimensions is presented.

  4. Numerical and structural aberrations in advanced neuroblastoma tumours by CGH analysis; survival correlates with chromosome 17 status

    PubMed Central

    Cunsolo, C Lo; Bicocchi, M P; Petti, A R; Tonini, G P

    2000-01-01

    Rapid tumour progression in neuroblastoma is associated with MYCN amplification, deletion of the short arm of chromosome 1 and gain of 17q. However, patients with advanced disease without MYCN amplification and/or 1p deletion have a very poor outcome too, which suggests other genetic defects may predict an unfavourable prognosis. We employed CGH to study 22 tumours of patients at stages 3 and 4 over one year of age (6 and 16 cases respectively). Patients were divided in groups (A) long-term survivors and (B) short-term survivors. CGH showed a total of 226 chromosome imbalances (110 in group A and 116 in group B). The neuroblastoma cells of long-term survivors showed a preponderance of numerical aberrations (54%vs 43%); particularly gains of entire chromosomes 1 (P< 0.03), 7 (P< 0.04) and 19 (P< 0.05). An extra copy of 17 was detected in 6/8 (75%) samples of group A and only 1/14 (7%) samples of group B (P< 0.002). Conversely, tumours of patients who died from disease progression displayed a higher frequency of structural abnormalities (43%vs 35%), including loss of 1p, 9p, 11q, 15q and 18q and gain of 12q, although the difference was not significant (P= 0.24). Unbalanced gain of 17q was detected in 8/14 (57%) tumours of group B and only 1/8 (13%) tumours of group A (P< 0.05). The peculiar genetic difference observed in the tumours of long and short-term survivors may have prognostic relevance. © 2000 Cancer Research Campaign PMID:11044353

  5. Trefftz difference schemes on irregular stencils

    SciTech Connect

    Tsukerman, Igor

    2010-04-20

    The recently developed Flexible Local Approximation MEthod (FLAME) produces accurate difference schemes by replacing the usual Taylor expansion with Trefftz functions - local solutions of the underlying differential equation. This paper advances and casts in a general form a significant modification of FLAME proposed recently by Pinheiro and Webb: a least-squares fit instead of the exact match of the approximate solution at the stencil nodes. As a consequence of that, FLAME schemes can now be generated on irregular stencils with the number of nodes substantially greater than the number of approximating functions. The accuracy of the method is preserved but its robustness is improved. For demonstration, the paper presents a number of numerical examples in 2D and 3D: electrostatic (magnetostatic) particle interactions, scattering of electromagnetic (acoustic) waves, and wave propagation in a photonic crystal. The examples explore the role of the grid and stencil size, of the number of approximating functions, and of the irregularity of the stencils.

  6. Multi-moment advection scheme in three dimension for Vlasov simulations of magnetized plasma

    SciTech Connect

    Minoshima, Takashi; Matsumoto, Yosuke; Amano, Takanobu

    2013-03-01

    We present an extension of the multi-moment advection scheme [T. Minoshima, Y. Matsumoto, T. Amano, Multi-moment advection scheme for Vlasov simulations, Journal of Computational Physics 230 (2011) 6800–6823] to the three-dimensional case, for full electromagnetic Vlasov simulations of magnetized plasma. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, and advances them on the basis of their governing equations. Similar to the two-dimensional scheme, the three-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile with little numerical dispersion or diffusion. This is a very important property for Vlasov simulations of magnetized plasma. We apply the scheme to electromagnetic Vlasov simulations. Propagation of linear waves and nonlinear evolution of the electron temperature anisotropy instability are successfully simulated with a good accuracy of the energy conservation.

  7. Stability analysis of pressure correction schemes for the Navier–Stokes equations with traction boundary conditions

    NASA Astrophysics Data System (ADS)

    Lee, Sanghyun; Salgado, Abner J.

    2016-09-01

    We present a stability analysis for two different rotational pressure correction schemes with open and traction boundary conditions. First, we provide a stability analysis for a rotational version of the grad-div stabilized scheme of [A. Bonito, J.-L. Guermond, and S. Lee. Modified pressure-correction projection methods: Open boundary and variable time stepping. In Numerical Mathematics and Advanced Applications - ENUMATH 2013, volume 103 of Lecture Notes in Computational Science and Engineering, pages 623-631. Springer, 2015]. This scheme turns out to be unconditionally stable, provided the stabilization parameter is suitably chosen. We also establish a conditional stability result for the boundary correction scheme presented in [E. Bansch. A finite element pressure correction scheme for the Navier-Stokes equations with traction boundary condition. Comput. Methods Appl. Mech. Engrg., 279:198-211, 2014]. These results are shown by employing the equivalence between stabilized gauge Uzawa methods and rotational pressure correction schemes with traction boundary conditions.

  8. New, Improved Bulk-microphysical Schemes for Studying Precipitation Processes in WRF. Part 1; Comparisons with Other Schemes

    NASA Technical Reports Server (NTRS)

    Tao, W.-K.; Shi, J.; Chen, S. S> ; Lang, S.; Hong, S.-Y.; Thompson, G.; Peters-Lidard, C.; Hou, A.; Braun, S.; Simpson, J.

    2007-01-01

    Advances in computing power allow atmospheric prediction models to be mn at progressively finer scales of resolution, using increasingly more sophisticated physical parameterizations and numerical methods. The representation of cloud microphysical processes is a key component of these models, over the past decade both research and operational numerical weather prediction models have started using more complex microphysical schemes that were originally developed for high-resolution cloud-resolving models (CRMs). A recent report to the United States Weather Research Program (USWRP) Science Steering Committee specifically calls for the replacement of implicit cumulus parameterization schemes with explicit bulk schemes in numerical weather prediction (NWP) as part of a community effort to improve quantitative precipitation forecasts (QPF). An improved Goddard bulk microphysical parameterization is implemented into a state-of the-art of next generation of Weather Research and Forecasting (WRF) model. High-resolution model simulations are conducted to examine the impact of microphysical schemes on two different weather events (a midlatitude linear convective system and an Atllan"ic hurricane). The results suggest that microphysics has a major impact on the organization and precipitation processes associated with a summer midlatitude convective line system. The 31CE scheme with a cloud ice-snow-hail configuration led to a better agreement with observation in terms of simulated narrow convective line and rainfall intensity. This is because the 3ICE-hail scheme includes dense ice precipitating (hail) particle with very fast fall speed (over 10 m/s). For an Atlantic hurricane case, varying the microphysical schemes had no significant impact on the track forecast but did affect the intensity (important for air-sea interaction)

  9. Numerical Relativity

    NASA Technical Reports Server (NTRS)

    Baker, John G.

    2009-01-01

    Recent advances in numerical relativity have fueled an explosion of progress in understanding the predictions of Einstein's theory of gravity, General Relativity, for the strong field dynamics, the gravitational radiation wave forms, and consequently the state of the remnant produced from the merger of compact binary objects. I will review recent results from the field, focusing on mergers of two black holes.

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

    NASA Astrophysics Data System (ADS)

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

    2011-08-01

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

  11. Simplification of the unified gas kinetic scheme.

    PubMed

    Chen, Songze; Guo, Zhaoli; Xu, Kun

    2016-08-01

    The unified gas kinetic scheme (UGKS) is an asymptotic preserving (AP) scheme for kinetic equations. It is superior for transition flow simulation and has been validated in the past years. However, compared to the well-known discrete ordinate method (DOM), which is a classical numerical method solving the kinetic equations, the UGKS needs more computational resources. In this study, we propose a simplification of the unified gas kinetic scheme. It allows almost identical numerical cost as the DOM, but predicts numerical results as accurate as the UGKS. In the simplified scheme, the numerical flux for the velocity distribution function and the numerical flux for the macroscopic conservative quantities are evaluated separately. The equilibrium part of the UGKS flux is calculated by analytical solution instead of the numerical quadrature in velocity space. The simplification is equivalent to a flux hybridization of the gas kinetic scheme for the Navier-Stokes (NS) equations and the conventional discrete ordinate method. Several simplification strategies are tested, through which we can identify the key ingredient of the Navier-Stokes asymptotic preserving property. Numerical tests show that, as long as the collision effect is built into the macroscopic numerical flux, the numerical scheme is Navier-Stokes asymptotic preserving, regardless the accuracy of the microscopic numerical flux for the velocity distribution function. PMID:27627418

  12. Simplification of the unified gas kinetic scheme

    NASA Astrophysics Data System (ADS)

    Chen, Songze; Guo, Zhaoli; Xu, Kun

    2016-08-01

    The unified gas kinetic scheme (UGKS) is an asymptotic preserving (AP) scheme for kinetic equations. It is superior for transition flow simulation and has been validated in the past years. However, compared to the well-known discrete ordinate method (DOM), which is a classical numerical method solving the kinetic equations, the UGKS needs more computational resources. In this study, we propose a simplification of the unified gas kinetic scheme. It allows almost identical numerical cost as the DOM, but predicts numerical results as accurate as the UGKS. In the simplified scheme, the numerical flux for the velocity distribution function and the numerical flux for the macroscopic conservative quantities are evaluated separately. The equilibrium part of the UGKS flux is calculated by analytical solution instead of the numerical quadrature in velocity space. The simplification is equivalent to a flux hybridization of the gas kinetic scheme for the Navier-Stokes (NS) equations and the conventional discrete ordinate method. Several simplification strategies are tested, through which we can identify the key ingredient of the Navier-Stokes asymptotic preserving property. Numerical tests show that, as long as the collision effect is built into the macroscopic numerical flux, the numerical scheme is Navier-Stokes asymptotic preserving, regardless the accuracy of the microscopic numerical flux for the velocity distribution function.

  13. Impact of precipitating ice on the simulation of a heavy rainfall event with advanced research WRF using two bulk microphysical schemes

    NASA Astrophysics Data System (ADS)

    Efstathiou, G. A.; Zoumakis, N. M.; Melas, D.; Kassomenos, P.

    2012-11-01

    In this study, the Weather Research and Forecasting (WRF) model version 3.2 is used to examine the impact of precipitating ice and especially snow-graupel partitioning in the simulation of a heavy rainfall event over Chalkidiki peninsula in Northern Greece. This major precipitation event, associated with a case of cyclogenesis over the Aegean Sea, occurred on the 8th of October 2006 causing severe flooding and damage. Two widely used microphysical parameterizations, the Purdue Lin (PLIN) and WRF Single-Moment 6-class scheme (WSM6) are compared with available raingauge measurements over the complex topography of Chalkidiki. To further investigate the importance of snow and graupel relative mass content and the treatment of precipitating ice sedimentation velocity, two older versions of the WSM6 scheme were compiled and run with the current model. The verification results indicate that all simulations were found to match raingauge data more closely over the eastern mountainous Chalkidiki peninsula where maximum accumulations were observed. In other stations all schemes overestimate 24h accumulated rainfall except a station situated at the western part of the peninsula, where none of the simulations was able to reproduce observed rainfall. Graupel dominance in PLIN generates rapid precipitation fallout at the point of maximum predicted 24h accumulation. Similar behavior is shown in WSM6 from WRF version 2, but with significant less rainfall. Increasing snow amounts aloft, due to the unified treatment of precipitating ice in WSM6 from WRF version 3, modifies rain dynamics which decrease rainfall rates, but increases 24h accumulations. A sensitivity experiment where PLIN is used with snow accretion by graupel turned off, indicated that this process seems to be the most important factor controlling the differences in surface precipitation between PLIN and WSM6 from WRF version 3, determining the spatial and temporal distribution of this heavy precipitation event. The

  14. A high order accurate difference scheme for complex flow fields

    SciTech Connect

    Dexun Fu; Yanwen Ma

    1997-06-01

    A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed. It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible N-S equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage R-K method is used to advance in time. In order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets. 18 refs., 12 figs., 1 tab.

  15. Numerical Modeling for Springback Predictions by Considering the Variations of Elastic Modulus in Stamping Advanced High-Strength Steels (AHSS)

    NASA Astrophysics Data System (ADS)

    Kim, Hyunok; Kimchi, Menachem

    2011-08-01

    This paper presents a numerical modeling approach for predicting springback by considering the variations of elastic modulus on springback in stamping AHSS. Various stamping tests and finite-element method (FEM) simulation codes were used in this study. The cyclic loading-unloading tensile tests were conducted to determine the variations of elastic modulus for dual-phase (DP) 780 sheet steel. The biaxial bulge test was used to obtain plastic flow stress data. The non-linear reduction of elastic modulus for increasing the plastic strain was formulated by using the Yoshida model that was implemented in FEM simulations for springback. To understand the effects of material properties on springback, experiments were conducted with a simple geometry such as U-shape bending and the more complex geometry such as the curved flanging and S-rail stamping. Different measurement methods were used to confirm the final part geometry. Two different commercial FEM codes, LS-DYNA and DEFORM, were used to compare the experiments. The variable elastic modulus improved springback predictions in U-shape bending and curved flanging tests compared to FEM with the constant elastic modulus. However, in S-rail stamping tests, both FEM models with the isotropic hardening model showed limitations in predicting the sidewall curl of the S-rail part after springback. To consider the kinematic hardening and Bauschinger effects that result from material bending-unbending in S-rail stamping, the Yoshida model was used for FEM simulation of S-rail stamping and springback. The FEM predictions showed good improvement in correlating with experiments.

  16. Construction of weighted upwind compact scheme

    NASA Astrophysics Data System (ADS)

    Wang, Zhengjie

    Enormous endeavor has been devoted in spatial high order high resolution schemes in more than twenty five years previously, like total variation diminishing (TVD), essentially non-oscillatory scheme, weighted essentially non-oscillatory scheme for finite difference, and Discontinuous Galerkin methods for finite element and the finite volume. In this dissertation, a high order finite difference Weighted Upwind Compact Scheme has been constructed by dissipation and dispersion analysis. Secondly, a new method to construct global weights has been tested. Thirdly, a methodology to compromise dissipation and dispersion in constructing Weighted Upwind Compact Scheme has been derived. Finally, several numerical test cases have been shown.

  17. Upwind Compact Finite Difference Schemes

    NASA Astrophysics Data System (ADS)

    Christie, I.

    1985-07-01

    It was shown by Ciment, Leventhal, and Weinberg ( J. Comput. Phys.28 (1978), 135) that the standard compact finite difference scheme may break down in convection dominated problems. An upwinding of the method, which maintains the fourth order accuracy, is suggested and favorable numerical results are found for a number of test problems.

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

    NASA Astrophysics Data System (ADS)

    Xiao, Wenbin; Dong, Wencai

    2016-06-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-05-01

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

  20. The basic function scheme of polynomial type

    SciTech Connect

    WU, Wang-yi; Lin, Guang

    2009-12-01

    A new numerical method---Basic Function Method is proposed. This method can directly discrete differential operator on unstructured grids. By using the expansion of basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as basic function and applying the technique of flux splitting method and the combination of central and upwind schemes to suppress the non-physical fluctuation near the shock wave, the second-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper. Several numerical results of many typical examples for two dimensional inviscid compressible transonic and supersonic steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave. Especially, combining with the adaptive remeshing technique, the satisfactory results can be obtained by these schemes.

  1. High-Order Energy Stable WENO Schemes

    NASA Technical Reports Server (NTRS)

    Yamaleev, Nail K.; Carpenter, Mark H.

    2008-01-01

    A new third-order Energy Stable Weighted Essentially NonOscillatory (ESWENO) finite difference scheme for scalar and vector linear hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. A rigorous truncation error analysis is presented showing that the accuracy of the 3rd-order ESWENO scheme is drastically improved if the tuning parameters of the weight functions satisfy certain criteria. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO finite difference scheme of Jiang and Shu in terms of accuracy, while providing essentially nonoscillatory solutions near strong discontinuities.

  2. High resolution TVD schemes for interface tracking

    NASA Astrophysics Data System (ADS)

    Nandi, K.; Walker, S. P.; Date, A. W.

    2016-06-01

    A first order upwind difference scheme (UDS) is routinely adopted for representing convection terms in a discretised space. UDS provides stable solutions. However it also introduces false diffusion in situations in which the flow direction is oblique relative to the numerical grid or when the cell-Peclet number is large. In order to predict sharp interface, higher order upwind schemes are preferred because of they reduce numerical dissipation. In interfacial flows, density and viscosity vary sharply in space. Representation of convective terms by Total variation diminishing (TVD) schemes ensures reduced smearing without impairing convergence property. TVD schemes develop formulae for interpolation of a cell-face value of the transported variable. If the interpolated value is bounded by the neighbouring nodal values then the scheme is `Bounded'. However, not all TVD schemes possess this property of `Boundedness'. The Normalised Variable Diagram (NVD) defines a domain within which the TVD scheme is bounded. Thus by combining the features of both TVD schemes and ensuring that they fall with the defined area of NVD, the convergence as well as the boundedness of a computational scheme can be ensured. In this paper, six different higher order schemes are considered some which are TVD bounded or unbounded, to solve the well known interface tracking problem of Rayleigh-Taylor Instability. To the best of our knowledge, a comparison of combined TVD/NVD principles in the case of interface tracking problems has not been reported in published literature.

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

    NASA Technical Reports Server (NTRS)

    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.

  4. The Impact of Microphysical Schemes on Hurricane Intensity and Track

    NASA Technical Reports Server (NTRS)

    Tao, Wei-Kuo; Shi, Jainn Jong; Chen, Shuyi S.; Lang, Stephen; Lin, Pay-Liam; Hong, Song-You; Peters-Lidard, Christa; Hou, Arthur

    2011-01-01

    During the past decade, both research and operational numerical weather prediction models [e.g. the Weather Research and Forecasting Model (WRF)] have started using more complex microphysical schemes originally developed for high-resolution cloud resolving models (CRMs) with 1-2 km or less horizontal resolutions. WRF is a next-generation meso-scale forecast model and assimilation system. It incorporates a modern software framework, advanced dynamics, numerics and data assimilation techniques, a multiple moveable nesting capability, and improved physical packages. WRF can be used for a wide range of applications, from idealized research to operational forecasting, with an emphasis on horizontal grid sizes in the range of 1-10 km. The current WRF includes several different microphysics options. At NASA Goddard, four different cloud microphysics options have been implemented into WRF. The performance of these schemes is compared to those of the other microphysics schemes available in WRF for an Atlantic hurricane case (Katrina). In addition, a brief review of previous modeling studies on the impact of microphysics schemes and processes on the intensity and track of hurricanes is presented and compared against the current Katrina study. In general, all of the studies show that microphysics schemes do not have a major impact on track forecasts but do have more of an effect on the simulated intensity. Also, nearly all of the previous studies found that simulated hurricanes had the strongest deepening or intensification when using only warm rain physics. This is because all of the simulated precipitating hydrometeors are large raindrops that quickly fall out near the eye-wall region, which would hydrostatically produce the lowest pressure. In addition, these studies suggested that intensities become unrealistically strong when evaporative cooling from cloud droplets and melting from ice particles are removed as this results in much weaker downdrafts in the simulated

  5. Final Progress Report: Collaborative Research: Decadal-to-Centennial Climate & Climate Change Studies with Enhanced Variable and Uniform Resolution GCMs Using Advanced Numerical Techniques

    SciTech Connect

    Fox-Rabinovitz, M; Cote, J

    2009-06-05

    The joint U.S-Canadian project has been devoted to: (a) decadal climate studies using developed state-of-the-art GCMs (General Circulation Models) with enhanced variable and uniform resolution; (b) development and implementation of advanced numerical techniques; (c) research in parallel computing and associated numerical methods; (d) atmospheric chemistry experiments related to climate issues; (e) validation of regional climate modeling strategies for nested- and stretched-grid models. The variable-resolution stretched-grid (SG) GCMs produce accurate and cost-efficient regional climate simulations with mesoscale resolution. The advantage of the stretched grid approach is that it allows us to preserve the high quality of both global and regional circulations while providing consistent interactions between global and regional scales and phenomena. The major accomplishment for the project has been the successful international SGMIP-1 and SGMIP-2 (Stretched-Grid Model Intercomparison Project, phase-1 and phase-2) based on this research developments and activities. The SGMIP provides unique high-resolution regional and global multi-model ensembles beneficial for regional climate modeling and broader modeling community. The U.S SGMIP simulations have been produced using SciDAC ORNL supercomputers. Collaborations with other international participants M. Deque (Meteo-France) and J. McGregor (CSIRO, Australia) and their centers and groups have been beneficial for the strong joint effort, especially for the SGMIP activities. The WMO/WCRP/WGNE endorsed the SGMIP activities in 2004-2008. This project reflects a trend in the modeling and broader communities to move towards regional and sub-regional assessments and applications important for the U.S. and Canadian public, business and policy decision makers, as well as for international collaborations on regional, and especially climate related issues.

  6. Numerical simulation of shrouded propellers

    NASA Technical Reports Server (NTRS)

    Afjeh, Abdollah A.

    1991-01-01

    A numerical model was developed for the evaluation of the performance characteristics of a shrouded propeller. Using this model, a computational study was carried out to investigate the feasibility of improving the aerodynamic performance of a propeller by encasing it in a shroud. The propeller blade was modeled by a segmented bound vortex positioned along the span of the blade at its quarter-chord-line. The shroud was modeled by a number of discrete vortex rings. Due to the mutual dependence of shroud and propeller vortex strengths and the propeller vortex wake an iterative scheme was employed. Three shroud configurations were considered: a cylindrical and two conical shrouds. The computed performance of the shrouded propeller was compared with that of a free propeller of identical propeller geometry. The numerical results indicated that the cylindrical shroud outperformed the conical shroud configurations for the cases considered. Furthermore, when compared to the free propeller performance, the cylindrical shroud showed a considerable performance enhancement over the free propeller. However, the improvements were found to decrease with an increase in the advance ratio and to virtually diminish at advance ratios of about 2.5.

  7. A classification scheme for chimera states

    NASA Astrophysics Data System (ADS)

    Kemeth, Felix P.; Haugland, Sindre W.; Schmidt, Lennart; Kevrekidis, Ioannis G.; Krischer, Katharina

    2016-09-01

    We present a universal characterization scheme for chimera states applicable to both numerical and experimental data sets. The scheme is based on two correlation measures that enable a meaningful definition of chimera states as well as their classification into three categories: stationary, turbulent, and breathing. In addition, these categories can be further subdivided according to the time-stationarity of these two measures. We demonstrate that this approach is both consistent with previously recognized chimera states and enables us to classify states as chimeras which have not been categorized as such before. Furthermore, the scheme allows for a qualitative and quantitative comparison of experimental chimeras with chimeras obtained through numerical simulations.

  8. Uncertainty of Microphysics Schemes in CRMs

    NASA Astrophysics Data System (ADS)

    Tao, W. K.; van den Heever, S. C.; Wu, D.; Saleeby, S. M.; Lang, S. E.

    2015-12-01

    Microphysics is the framework through which to understand the links between interactive aerosol, cloud and precipitation processes. These processes play a critical role in the water and energy cycle. CRMs with advanced microphysics schemes have been used to study the interaction between aerosol, cloud and precipitation processes at high resolution. But, there are still many uncertainties associated with these microphysics schemes. This has arisen, in part, from the fact microphysical processes cannot be measured directly; instead, cloud properties, which can be measured, are and have been used to validate model results. The utilization of current and future global high-resolution models is rapidly increasing and are at what has been traditional CRM resolutions and are using microphysics schemes that were developed in traditional CRMs. A potential NASA satellite mission called the Cloud and Precipitation Processes Mission (CaPPM) is currently being planned for submission to the NASA Earth Science Decadal Survey. This mission could provide the necessary global estimates of cloud and precipitation properties with which to evaluate and improve dynamical and microphysical parameterizations and the feedbacks. In order to facilitate the development of this mission, CRM simulations have been conducted to identify microphysical processes responsible for the greatest uncertainties in CRMs. In this talk, we will present results from numerical simulations conducted using two CRMs (NU-WRF and RAMS) with different dynamics, radiation, land surface and microphysics schemes. Specifically, we will conduct sensitivity tests to examine the uncertainty of the some of the key ice processes (i.e. riming, melting, freezing and shedding) in these two-microphysics schemes. The idea is to quantify how these two different models' respond (surface rainfall and its intensity, strength of cloud drafts, LWP/IWP, convective-stratiform-anvil area distribution) to changes of these key ice

  9. Advanced Nodal P3/SP3 Axial Transport Solvers for the MPACT 2D/1D Scheme

    SciTech Connect

    Stimpson, Shane G; Collins, Benjamin S

    2015-01-01

    As part of its initiative to provide multiphysics simulations of nuclear reactor cores, the Consortium for Advanced Simulation of Light Water Reactors (CASL) is developing the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). The MPACT code, which is the primary neutron transport solver of VERA-CS, employs the two-dimensional/one-dimensional (2D/1D) method to solve 3-dimensional neutron transport problems and provide sub-pin-level resolution of the power distribution. While 2D method of characteristics is used to solve for the transport effects within each plane, 1D-nodal methods are used axially. There have been extensive studies of the 2D/1D method with a variety nodal methods, and the P3/SP3 solver has proved to be an effective method of providing higher-fidelity solutions while maintaining a low computational burden.The current implementation in MPACT wraps a one-node nodal expansion method (NEM) kernel for each moment, iterating between them and performing multiple sweeps to resolve flux distributions. However, it has been observed that this approach is more sensitive to convergence problems. This paper documents the theory and application two new nodal P3/SP3 approaches to be used within the 2D/1D method in MPACT. These two approaches aim to provide enhanced stability compared with the pre-existing one-node approach. Results from the HY-NEM-SP3 solver show that the accuracy is consistent with the one-node formulations and provides improved convergence for some problems; but the solver has issues with cases in thin planes. Although the 2N-SENM-SP3 solver is still under development, it is intended to resolve the issues with HY-NEM-SP3 but it will incur some additional computational burden by necessitating an additional 1D-CMFD-P3 solver to generate the second moment cell-averaged scalar flux.

  10. On Tenth Order Central Spatial Schemes

    SciTech Connect

    Sjogreen, B; Yee, H C

    2007-05-14

    This paper explores the performance of the tenth-order central spatial scheme and derives the accompanying energy-norm stable summation-by-parts (SBP) boundary operators. The objective is to employ the resulting tenth-order spatial differencing with the stable SBP boundary operators as a base scheme in the framework of adaptive numerical dissipation control in high order multistep filter schemes of Yee et al. (1999), Yee and Sj{umlt o}green (2002, 2005, 2006, 2007), and Sj{umlt o}green and Yee (2004). These schemes were designed for multiscale turbulence flows including strong shock waves and combustion.

  11. On central-difference and upwind schemes

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Turkel, Eli

    1990-01-01

    A class of numerical dissipation models for central-difference schemes constructed with second- and fourth-difference terms is considered. The notion of matrix dissipation associated with upwind schemes is used to establish improved shock capturing capability for these models. In addition, conditions are given that guarantee that such dissipation models produce a Total Variation Diminishing (TVD) scheme. Appropriate switches for this type of model to ensure satisfaction of the TVD property are presented. Significant improvements in the accuracy of a central-difference scheme are demonstrated by computing both inviscid and viscous transonic airfoil flows.

  12. Implicit Space-Time Conservation Element and Solution Element Schemes

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung; Himansu, Ananda; Wang, Xiao-Yen

    1999-01-01

    Artificial numerical dissipation is in important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate implicit numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The new schemes presented are two highly accurate implicit solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to convection-dominated equations with very small viscosity. The stability and consistency of the schemes are analysed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

  13. On the Dynamics of TVD Schemes

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sweby, P. K.; Kutler, Paul (Technical Monitor)

    1994-01-01

    The dynamics of a class of TVD schemes for model hyperbolic and parabolic equations is studied numerically using a highly parallel supercomputer (CM-5). The objective is to utilize the highly parallel property of the CM-5 to reveal the reliable time step and entropy parameter ranges, and the degree of compressible flux limiters to avoid slow convergence and the production of nonphysical numerical solutions. We choose to study the nonlinear stability property of TVD schemes numerically since it is otherwise not amenable analytically.

  14. Dispersion-relation-preserving schemes for computational aeroacoustics

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.; Webb, Jay C.

    1992-01-01

    Finite difference schemes that have the same dispersion relations as the original partial differential equations are referred to as dispersion-relation-preserving (DRP) schemes. A method to construct time marching DRP schemes by optimizing the finite difference approximations of the space and time derivatives in the wave number and frequency space is presented. A sequence of numerical simulations is then performed.

  15. State of the art of control schemes for smart systems featuring magneto-rheological materials

    NASA Astrophysics Data System (ADS)

    Choi, Seung-Bok; Li, Weihua; Yu, Miao; Du, Haiping; Fu, Jie; Do, Phu Xuan

    2016-04-01

    This review presents various control strategies for application systems utilizing smart magneto-rheological fluid (MRF) and magneto-rheological elastomers (MRE). It is well known that both MRF and MRE are actively studied and applied to many practical systems such as vehicle dampers. The mandatory requirements for successful applications of MRF and MRE include several factors: advanced material properties, optimal mechanisms, suitable modeling, and appropriate control schemes. Among these requirements, the use of an appropriate control scheme is a crucial factor since it is the final action stage of the application systems to achieve the desired output responses. There are numerous different control strategies which have been applied to many different application systems of MRF and MRE, summarized in this review. In the literature review, advantages and disadvantages of each control scheme are discussed so that potential researchers can develop more effective strategies to achieve higher control performance of many application systems utilizing magneto-rheological materials.

  16. A Numerical Instability in an ADI Algorithm for Gyrokinetics

    SciTech Connect

    E.A. Belli; G.W. Hammett

    2004-12-17

    We explore the implementation of an Alternating Direction Implicit (ADI) algorithm for a gyrokinetic plasma problem and its resulting numerical stability properties. This algorithm, which uses a standard ADI scheme to divide the field solve from the particle distribution function advance, has previously been found to work well for certain plasma kinetic problems involving one spatial and two velocity dimensions, including collisions and an electric field. However, for the gyrokinetic problem we find a severe stability restriction on the time step. Furthermore, we find that this numerical instability limitation also affects some other algorithms, such as a partially implicit Adams-Bashforth algorithm, where the parallel motion operator v{sub {parallel}} {partial_derivative}/{partial_derivative}z is treated implicitly and the field terms are treated with an Adams-Bashforth explicit scheme. Fully explicit algorithms applied to all terms can be better at long wavelengths than these ADI or partially implicit algorithms.

  17. Towards an "All Speed" Unstructured Upwind Scheme

    NASA Technical Reports Server (NTRS)

    Loh, Ching Y.; Jorgenson, Philip C.E.

    2009-01-01

    In the authors previous studies [1], a time-accurate, upwind finite volume method (ETAU scheme) for computing compressible flows on unstructured grids was proposed. The scheme is second order accurate in space and time and yields high resolution in the presence of discontinuities. The scheme features a multidimensional limiter and multidimensional numerical dissipation. These help to stabilize the numerical process and to overcome the annoying pathological behaviors of upwind schemes. In the present paper, it will be further shown that such multidimensional treatments also lead to a nearly all-speed or Mach number insensitive upwind scheme. For flows at very high Mach number, e.g., 10, local numerical instabilities or the pathological behaviors are suppressed, while for flows at very low Mach number, e.g., 0.02, computation can be directly carried out without invoking preconditioning. For flows in different Mach number regimes, i.e., low, medium, and high Mach numbers, one only needs to adjust one or two parameters in the scheme. Several examples with low and high Mach numbers are demonstrated in this paper. Thus, the ETAU scheme is applicable to a broad spectrum of flow regimes ranging from high supersonic to low subsonic, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics).

  18. Well-balanced schemes for the Euler equations with gravitation

    NASA Astrophysics Data System (ADS)

    Käppeli, R.; Mishra, S.

    2014-02-01

    Well-balanced high-order finite volume schemes are designed to approximate the Euler equations with gravitation. The schemes preserve discrete equilibria, corresponding to a large class of physically stable hydrostatic steady states. Based on a novel local hydrostatic reconstruction, the derived schemes are well-balanced for any consistent numerical flux for the Euler equations. The form of the hydrostatic reconstruction is both very simple and computationally efficient as it requires no analytical or numerical integration. Moreover, as required by many interesting astrophysical scenarios, the schemes are applicable beyond the ideal gas law. Both first- and second-order accurate versions of the schemes and their extension to multi-dimensional equilibria are presented. Several numerical experiments demonstrating the superior performance of the well-balanced schemes, as compared to standard finite volume schemes, are also presented.

  19. Advanced coding and modulation schemes for TDRSS

    NASA Technical Reports Server (NTRS)

    Harrell, Linda; Kaplan, Ted; Berman, Ted; Chang, Susan

    1993-01-01

    This paper describes the performance of the Ungerboeck and pragmatic 8-Phase Shift Key (PSK) Trellis Code Modulation (TCM) coding techniques with and without a (255,223) Reed-Solomon outer code as they are used for Tracking Data and Relay Satellite System (TDRSS) S-Band and Ku-Band return services. The performance of these codes at high data rates is compared to uncoded Quadrature PSK (QPSK) and rate 1/2 convolutionally coded QPSK in the presence of Radio Frequency Interference (RFI), self-interference, and hardware distortions. This paper shows that the outer Reed-Solomon code is necessary to achieve a 10(exp -5) Bit Error Rate (BER) with an acceptable level of degradation in the presence of RFI. This paper also shows that the TCM codes with or without the Reed-Solomon outer code do not perform well in the presence of self-interference. In fact, the uncoded QPSK signal performs better than the TCM coded signal in the self-interference situation considered in this analysis. Finally, this paper shows that the E(sub b)/N(sub 0) degradation due to TDRSS hardware distortions is approximately 1.3 dB with a TCM coded signal or a rate 1/2 convolutionally coded QPSK signal and is 3.2 dB with an uncoded QPSK signal.

  20. Three-dimensional convection in horizontal cylinders - Numerical solutions and comparison with experimental and analytical results

    NASA Technical Reports Server (NTRS)

    Smutek, C.; Bontoux, P.; Roux, B.; Schiroky, G. H.; Hurford, A. C.

    1985-01-01

    The results of a three-dimensional numerical simulation of Boussinesq free convection in a horizontal differentially heated cylinder are presented. The computation was based on a Samarskii-Andreyev scheme (described by Leong, 1981) and a false-transient advancement in time, with vorticity, velocity, and temperature as dependent variables. Solutions for velocity and temperature distributions were obtained for Rayleigh numbers (based on the radius) Ra = 74-18,700, thus covering the core- and boundary-layer-driven regimes. Numerical solutions are compared with asymptotic analytical solutions and experimental data. The numerical results well represent the complex three-dimensional flows found experimentally.

  1. On the application of ENO scheme with subcell resolution to conservation laws with stiff source terms

    NASA Technical Reports Server (NTRS)

    Chang, Shih-Hung

    1991-01-01

    Two approaches are used to extend the essentially non-oscillatory (ENO) schemes to treat conservation laws with stiff source terms. One approach is the application of the Strang time-splitting method. Here the basic ENO scheme and the Harten modification using subcell resolution (SR), ENO/SR scheme, are extended this way. The other approach is a direct method and a modification of the ENO/SR. Here the technique of ENO reconstruction with subcell resolution is used to locate the discontinuity within a cell and the time evolution is then accomplished by solving the differential equation along characteristics locally and advancing in the characteristic direction. This scheme is denoted ENO/SRCD (subcell resolution - characteristic direction). All the schemes are tested on the equation of LeVeque and Yee (NASA-TM-100075, 1988) modeling reacting flow problems. Numerical results show that these schemes handle this intriguing model problem very well, especially with ENO/SRCD which produces perfect resolution at the discontinuity.

  2. Weak second-order splitting schemes for Lagrangian Monte Carlo particle methods for the composition PDF/FDF transport equations

    SciTech Connect

    Wang Haifeng Popov, Pavel P.; Pope, Stephen B.

    2010-03-01

    We study a class of methods for the numerical solution of the system of stochastic differential equations (SDEs) that arises in the modeling of turbulent combustion, specifically in the Monte Carlo particle method for the solution of the model equations for the composition probability density function (PDF) and the filtered density function (FDF). This system consists of an SDE for particle position and a random differential equation for particle composition. The numerical methods considered advance the solution in time with (weak) second-order accuracy with respect to the time step size. The four primary contributions of the paper are: (i) establishing that the coefficients in the particle equations can be frozen at the mid-time (while preserving second-order accuracy), (ii) examining the performance of three existing schemes for integrating the SDEs, (iii) developing and evaluating different splitting schemes (which treat particle motion, reaction and mixing on different sub-steps), and (iv) developing the method of manufactured solutions (MMS) to assess the convergence of Monte Carlo particle methods. Tests using MMS confirm the second-order accuracy of the schemes. In general, the use of frozen coefficients reduces the numerical errors. Otherwise no significant differences are observed in the performance of the different SDE schemes and splitting schemes.

  3. Assessment of Planetary Boundary-Layer Schemes in the Weather Research and Forecasting Mesoscale Model Using MATERHORN Field Data

    NASA Astrophysics Data System (ADS)

    Dimitrova, Reneta; Silver, Zachariah; Zsedrovits, Tamas; Hocut, Christopher M.; Leo, Laura S.; Di Sabatino, Silvana; Fernando, Harindra J. S.

    2016-06-01

    The study was aimed at understanding the deficiencies of numerical mesoscale models by comparing predictions with a new high-resolution meteorological dataset collected during the Mountain Terrain Atmospheric Modelling and Observations (MATERHORN) Program. The simulations focussed on the stable boundary layer (SBL), the predictions of which continue to be challenging. High resolution numerical simulations (0.5-km horizontal grid size) were conducted to investigate the efficacy of six planetary boundary-layer (PBL) parametrizations available in the advanced research version of the Weather Research and Forecasting model. One of the commonly used PBL schemes was modified to include eddy diffusivities that account for enhanced momentum transport compared to heat transport in the SBL, representing internal wave dynamics. All of the tested PBL schemes, including the modified scheme, showed a positive surface temperature bias. None of the PBL schemes was found to be superior in predicting the vertical wind and temperature profiles over the lowest 500 m, however two of the schemes appeared superior in capturing the lower PBL structure. The lowest model layers appear to have a significant impact on the predictions aloft. Regions of sporadic flow interactions delineated by the MATERHORN observations were poorly predicted, given such interactions are not represented in typical PBL schemes.

  4. Experimenting with a Convective Parameterization Scheme Suitable for High-Resolution Mesoscale Models in Tropical Cyclone Simulations

    NASA Astrophysics Data System (ADS)

    Grell, Evelyn; Grell, Georg; Bao, Jian-Wen

    2013-04-01

    Results from numerical experiments using high-resolution mesoscale models have presented evidence that the use of the explicit microphysics scheme only at grid spacing from few hundred meters to a few kilometers is often not sufficient to neutralize moist instability within the grid box. A consequence of such a problem is that artificial grid-point storms may occur, which in tropical cyclone simulations can lead to erroneous representation of tropical cyclone development. The use of conventional sub-grid convection parameterization schemes to alleviate artificial grid-point storms is not appropriate in this situation since these schemes assume that the updraft area is much smaller than the model grid spacing and this assumption becomes invalid when the grid size is a few kilometers or smaller. A sub-grid convection scheme suitable for high-resolution mesoscale models has been developed by Grell and Freitas (2013) to remove the aforementioned assumption used in conventional sub-grid convection parameterization schemes. This scheme can be used for grid spacing equal to or smaller than a few kilometers to help sufficiently remove moist instability for the entire grid point. This scheme behaves similarly to conventional schemes when the updraft area is much smaller than the grids size. As the updraft area in a grid box approaches the grid size, the parameterized sub-grid convection gradually diminishes. This presentation highlights major results from experimenting with this newly developed scheme in the Advanced Research WRF (ARW) model with an idealized tropical cyclone intensification case. We will demonstrate the scheme converges (i.e., the parameterized convection diminishes as the updraft area in a grid box approaches the grid size) using the change of the intensity of parameterized sub-grid convection with the decrease in grid size. We will also discuss the issues and challenges in refining this scheme for its application in operational models.

  5. A comparison of ENO and TVD schemes

    NASA Technical Reports Server (NTRS)

    Chang, Shih-Hung; Liou, Meng-Sing

    1988-01-01

    The numerical performance of a second-order upwind-based TVD scheme is compared with that of a uniform second-order ENO scheme on shock capturing. The cases considered include flows with Mach numbers of 2.9, 5.0, and 10.0. For cases with Mach numbers of 5.0 and 10.0, the computed ENO results are inferior to the corresponding TVD results.

  6. Dynamic Restarting Schemes for Eigenvalue Problems

    SciTech Connect

    Wu, Kesheng; Simon, Horst D.

    1999-03-10

    In studies of restarted Davidson method, a dynamic thick-restart scheme was found to be excellent in improving the overall effectiveness of the eigen value method. This paper extends the study of the dynamic thick-restart scheme to the Lanczos method for symmetric eigen value problems and systematically explore a range of heuristics and strategies. We conduct a series of numerical tests to determine their relative strength and weakness on a class of electronic structure calculation problems.

  7. A diagonally inverted LU implicit multigrid scheme

    NASA Technical Reports Server (NTRS)

    Yokota, Jeffrey W.; Caughey, David A.; Chima, Rodrick V.

    1988-01-01

    A new Diagonally Inverted LU Implicit scheme is developed within the framework of the multigrid method for the 3-D unsteady Euler equations. The matrix systems that are to be inverted in the LU scheme are treated by local diagonalizing transformations that decouple them into systems of scalar equations. Unlike the Diagonalized ADI method, the time accuracy of the LU scheme is not reduced since the diagonalization procedure does not destroy time conservation. Even more importantly, this diagonalization significantly reduces the computational effort required to solve the LU approximation and therefore transforms it into a more efficient method of numerically solving the 3-D Euler equations.

  8. Renormalization schemes: Where do we stand

    SciTech Connect

    Ward, B.F.L.

    1989-07-01

    We consider the status of the current approaches to the application of the renormalization program to the standard SU/sub 2L/ /times/ U/sub 1/ theory from the standpoint of the interplay of the scheme chosen for such an application and the attendant high-precision tests of the respective loop effects. We thus review the available schemes and discuss their theoretical relationships. We also show how such schemes stand in numerical relation to one another in the context of high-precision Z/sup 0/ physics, as an illustration. 15 refs., 2 figs., 2 tabs.

  9. TVD finite difference schemes and artificial viscosity

    NASA Technical Reports Server (NTRS)

    Davis, S. F.

    1984-01-01

    The total variation diminishing (TVD) finite difference scheme can be interpreted as a Lax-Wendroff scheme plus an upwind weighted artificial dissipation term. If a particular flux limiter is chosen and the requirement for upwind weighting is removed, an artificial dissipation term which is based on the theory of TVD schemes is obtained which does not contain any problem dependent parameters and which can be added to existing MacCormack method codes. Numerical experiments to examine the performance of this new method are discussed.

  10. Comprehensive numerical methodology for direct numerical simulations of compressible Rayleigh-Taylor instability

    NASA Astrophysics Data System (ADS)

    Reckinger, Scott J.; Livescu, Daniel; Vasilyev, Oleg V.

    2016-05-01

    An investigation of compressible Rayleigh-Taylor instability (RTI) using Direct Numerical Simulations (DNS) requires efficient numerical methods, advanced boundary conditions, and consistent initialization in order to capture the wide range of scales and vortex dynamics present in the system, while reducing the computational impact associated with acoustic wave generation and the subsequent interaction with the flow. An advanced computational framework is presented that handles the challenges introduced by considering the compressive nature of RTI systems, which include sharp interfacial density gradients on strongly stratified background states, acoustic wave generation and removal at computational boundaries, and stratification dependent vorticity production. The foundation of the numerical methodology described here is the wavelet-based grid adaptivity of the Parallel Adaptive Wavelet Collocation Method (PAWCM) that maintains symmetry in single-mode RTI systems to extreme late-times. PAWCM is combined with a consistent initialization, which reduces the generation of acoustic disturbances, and effective boundary treatments, which prevent acoustic reflections. A dynamic time integration scheme that can handle highly nonlinear and potentially stiff systems, such as compressible RTI, completes the computational framework. The numerical methodology is used to simulate two-dimensional single-mode RTI to extreme late-times for a wide range of flow compressibility and variable density effects. The results show that flow compressibility acts to reduce the growth of RTI for low Atwood numbers, as predicted from linear stability analysis.

  11. Numerical solution of the full potential equation using a chimera grid approach

    NASA Technical Reports Server (NTRS)

    Holst, Terry L.

    1995-01-01

    A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

  12. Edward A. Bouchet Award Talk: NSFD Schemes: Genesis, Methodology and Applications

    NASA Astrophysics Data System (ADS)

    Mickens, Ronald

    2008-04-01

    Nonstandard finite difference (NSFD) schemes are based on a generalization of the usual discrete representations of first derivatives and the use of nonlocal discrete replacements for both linear and nonlinear functions of dependent variables. These numerical integration techniques for differential equations had their genesis in a 1989 publication.^1) In the past decade much progress has occurred on the general methodology of these techniques and the range of phenomena to which these schemes have been applied.^2) This talk will give a broad introduction to NSFD schemes and show that the principle of dynamic consistency (DC)^3) can be used to place great restrictions on the constructions of such discretizations for both ODE's and PDE's. The essential features of the NSFD methodology will be illustrated by means of several ``toy" models.^4) ^1)R. E. Mickens, Numerical Methods for PDE's, 5 (1989), 313--325. ^2)K. C. Patidar, Journal of Difference Equations and Applications 11 (2005), 735--758. ^3)R. E. Mickens, Journal of Difference Equations and Applications 11 (2005), 645--653. ^4)R. E. Mickens (editor), Advances in the Applications of Nonstandard Finite Difference Schemes. World Scientific, Singapore, 2006.

  13. Numerical computation of transonic flow governed by the full-potential equation

    NASA Technical Reports Server (NTRS)

    Holst, T. L.

    1983-01-01

    Numerical solution techniques for solving transonic flow fields governed by the full potential equation are discussed. In a general sense relaxation schemes suitable for the numerical solution of elliptic partial differential equations are presented and discussed with emphasis on transonic flow applications. The presentation can be divided into two general categories: An introductory treatment of the basic concepts associated with the numerical solution of elliptic partial differential equations and a more advanced treatment of current procedures used to solve the full potential equation for transonic flow fields. The introductory material is presented for completeness and includes a brief introduction (Chapter 1), governing equations (Chapter 2), classical relaxation schemes (Chapter 3), and early concepts regarding transonic full potential equation algorithms (Chapter 4).

  14. Nonlinear wave propagation using three different finite difference schemes (category 2 application)

    NASA Technical Reports Server (NTRS)

    Pope, D. Stuart; Hardin, J. C.

    1995-01-01

    Three common finite difference schemes are used to examine the computation of one-dimensional nonlinear wave propagation. The schemes are studied for their responses to numerical parameters such as time step selection, boundary condition implementation, and discretization of governing equations. The performance of the schemes is compared and various numerical phenomena peculiar to each is discussed.

  15. Sparse Parallel MRI Based on Accelerated Operator Splitting Schemes

    PubMed Central

    Xie, Weisi; Su, Zhenghang

    2016-01-01

    Recently, the sparsity which is implicit in MR images has been successfully exploited for fast MR imaging with incomplete acquisitions. In this paper, two novel algorithms are proposed to solve the sparse parallel MR imaging problem, which consists of l1 regularization and fidelity terms. The two algorithms combine forward-backward operator splitting and Barzilai-Borwein schemes. Theoretically, the presented algorithms overcome the nondifferentiable property in l1 regularization term. Meanwhile, they are able to treat a general matrix operator that may not be diagonalized by fast Fourier transform and to ensure that a well-conditioned optimization system of equations is simply solved. In addition, we build connections between the proposed algorithms and the state-of-the-art existing methods and prove their convergence with a constant stepsize in Appendix. Numerical results and comparisons with the advanced methods demonstrate the efficiency of proposed algorithms. PMID:27746824

  16. A compatible Lagrangian hydrodynamic scheme for multicomponent flows with mixing

    SciTech Connect

    Chang, Chong; Stagg, Alan K

    2012-01-01

    We present a Lagrangian time integration scheme and compatible discretization for total energy conservation in multicomponent mixing simulations. Mixing behavior results from relative motion between species. Species velocities are determined by solving species momentum equations in a Lagrangian manner. Included in the species momentum equations are species artificial viscosity (since each species can undergo compression) and inter-species momentum exchange. Thermal energy for each species is also solved, including compression work and thermal dissipation caused by momentum exchange. The present procedure is applicable to mixing of an arbitrary number of species that may not be in pressure or temperature equilibrium. A traditional staggered stencil has been adopted to describe motion of each species. The computational mesh for the mixture is constructed in a Lagrangian manner using the mass-averaged mixture velocity. Species momentum equations are solved at the vertices of the mesh, and temporary species meshes are constructed and advanced in time using the resulting species velocities. Following the Lagrangian step, species quantities are advected (mapped) from the species meshes to the mixture mesh. Momentum exchange between species introduces work that must be included in an energy-conserving discretization scheme. This work has to be transformed to dissipation in order to effect a net change in species thermal energy. The dissipation between interacting species pairs is obtained by combining the momentum exchange work. The dissipation is then distributed to the species involved using a distribution factor based on species specific heats. The resulting compatible discretization scheme provides total energy conservation of the whole mixture. In addition, the numerical scheme includes conservative local energy exchange between species in mixture. Due to the relatively large species interaction coefficients, both the species momenta and energies are calculated

  17. An authentication scheme for secure access to healthcare services.

    PubMed

    Khan, Muhammad Khurram; Kumari, Saru

    2013-08-01

    Last few decades have witnessed boom in the development of information and communication technologies. Health-sector has also been benefitted with this advancement. To ensure secure access to healthcare services some user authentication mechanisms have been proposed. In 2012, Wei et al. proposed a user authentication scheme for telecare medical information system (TMIS). Recently, Zhu pointed out offline password guessing attack on Wei et al.'s scheme and proposed an improved scheme. In this article, we analyze both of these schemes for their effectiveness in TMIS. We show that Wei et al.'s scheme and its improvement proposed by Zhu fail to achieve some important characteristics necessary for secure user authentication. We find that security problems of Wei et al.'s scheme stick with Zhu's scheme; like undetectable online password guessing attack, inefficacy of password change phase, traceability of user's stolen/lost smart card and denial-of-service threat. We also identify that Wei et al.'s scheme lacks forward secrecy and Zhu's scheme lacks session key between user and healthcare server. We therefore propose an authentication scheme for TMIS with forward secrecy which preserves the confidentiality of air messages even if master secret key of healthcare server is compromised. Our scheme retains advantages of Wei et al.'s scheme and Zhu's scheme, and offers additional security. The security analysis and comparison results show the enhanced suitability of our scheme for TMIS.

  18. An authentication scheme for secure access to healthcare services.

    PubMed

    Khan, Muhammad Khurram; Kumari, Saru

    2013-08-01

    Last few decades have witnessed boom in the development of information and communication technologies. Health-sector has also been benefitted with this advancement. To ensure secure access to healthcare services some user authentication mechanisms have been proposed. In 2012, Wei et al. proposed a user authentication scheme for telecare medical information system (TMIS). Recently, Zhu pointed out offline password guessing attack on Wei et al.'s scheme and proposed an improved scheme. In this article, we analyze both of these schemes for their effectiveness in TMIS. We show that Wei et al.'s scheme and its improvement proposed by Zhu fail to achieve some important characteristics necessary for secure user authentication. We find that security problems of Wei et al.'s scheme stick with Zhu's scheme; like undetectable online password guessing attack, inefficacy of password change phase, traceability of user's stolen/lost smart card and denial-of-service threat. We also identify that Wei et al.'s scheme lacks forward secrecy and Zhu's scheme lacks session key between user and healthcare server. We therefore propose an authentication scheme for TMIS with forward secrecy which preserves the confidentiality of air messages even if master secret key of healthcare server is compromised. Our scheme retains advantages of Wei et al.'s scheme and Zhu's scheme, and offers additional security. The security analysis and comparison results show the enhanced suitability of our scheme for TMIS. PMID:23828650

  19. Hybrid undulator numerical optimization

    SciTech Connect

    Hairetdinov, A.H.; Zukov, A.A.

    1995-12-31

    3D properties of the hybrid undulator scheme arc studied numerically using PANDIRA code. It is shown that there exist two well defined sets of undulator parameters which provide either maximum on-axis field amplitude or minimal higher harmonics amplitude of the basic undulator field. Thus the alternative between higher field amplitude or pure sinusoidal field exists. The behavior of the undulator field amplitude and harmonics structure for a large set of (undulator gap)/(undulator wavelength) values is demonstrated.

  20. Numerical simulations in combustion

    NASA Technical Reports Server (NTRS)

    Chung, T. J.

    1989-01-01

    This paper reviews numerical simulations in reacting flows in general and combustion phenomena in particular. It is shown that use of implicit schemes and/or adaptive mesh strategies can improve convergence, stability, and accuracy of the solution. Difficulties increase as turbulence and multidimensions are considered, particularly when finite-rate chemistry governs the given combustion problem. Particular attention is given to the areas of solid-propellant combustion dynamics, turbulent diffusion flames, and spray droplet vaporization.

  1. On the monotonicity of multidimensional finite difference schemes

    NASA Astrophysics Data System (ADS)

    Kovyrkina, O.; Ostapenko, V.

    2016-10-01

    The classical concept of monotonicity, introduced by Godunov for linear one-dimensional difference schemes, is extended to multidimensional case. Necessary and sufficient conditions of monotonicity are obtained for linear multidimensional difference schemes of first order. The constraints on the numerical viscosity are given that ensure the monotonicity of a difference scheme in the multidimensional case. It is proposed a modification of the second order multidimensional CABARET scheme that preserves the monotonicity of one-dimensional discrete solutions and, as a result, ensures higher smoothness in the computation of multidimensional discontinuous solutions. The results of two-dimensional test computations illustrating the advantages of the modified CABARET scheme are presented.

  2. Upwind and symmetric shock-capturing schemes

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1987-01-01

    The development of numerical methods for hyperbolic conservation laws has been a rapidly growing area for the last ten years. Many of the fundamental concepts and state-of-the-art developments can only be found in meeting proceedings or internal reports. This review paper attempts to give an overview and a unified formulation of a class of shock-capturing methods. Special emphasis is on the construction of the basic nonlinear scalar second-order schemes and the methods of extending these nonlinear scalar schemes to nonlinear systems via the extact Riemann solver, approximate Riemann solvers, and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows is discussed. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas dynamics problems.

  3. A nonconservative scheme for isentropic gas dynamics

    SciTech Connect

    Chen, Gui-Qiang |; Liu, Jian-Guo

    1994-05-01

    In this paper, we construct a second-order nonconservative for the system of isentropic gas dynamics to capture the physical invariant regions for preventing negative density, to treat the vacuum singularity, and to control the local entropy from dramatically increasing near shock waves. The main difference in the construction of the scheme discussed here is that we use piecewise linear functions to approximate the Riemann invariants w and z instead of the physical variables {rho} and m. Our scheme is a natural extension of the schemes for scalar conservation laws and it can be numerical implemented easily because the system is diagonalized in this coordinate system. Another advantage of using Riemann invariants is that the Hessian matrix of any weak entropy has no singularity in the Riemann invariant plane w-z, whereas the Hessian matrices of the weak entropies have singularity at the vacuum points in the physical plane p-m. We prove that this scheme converges to an entropy solution for the Cauchy problem with L{sup {infinity}} initial data. By convergence here we mean that there is a subsequent convergence to a generalized solution satisfying the entrophy condition. As long as the entropy solution is unique, the whole sequence converges to a physical solution. This shows that this kind of scheme is quite reliable from theoretical view of point. In addition to being interested in the scheme itself, we wish to provide an approach to rigorously analyze nonconservative finite difference schemes.

  4. A Spatial Discretization Scheme for Solving the Transport Equation on Unstructured Grids of Polyhedra

    SciTech Connect

    Thompson, K.G.

    2000-11-01

    In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness in a

  5. Numerical simulation of conservation laws

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung; To, Wai-Ming

    1992-01-01

    A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

  6. An Improved Bulk Microphysical Scheme for Studying Precipitation Processes: Comparisons with Other Schemes

    NASA Technical Reports Server (NTRS)

    Tao, W. K.; Shi, J. J.; Lang, S.; Chen, S.; Hong, S-Y.; Peters-Lidard, C.

    2007-01-01

    Cloud microphysical processes play an important role in non-hydrostatic high-resolution simulations. Over the past decade both research and operational numerical weather prediction models have started using more complex cloud microphysical schemes that were originally developed for high-resolution cloud-resolving models. An improved bulk microphysical parameterization (adopted from the Goddard microphysics schemes) has recently implemented into the Weather Research and Forecasting (WRF) model. This bulk microphysical scheme has three different options --- 2ICE (cloud ice & snow), 3ICE-graupel (cloud ice, snow & graupel) and 3ICE-hail (cloud ice, snow & hail). High-resolution model simulations are conducted to examine the impact of microphysical schemes on two different weather events (a midlatitude linear convective system and an Atlantic hurricane). In addition, this bulk microphysical parameterization is compared with WIRF's three other bulk microphysical schemes.

  7. A high-order WENO-based staggered Godunov-type scheme with constrained transport for force-free electrodynamics

    NASA Astrophysics Data System (ADS)

    Yu, Cong

    2011-03-01

    The force-free (or low inertia) limit of magnetohydrodynamics (MHD) can be applied to many astrophysical objects, including black holes, neutron stars and accretion discs, where the electromagnetic field is so strong that the inertia and pressure of the plasma can be ignored. This is difficult to achieve with the standard MHD numerical methods because they still have to deal with plasma inertial terms even when these terms are much smaller than the electromagnetic terms. Under the force-free approximation, the plasma dynamics is entirely determined by the magnetic field. The plasma provides the currents and charge densities required by the dynamics of electromagnetic fields, but these currents carry no inertia. We present a high-order Godunov scheme to study such force-free electrodynamics. We have implemented weighted essentially non-oscillatory (WENO) spatial interpolations in our scheme. An exact Riemann solver is implemented, which requires spectral decomposition into characteristic waves. We advance the magnetic field with the constrained transport (CT) scheme to preserve the divergence-free condition to machine round-off error. We apply the third-order total variation diminishing (TVD) Runge-Kutta scheme for the temporal integration. The mapping from face-centred variables to volume-centred variables is carefully considered. Extensive testing are performed to demonstrate the ability of our scheme to address force-free electrodynamics correctly. We finally apply the scheme to study relativistic magnetically dominated tearing instabilities and neutron star magnetospheres.

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

  9. The science of and advanced technology for cost-effective manufacture of high precision engineering products. Volume 4. Thermal effects on the accuracy of numerically controlled machine tool

    NASA Astrophysics Data System (ADS)

    Venugopal, R.; Barash, M. M.; Liu, C. R.

    1985-10-01

    Thermal effects on the accuracy of numerically controlled machine tools are specially important in the context of unmanned manufacture or under conditions of precision metal cutting. Removal of the operator from the direct control of the metal cutting process has created problems in terms of maintaining accuracy. The objective of this research is to study thermal effects on the accuracy of numerically controlled machine tools. The initial part of the research report is concerned with the analysis of a hypothetical machine. The thermal characteristics of this machine are studied. Numerical methods for evaluating the errors exhibited by the slides of the machine are proposed and the possibility of predicting thermally induced errors by the use of regression equations is investigated. A method for computing the workspace error is also presented. The final part is concerned with the actual measurement of errors on a modern CNC machining center. Thermal influences on the errors is the main objective of the experimental work. Thermal influences on the errors of machine tools are predictable. Techniques for determining thermal effects on machine tools at a design stage are also presented. ; Error models and prediction; Metrology; Automation.

  10. Numerical modeling of late Glacial Laurentide advance of ice across Hudson Strait: Insights into terrestrial and marine geology, mass balance, and calving flux

    USGS Publications Warehouse

    Pfeffer, W.T.; Dyurgerov, M.; Kaplan, M.; Dwyer, J.; Sassolas, C.; Jennings, A.; Raup, B.; Manley, W.

    1997-01-01

    A time-dependent finite element model was used to reconstruct the advance of ice from a late Glacial dome on northern Quebec/Labrador across Hudson Strait to Meta Incognita Peninsula (Baffin Island) and subsequently to the 9.9-9.6 ka 14C Gold Cove position on Hall Peninsula. Terrestrial geological and geophysical information from Quebec and Labrador was used to constrain initial and boundary conditions, and the model results are compared with terrestrial geological information from Baffin Island and considered in the context of the marine event DC-0 and the Younger Dryas cooling. We conclude that advance across Hudson Strait from Ungava Bay to Baffin Island is possible using realistic glacier physics under a variety of reasonable boundary conditions. Production of ice flux from a dome centered on northeastern Quebec and Labrador sufficient to deliver geologically inferred ice thickness at Gold Cove (Hall Peninsula) appears to require extensive penetration of sliding south from Ungava Bay. The discharge of ice into the ocean associated with advance and retreat across Hudson Strait does not peak at a time coincident with the start of the Younger Dryas and is less than minimum values proposed to influence North Atlantic thermohaline circulation; nevertheless, a significant fraction of freshwater input to the North Atlantic may have been provided abruptly and at a critical time by this event.

  11. On the novel chaotic secure communication scheme design

    NASA Astrophysics Data System (ADS)

    Wang, B.; Zhong, S. M.; Dong, X. C.

    2016-10-01

    In this paper, the problem on the chaotic secure communication is discussed. First a new dual channel transmission mechanism is presented and used in secure communication scheme design, then the channel-switching techniques are adopted to further improve the security of information transmission. Finally some typical numerical simulations are carried out to demonstrate the effectiveness of the proposed secure communication scheme.

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

    SciTech Connect

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

    2001-11-26

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

  13. On the dynamics of some grid adaption schemes

    NASA Technical Reports Server (NTRS)

    Sweby, Peter K.; Yee, Helen C.

    1994-01-01

    The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.

  14. Tabled Execution in Scheme

    SciTech Connect

    Willcock, J J; Lumsdaine, A; Quinlan, D J

    2008-08-19

    Tabled execution is a generalization of memorization developed by the logic programming community. It not only saves results from tabled predicates, but also stores the set of currently active calls to them; tabled execution can thus provide meaningful semantics for programs that seemingly contain infinite recursions with the same arguments. In logic programming, tabled execution is used for many purposes, both for improving the efficiency of programs, and making tasks simpler and more direct to express than with normal logic programs. However, tabled execution is only infrequently applied in mainstream functional languages such as Scheme. We demonstrate an elegant implementation of tabled execution in Scheme, using a mix of continuation-passing style and mutable data. We also show the use of tabled execution in Scheme for a problem in formal language and automata theory, demonstrating that tabled execution can be a valuable tool for Scheme users.

  15. The NEC Link Scheme

    ERIC Educational Resources Information Center

    Noakes, Peter

    1976-01-01

    Describes the operation of the National Electronics Council (NEC) Link Scheme for schools in Great Britain. The service is intended to provide technical assistance, information concerning surplus equipment, and guest speakers for school aspiring professional electronic counsel. (CP)

  16. Advanced Tsunami Numerical Simulations and Energy Considerations by use of 3D-2D Coupled Models: The October 11, 1918, Mona Passage Tsunami

    NASA Astrophysics Data System (ADS)

    López-Venegas, Alberto M.; Horrillo, Juan; Pampell-Manis, Alyssa; Huérfano, Victor; Mercado, Aurelio

    2015-06-01

    The most recent tsunami observed along the coast of the island of Puerto Rico occurred on October 11, 1918, after a magnitude 7.2 earthquake in the Mona Passage. The earthquake was responsible for initiating a tsunami that mostly affected the northwestern coast of the island. Runup values from a post-tsunami survey indicated the waves reached up to 6 m. A controversy regarding the source of the tsunami has resulted in several numerical simulations involving either fault rupture or a submarine landslide as the most probable cause of the tsunami. Here we follow up on previous simulations of the tsunami from a submarine landslide source off the western coast of Puerto Rico as initiated by the earthquake. Improvements on our previous study include: (1) higher-resolution bathymetry; (2) a 3D-2D coupled numerical model specifically developed for the tsunami; (3) use of the non-hydrostatic numerical model NEOWAVE (non-hydrostatic evolution of ocean WAVE) featuring two-way nesting capabilities; and (4) comprehensive energy analysis to determine the time of full tsunami wave development. The three-dimensional Navier-Stokes model tsunami solution using the Navier-Stokes algorithm with multiple interfaces for two fluids (water and landslide) was used to determine the initial wave characteristic generated by the submarine landslide. Use of NEOWAVE enabled us to solve for coastal inundation, wave propagation, and detailed runup. Our results were in agreement with previous work in which a submarine landslide is favored as the most probable source of the tsunami, and improvement in the resolution of the bathymetry yielded inundation of the coastal areas that compare well with values from a post-tsunami survey. Our unique energy analysis indicates that most of the wave energy is isolated in the wave generation region, particularly at depths near the landslide, and once the initial wave propagates from the generation region its energy begins to stabilize.

  17. Highly accurate adaptive finite element schemes for nonlinear hyperbolic problems

    NASA Astrophysics Data System (ADS)

    Oden, J. T.

    1992-08-01

    This document is a final report of research activities supported under General Contract DAAL03-89-K-0120 between the Army Research Office and the University of Texas at Austin from July 1, 1989 through June 30, 1992. The project supported several Ph.D. students over the contract period, two of which are scheduled to complete dissertations during the 1992-93 academic year. Research results produced during the course of this effort led to 6 journal articles, 5 research reports, 4 conference papers and presentations, 1 book chapter, and two dissertations (nearing completion). It is felt that several significant advances were made during the course of this project that should have an impact on the field of numerical analysis of wave phenomena. These include the development of high-order, adaptive, hp-finite element methods for elastodynamic calculations and high-order schemes for linear and nonlinear hyperbolic systems. Also, a theory of multi-stage Taylor-Galerkin schemes was developed and implemented in the analysis of several wave propagation problems, and was configured within a general hp-adaptive strategy for these types of problems. Further details on research results and on areas requiring additional study are given in the Appendix.

  18. Total Variation Diminishing (TVD) schemes of uniform accuracy

    NASA Technical Reports Server (NTRS)

    Hartwich, PETER-M.; Hsu, Chung-Hao; Liu, C. H.

    1988-01-01

    Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.

  19. Matching multistage schemes to viscous flow

    NASA Astrophysics Data System (ADS)

    Kleb, William Leonard

    A method to accelerate convergence to steady state by explicit time-marching schemes for the compressible Navier-Stokes equations is presented. The combination of cell-Reynolds-number-based multistage time stepping and local preconditioning makes solving steady-state viscous flow problems competitive with the convergence rates typically associated with implicit methods, without the associated memory penalty. Initially, various methods are investigated to extend the range of multistage schemes to diffusion-dominated cases. It is determined that the Chebyshev polynomials are well suited to serve as amplification factors for these schemes; however, creating a method that can bridge the continuum from convection-dominated to diffusion-dominated regimes proves troublesome, until the Manteuffel family of polynomials is uncovered. This transformation provides a smooth transition between the two extremes; and armed with this information, sets of multistage coefficients are created for a given spatial discretization as a function of cell Reynolds number according to various design criteria. As part of this process, a precise definition for the numerical time step is hammered out, something which up to this time, has been set via algebraic arguments only. Next are numerical tests of these sets of variable multistage coefficients. To isolate the effects of the variable multistage coefficients, the test case chosen is very simple: circular advection-diffusion. The numerical results support the analytical analysis by demonstrating an order of magnitude improvement in convergence rate for single-grid relaxation and a factor of three for multigrid relaxation. Building upon the success of the scalar case, preconditioning is applied to make the Navier-Stokes system of equations behave more nearly as a single scalar equation. Then, by applying the variable multistage coefficient scheme to a typical boundary-layer flow problem, the results affirm the benefits of local preconditioning

  20. Engineering images designed by fractal subdivision scheme.

    PubMed

    Mustafa, Ghulam; Bari, Mehwish; Jamil, Saba

    2016-01-01

    This paper is concerned with the modeling of engineering images by the fractal properties of 6-point binary interpolating scheme. Association between the fractal behavior of the limit curve/surface and the parameter is obtained. The relationship between the subdivision parameter and the fractal dimension of the limit fractal curve of subdivision fractal is also presented. Numerical examples and visual demonstrations show that 6-point scheme is good choice for the generation of fractals for the modeling of fractal antennas, bearings, garari's and rock etc. PMID:27652066

  1. A low-order coupled chemistry meteorology model for testing online and offline data assimilation schemes

    NASA Astrophysics Data System (ADS)

    Haussaire, J.-M.; Bocquet, M.

    2015-08-01

    Bocquet and Sakov (2013) have introduced a low-order model based on the coupling of the chaotic Lorenz-95 model which simulates winds along a mid-latitude circle, with the transport of a tracer species advected by this zonal wind field. This model, named L95-T, can serve as a playground for testing data assimilation schemes with an online model. Here, the tracer part of the model is extended to a reduced photochemistry module. This coupled chemistry meteorology model (CCMM), the L95-GRS model, mimics continental and transcontinental transport and the photochemistry of ozone, volatile organic compounds and nitrogen oxides. Its numerical implementation is described. The model is shown to reproduce the major physical and chemical processes being considered. L95-T and L95-GRS are specifically designed and useful for testing advanced data assimilation schemes, such as the iterative ensemble Kalman smoother (IEnKS) which combines the best of ensemble and variational methods. These models provide useful insights prior to the implementation of data assimilation methods on larger models. We illustrate their use with data assimilation schemes on preliminary, yet instructive numerical experiments. In particular, online and offline data assimilation strategies can be conveniently tested and discussed with this low-order CCMM. The impact of observed chemical species concentrations on the wind field can be quantitatively estimated. The impacts of the wind chaotic dynamics and of the chemical species non-chaotic but highly nonlinear dynamics on the data assimilation strategies are illustrated.

  2. Numerical simulation of small perturbation transonic flows

    NASA Technical Reports Server (NTRS)

    Seebass, A. R.; Yu, N. J.

    1976-01-01

    The results of a systematic study of small perturbation transonic flows are presented. Both the flow over thin airfoils and the flow over wedges were investigated. Various numerical schemes were employed in the study. The prime goal of the research was to determine the efficiency of various numerical procedures by accurately evaluating the wave drag, both by computing the pressure integral around the body and by integrating the momentum loss across the shock. Numerical errors involved in the computations that affect the accuracy of drag evaluations were analyzed. The factors that effect numerical stability and the rate of convergence of the iterative schemes were also systematically studied.

  3. An Energy Decaying Scheme for Nonlinear Dynamics of Shells

    NASA Technical Reports Server (NTRS)

    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.

  4. Triangle based TVD schemes for hyperbolic conservation laws

    NASA Technical Reports Server (NTRS)

    Durlofsky, Louis J.; Osher, Stanley; Engquist, Bjorn

    1990-01-01

    A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

  5. Improved Boundary Conditions for Cell-centered Difference Schemes

    NASA Technical Reports Server (NTRS)

    VanderWijngaart, Rob F.; Klopfer, Goetz H.; Chancellor, Marisa K. (Technical Monitor)

    1997-01-01

    Cell-centered finite-volume (CCFV) schemes have certain attractive properties for the solution of the equations governing compressible fluid flow. Among others, they provide a natural vehicle for specifying flux conditions at the boundaries of the physical domain. Unfortunately, they lead to slow convergence for numerical programs utilizing them. In this report a method for investigating and improving the convergence of CCFV schemes is presented, which focuses on the effect of the numerical boundary conditions. The key to the method is the computation of the spectral radius of the iteration matrix of the entire demoralized system of equations, not just of the interior point scheme or the boundary conditions.

  6. Numerical solution techniques for unsteady transonic aerodynamics problems

    NASA Technical Reports Server (NTRS)

    Ballhaus, W. F.; Bridgeman, J. O.

    1980-01-01

    Basic concepts of finite difference solution techniques for unsteady transonic flows are presented. The hierarchy of mathematical forumulations that approximate the Navier-Stokes equations are reviewed. The basic concepts involved in constructing numerical algorthms to solve these formulations are given. Semi-implicit and implicit schemes are constructed and analyzed. The discussion focuses primarily on techniques for solving the low frequency transonic small disturbance equation. This is the simplest formulation that contains the essence of inviscid unsteady transonic flow physics. The low frequency formulation is emphasized here because codes based on this theory can be run in minutes of processor time on currently available computers. Furthermore, numerical techniques involved in solving this simple formulation also apply to the more complicated formulations. Extensions to these formulations are briefly described. An indication of the present capability for solving unsteady transonic flows is provided. Important areas of future research for the advancement of computational unsteady transonic aerodynamics are described.

  7. Aerothermal modeling program. Phase 2, element A: Improved numerical methods for turbulent viscous recirculating flows

    NASA Technical Reports Server (NTRS)

    Karki, K. C.; Mongia, H. C.; Patankar, Suhas V.; Runchal, A. K.

    1987-01-01

    The objective of this effort is to develop improved numerical schemes for predicting combustor flow fields. Various candidate numerical schemes were evaluated, and promising schemes were selected for detailed assessment. The criteria for evaluation included accuracy, computational efficiency, stability, and ease of extension to multidimensions. The candidate schemes were assessed against a variety of simple one- and two-dimensional problems. These results led to the selection of the following schemes for further evaluation: flux spline schemes (linear and cubic) and controlled numerical diffusion with internal feedback (CONDIF). The incorporation of the flux spline scheme and direct solution strategy in a computer program for three-dimensional flows is in progress.

  8. A composite scheme for gas dynamics in Lagrangian coordinates

    SciTech Connect

    Shashkov, M.; Wendroff, B.

    1999-04-10

    One cycle of a composite finite difference scheme is defined as several time steps of an oscillatory scheme such as Lax-Wendroff followed by one step of a diffusive scheme such as Lax-Friedrichs. The authors apply this idea to gas dynamics in Lagrangian coordinates. They show numerical results in two dimensions for Noh`s infinite strength shock problem and the Sedov blast wave problem, and for several one-dimensional problems including a Riemann problem with a contact discontinuity. For Noh`s problem the composite scheme produces a better result than that obtained with a more conventional Lagrangian code.

  9. Effect of Prandtl number and computational schemes on the oscillatory natural convection in an enclosure

    SciTech Connect

    Tagawa, Toshio; Ozoe, Hiroyuki

    1996-08-23

    Numerical calculations were carried out for natural convection of low-Prandtl-number fluid. These calculations include the inertial terms that were approximated by six kinds of schemes, i.e., upwind scheme, hybrid scheme, second-order central difference method, Kawamura-Kuwahara scheme, Utopia scheme, and fourth-order central difference method. The average Nusselt number depended significantly on the schemes. The occurrence of oscillatory flow also depended on the schemes for inertial terms. Higher order up-winding approximations for inertial terms appear to be required to calculate natural convection of low-Prandtl-number fluids like liquid metal, even if the Rayleigh number is not large enough.

  10. Numerical Development

    ERIC Educational Resources Information Center

    Siegler, Robert S.; Braithwaite, David W.

    2016-01-01

    In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…

  11. Compact Spreader Schemes

    SciTech Connect

    Placidi, M.; Jung, J. -Y.; Ratti, A.; Sun, C.

    2014-07-25

    This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.

  12. Compact spreader schemes

    NASA Astrophysics Data System (ADS)

    Placidi, M.; Jung, J.-Y.; Ratti, A.; Sun, C.

    2014-12-01

    This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.

  13. Force-controlled absorption in a fully-nonlinear numerical wave tank

    SciTech Connect

    Spinneken, Johannes Christou, Marios; Swan, Chris

    2014-09-01

    An active control methodology for the absorption of water waves in a numerical wave tank is introduced. This methodology is based upon a force-feedback technique which has previously been shown to be very effective in physical wave tanks. Unlike other methods, an a-priori knowledge of the wave conditions in the tank is not required; the absorption controller being designed to automatically respond to a wide range of wave conditions. In comparison to numerical sponge layers, effective wave absorption is achieved on the boundary, thereby minimising the spatial extent of the numerical wave tank. In contrast to the imposition of radiation conditions, the scheme is inherently capable of absorbing irregular waves. Most importantly, simultaneous generation and absorption can be achieved. This is an important advance when considering inclusion of reflective bodies within the numerical wave tank. In designing the absorption controller, an infinite impulse response filter is adopted, thereby eliminating the problem of non-causality in the controller optimisation. Two alternative controllers are considered, both implemented in a fully-nonlinear wave tank based on a multiple-flux boundary element scheme. To simplify the problem under consideration, the present analysis is limited to water waves propagating in a two-dimensional domain. The paper presents an extensive numerical validation which demonstrates the success of the method for a wide range of wave conditions including regular, focused and random waves. The numerical investigation also highlights some of the limitations of the method, particularly in simultaneously generating and absorbing large amplitude or highly-nonlinear waves. The findings of the present numerical study are directly applicable to related fields where optimum absorption is sought; these include physical wavemaking, wave power absorption and a wide range of numerical wave tank schemes.

  14. Campylobacter biotyping scheme of epidemiological value.

    PubMed Central

    Bolton, F J; Holt, A V; Hutchinson, D N

    1984-01-01

    A biotyping scheme has been developed which utilises 12 tests, including growth at 28 degrees C, hippurate hydrolysis, and 10 resistotyping tests. These tests are arranged in groups of three, and by assigning a numerical value to each positive test a four figure code is produced for each strain. The order of the tests is such that campylobacters are both speciated and biotyped . This scheme recognises Campylobacter jejuni, C coli, "C laridis ," C fetus fetus, and C fetus subspecies venerealis. The reproducibility of the biotyping technique and the stability of the biotype code have been determined by testing campylobacter reference strains. The routine application of the scheme has also been evaluated by biotyping 1000 recent campylobacter isolates, and the epidemiological value has been confirmed by testing serotyped isolates from several milk borne outbreaks. PMID:6373839

  15. The Implicit and Explicit alpha-mu Schemes

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung; Himansu, Ananda

    1997-01-01

    Artificial numerical dissipation is an important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The method of space-time conservation element and solution element, currently under development, is a nontraditional numerical method for solving conservation laws. The method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. Explicit solvers for model and fluid dynamic conservation laws have previously been investigated. In this paper, we introduce a new concept in the design of implicit schemes, and use it to construct two highly accurate solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to purely inviscid (convective) equations. The stability and consistency of the schemes are analyzed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme. We also construct an explicit solver

  16. An improved WENO-Z scheme

    NASA Astrophysics Data System (ADS)

    Acker, F.; B. de R. Borges, R.; Costa, B.

    2016-05-01

    In this article, we show that for a WENO scheme to improve the numerical resolution of smooth waves, increasing to some extent the contribution of the substencils where the solution is less smooth is much more important than improving the accuracy at critical points. WENO-Z, for instance, achieved less dissipative results than classical WENO through the use of a high-order global smoothness measurement, τ, which increased the weights of less-smooth substencils. This time, we present a way of further increasing the relevance of less-smooth substencils by adding a new term to the WENO-Z weights that uses information which is already available in its formula. The improved scheme attains much better resolution at the smooth parts of the solution, while keeping the same numerical stability of the original WENO-Z at shocks and discontinuities.

  17. Conservation Properties of Numerical Schemes for the Shallow Water Equations

    NASA Astrophysics Data System (ADS)

    Eldred, Chris; Randall, David

    2014-05-01

    The shallow water equations provide a useful analogue of fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. With regards to conservation properties, there have been two major thrusts of research: Hamiltonian methods (work done by Salmon and Dubois, primarily) and Discrete Exterior Calculus (DEC; Thuburn, Cotter, Ringler, etc.). In particular, recent work done by Thuburn and Cotter (2011) introduced a generalized framework for energy-conservative C-grid discretizations of the rotating shallow water equation using ideas from Discrete Exterior Calculus. The current research elucidates the connections between the Hamiltonian and DEC approaches, and looks at potential enstrophy conservation in addition to energy conservation. Finally, a generalized framework for mimetic total energy and potential enstrophy conserving discretizations of the rotating shallow water equation in vorticity-divergence form (also using the DEC approach) is developed.

  18. High Order Semi-Lagrangian Advection Scheme

    NASA Astrophysics Data System (ADS)

    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).

  19. Splitting based finite volume schemes for ideal MHD equations

    NASA Astrophysics Data System (ADS)

    Fuchs, F. G.; Mishra, S.; Risebro, N. H.

    2009-02-01

    We design finite volume schemes for the equations of ideal magnetohydrodynamics (MHD) and based on splitting these equations into a fluid part and a magnetic induction part. The fluid part leads to an extended Euler system with magnetic forces as source terms. This set of equations are approximated by suitable two- and three-wave HLL solvers. The magnetic part is modeled by the magnetic induction equations which are approximated using stable upwind schemes devised in a recent paper [F. Fuchs, K.H. Karlsen, S. Mishra, N.H. Risebro, Stable upwind schemes for the Magnetic Induction equation. Math. Model. Num. Anal., Available on conservation laws preprint server, submitted for publication, URL: ]. These two sets of schemes can be combined either component by component, or by using an operator splitting procedure to obtain a finite volume scheme for the MHD equations. The resulting schemes are simple to design and implement. These schemes are compared with existing HLL type and Roe type schemes for MHD equations in a series of numerical experiments. These tests reveal that the proposed schemes are robust and have a greater numerical resolution than HLL type solvers, particularly in several space dimensions. In fact, the numerical resolution is comparable to that of the Roe scheme on most test problems with the computational cost being at the level of a HLL type solver. Furthermore, the schemes are remarkably stable even at very fine mesh resolutions and handle the divergence constraint efficiently with low divergence errors.

  20. A 4OEC scheme for the biharmonic steady Navier-Stokes equations in non-rectangular domains

    NASA Astrophysics Data System (ADS)

    Sen, Shuvam; Kalita, Jiten C.

    2015-11-01

    Recently the biharmonic form of the Navier-Stokes (N-S) equations have been solved in various domains by using second order compact discretization. In this paper, we present a fourth order essentially compact (4OEC) finite difference scheme for the steady N-S equations in geometries beyond rectangular. As a further advancement to the earlier formulations on the classical biharmonic equation that were developed for Cartesian coordinate system, this scheme is capable of numerically solving the two-dimensional N-S equations using body fitted coordinate system. Despite the presence of extra derivative terms in the quasi-linear form of the biharmonic equation, our extended formulation continues to maintain its fourth order accuracy on a nine-point compact stencil. A spectral analysis on the scheme reveals its superior resolution properties. The formulation has been tested on fluid flow problems of varied complexities on different geometries which includes flow past an impulsively started circular cylinder and elliptic aerofoil with angles of attack. We present our numerical results and validate them with established numerical and experimental observations available in the literature; excellent comparison is obtained in all the cases.

  1. Check-Digit Schemes.

    ERIC Educational Resources Information Center

    Wheeler, Mary L.

    1994-01-01

    Discusses the study of identification codes and check-digit schemes as a way to show students a practical application of mathematics and introduce them to coding theory. Examples include postal service money orders, parcel tracking numbers, ISBN codes, bank identification numbers, and UPC codes. (MKR)

  2. Advanced midwifery practice or advancing midwifery practice?

    PubMed

    Smith, Rachel; Leap, Nicky; Homer, Caroline

    2010-09-01

    Advanced midwifery practice is a controversial notion in midwifery, particularly at present in Australia. The proposed changes in legislation around access to the publicly funded Medical Benefits Scheme (MBS) and the Pharmaceutical Benefits Scheme (PBS) in 2009-2010 have meant that the issue of advanced midwifery practice has again taken prominence. Linking midwifery access to MBS and PBS to a safety and quality framework that includes an 'advanced midwifery credentialling framework' is particularly challenging. The Haxton and Fahy paper in the December 2009 edition of Women and Birth is timely as it enables a reflection upon these issues and encourages debate and discussion about exactly what is midwifery, what are we educating our students for and is working to the full scope of practice practising at advanced level? This paper seeks to address some of these questions and open up the topic for further debate.

  3. A flexible gridding scheme for reservoir simulation

    SciTech Connect

    Verma, S.

    1995-12-31

    This paper describes a new control volume based finite difference scheme for petroleum reservoir simulation which can be used with unstructured grids. The numerical scheme to model fluid flow is shown to be easily used for Voronoi grids in 2D. It can also be used with certain geometrical limitations for 3D Voronoi grids. The scheme can be used without any significant limitations for triangle or tetrahedron based grids where control volumes are constructed around their vertices. It assumes uniform properties inside such control volumes. Full, anisotropic and asymmetric permeability tensor can be easily handled with the proposed method. The permeability tensor can vary from block to block. Thus it will be of great value in modeling fluid flow in reservoirs where principal directions of permeability varies between beds or within a bed. The paper also presents an analysis of some of the published flexible gridding schemes which use a control volume type algebraic approximation and demonstrate the advantages of the method presented here. The technique for grid construction is also discussed. Test results presented here demonstrate the need for proper representation of reservoir geometry to predict the correct flow behavior. The gridding scheme described in this paper achieves that purpose.

  4. Semi-passive, Chemical Oxidation Schemes for the Long-term Treatment of Contaminants

    SciTech Connect

    Frank W. Schwartz

    2005-12-13

    This research involves a combined experimental and modeling study that builds on our previous DOE-sponsored work in investigating how KMnO{sub 4} can be better used with in situ remediation of groundwater contaminated by chlorinated ethylenes (e.g., PCE, TCE, DCE). This study aims to provide scientific basis for developing a new long-term, semi-passive ISCO scheme that uses controlled release KMnO{sub 4} as a reactive barrier component. Specific objectives of the study are (1) to construct controlled release KMnO{sub 4} as a new reactive barrier component that could deliver permanganate at a controlled rate over long time periods of years, (2) to quantitatively describe release mechanisms associated with the controlled release KMnO{sub 4}, (3) to demonstrate efficacy of the new remediation scheme using proof-of-concept experiments, and (4) to design advanced forms of controlled release systems through numerical optimization. The new scheme operates in a long-term, semi-passive manner to control spreading of a dissolved contaminant plume with periodic replacement of the controlled release KMnO{sub 4} installed in the subsurface. As a first step in developing this remedial concept, we manufactured various prototype controlled release KMnO{sub 4} forms. Then we demonstrated using column experiments that the controlled release KMnO{sub 4} could deliver small amount of permanganate into flowing water at controlled rates over long time periods of years. An analytical model was also used to estimate the diffusivities and durations of the controlled release KMnO{sub 4}. Finally, proof-of-concept flow-tank experiments were performed to demonstrate the efficacy of the controlled release KMnO{sub 4} scheme in controlling dissolved TCE plume in a long-term, semi-passive manner. Another important thrust of our research effort involved numerical optimization of controlled release systems. This study used a numerical model that is capable of describing release patterns of active

  5. Application of TVD schemes for the Euler equations of gas dynamics. [method of Total Variation Diminishing for shock wave computation

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Warming, R. F.; Harten, A.

    1985-01-01

    Highly accurate and yet stable shock-capturing finite difference schemes have been designed for the computation of the Euler equations of gas dynamics. Four different principles for the construction of high resolution total variation diminishing (TVD) schemes are available, including hybrid schemes, a second-order extension of Godunov's scheme by van Leer (1979), the modified flux approach of Harten (1983, 1984), and the numerical fluctuation approach of Roe (1985). The present paper has the objective to review the class of second-order TVD schemes via the modified flux approach. Attention is given to first-order TVD schemes, a second-order accurate explicit TVD scheme, the global order of accuracy of the second-order TVD scheme, extensions to systems and two-dimensional conservation laws, numerical experiments with a second-order explicit TVD scheme, implicit TVD schemes, and second-order implicit TVD schemes.

  6. On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II - Five-point schemes

    NASA Technical Reports Server (NTRS)

    Harten, A.; Tal-Ezer, H.

    1981-01-01

    This paper presents a family of two-level five-point implicit schemes for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson scheme to fourth order accuracy (4-4) in both time and space. These 4-4 schemes are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit schemes. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit schemes brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. Numerical results are presented to illustrate some properties of the proposed scheme.

  7. On a class of TVD schemes for gas dynamic calculations. [Total Variation Diminishing

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Warming, R. F.; Harten, A.

    1985-01-01

    The purpose of this paper is to review a class of explicit and implicit second-order accurate Total Variation Diminishing (TVD) schemes and to show by numerical experiments, the performance of these schemes to the Euler equations of gas dynamics. The method of constructing these second-order accurate TVD schemes is sometimes known as the modified flux approach.

  8. MultiScheme: a parallel-processing system based on MIT (Massachusetts Institute of Technology) scheme. Doctoral thesis

    SciTech Connect

    Miller, J.S.

    1987-09-01

    MultiScheme is a fully operational parallel-programming system based upon the Scheme dialect of Lisp. Like its Lisp ancestors, MultiScheme provides a conducive environment for prototyping and testing new linguistic structures and programming methodologies. MultiScheme supports a diverse community of users who have a wide range of interests in parallel programming. MultiScheme's flexible support for system-based experiments in parallel processing has enabled it to serve as a development vehicle for university and industrial research. At the same time, MultiScheme is sufficiently robust, and supports a sufficiently wide range of parallel-processing applications, that it has become the base for a commercial product, the Butterfly Lisp System produced by BBN Advanced Computers, Inc.

  9. High-order compact MacCormack scheme for two-dimensional compressible and non-hydrostatic equations of the atmosphere

    NASA Astrophysics Data System (ADS)

    JavanNezhad, R.; Meshkatee, A. H.; Ghader, S.; Ahmadi-Givi, F.

    2016-09-01

    This study is devoted to application of the fourth-order compact MacCormack scheme to spatial differencing of the conservative form of two-dimensional and non-hydrostatic equation of a dry atmosphere. To advance the solution in time a four-stage Runge-Kutta method is used. To perform the simulations, two test cases including evolution of a warm bubble and a cold bubble in a neutral atmosphere with open and rigid boundaries are employed. In addition, the second-order MacCormack and the standard fourth-order compact MacCormack schemes are used to perform the simulations. Qualitative and quantitative assessment of the numerical results for different test cases exhibit the superiority of the fourth-order compact MacCormack scheme on the second-order method.

  10. MIMO transmit scheme based on morphological perceptron with competitive learning.

    PubMed

    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. PMID:27135805

  11. NUMERICAL NOISE PM SIMULATION IN CMAQ

    EPA Science Inventory

    We have found that numerical noise in the latest release of CMAQ using the yamo advection scheme when compiled on Linux cluster with pgf90 (5.0 or 6.0). We recommend to use -C option to eliminate the numerical noise.

  12. Beyond Scheme F

    SciTech Connect

    Elliott, C.J.; Fisher, H.; Pepin, J.; Gillmann, R.

    1996-07-01

    Traffic classification techniques were evaluated using data from a 1993 investigation of the traffic flow patterns on I-20 in Georgia. First we improved the data by sifting through the data base, checking against the original video for questionable events and removing and/or repairing questionable events. We used this data base to critique the performance quantitatively of a classification method known as Scheme F. As a context for improving the approach, we show in this paper that scheme F can be represented as a McCullogh-Pitts neural network, oar as an equivalent decomposition of the plane. We found that Scheme F, among other things, severely misrepresents the number of vehicles in Class 3 by labeling them as Class 2. After discussing the basic classification problem in terms of what is measured, and what is the desired prediction goal, we set forth desirable characteristics of the classification scheme and describe a recurrent neural network system that partitions the high dimensional space up into bins for each axle separation. the collection of bin numbers, one for each of the axle separations, specifies a region in the axle space called a hyper-bin. All the vehicles counted that have the same set of in numbers are in the same hyper-bin. The probability of the occurrence of a particular class in that hyper- bin is the relative frequency with which that class occurs in that set of bin numbers. This type of algorithm produces classification results that are much more balanced and uniform with respect to Classes 2 and 3 and Class 10. In particular, the cancellation of errors of classification that occurs is for many applications the ideal classification scenario. The neural network results are presented in the form of a primary classification network and a reclassification network, the performance matrices for which are presented.

  13. Convergence Acceleration for Multistage Time-Stepping Schemes

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Turkel, Eli L.; Rossow, C-C; Vasta, V. N.

    2006-01-01

    The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.

  14. Numerical nebulae

    NASA Astrophysics Data System (ADS)

    Rijkhorst, Erik-Jan

    2005-12-01

    The late stages of evolution of stars like our Sun are dominated by several episodes of violent mass loss. Space based observations of the resulting objects, known as Planetary Nebulae, show a bewildering array of highly symmetric shapes. The interplay between gasdynamics and radiative processes determines the morphological outcome of these objects, and numerical models for astrophysical gasdynamics have to incorporate these effects. This thesis presents new numerical techniques for carrying out high-resolution three-dimensional radiation hydrodynamical simulations. Such calculations require parallelization of computer codes, and the use of state-of-the-art supercomputer technology. Numerical models in the context of the shaping of Planetary Nebulae are presented, providing insight into their origin and fate.

  15. Information field dynamics for simulation scheme construction

    NASA Astrophysics Data System (ADS)

    Enßlin, Torsten A.

    2013-01-01

    Information field dynamics (IFD) is introduced here as a framework to derive numerical schemes for the simulation of physical and other fields without assuming a particular subgrid structure as many schemes do. IFD constructs an ensemble of nonparametric subgrid field configurations from the combination of the data in computer memory, representing constraints on possible field configurations, and prior assumptions on the subgrid field statistics. Each of these field configurations can formally be evolved to a later moment since any differential operator of the dynamics can act on fields living in continuous space. However, these virtually evolved fields need again a representation by data in computer memory. The maximum entropy principle of information theory guides the construction of updated data sets via entropic matching, optimally representing these field configurations at the later time. The field dynamics thereby become represented by a finite set of evolution equations for the data that can be solved numerically. The subgrid dynamics is thereby treated within auxiliary analytic considerations. The resulting scheme acts solely on the data space. It should provide a more accurate description of the physical field dynamics than simulation schemes constructed ad hoc, due to the more rigorous accounting of subgrid physics and the space discretization process. Assimilation of measurement data into an IFD simulation is conceptually straightforward since measurement and simulation data can just be merged. The IFD approach is illustrated using the example of a coarsely discretized representation of a thermally excited classical Klein-Gordon field. This should pave the way towards the construction of schemes for more complex systems like turbulent hydrodynamics.

  16. Information field dynamics for simulation scheme construction.

    PubMed

    Ensslin, Torsten A

    2013-01-01

    Information field dynamics (IFD) is introduced here as a framework to derive numerical schemes for the simulation of physical and other fields without assuming a particular subgrid structure as many schemes do. IFD constructs an ensemble of nonparametric subgrid field configurations from the combination of the data in computer memory, representing constraints on possible field configurations, and prior assumptions on the subgrid field statistics. Each of these field configurations can formally be evolved to a later moment since any differential operator of the dynamics can act on fields living in continuous space. However, these virtually evolved fields need again a representation by data in computer memory. The maximum entropy principle of information theory guides the construction of updated data sets via entropic matching, optimally representing these field configurations at the later time. The field dynamics thereby become represented by a finite set of evolution equations for the data that can be solved numerically. The subgrid dynamics is thereby treated within auxiliary analytic considerations. The resulting scheme acts solely on the data space. It should provide a more accurate description of the physical field dynamics than simulation schemes constructed ad hoc, due to the more rigorous accounting of subgrid physics and the space discretization process. Assimilation of measurement data into an IFD simulation is conceptually straightforward since measurement and simulation data can just be merged. The IFD approach is illustrated using the example of a coarsely discretized representation of a thermally excited classical Klein-Gordon field. This should pave the way towards the construction of schemes for more complex systems like turbulent hydrodynamics.

  17. Explicit Von Neumann Stability Conditions for the c-tau Scheme: A Basic Scheme in the Development of the CE-SE Courant Number Insensitive Schemes

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung

    2005-01-01

    As part of the continuous development of the space-time conservation element and solution element (CE-SE) method, recently a set of so call ed "Courant number insensitive schemes" has been proposed. The key advantage of these new schemes is that the numerical dissipation associa ted with them generally does not increase as the Courant number decre ases. As such, they can be applied to problems with large Courant number disparities (such as what commonly occurs in Navier-Stokes problem s) without incurring excessive numerical dissipation.

  18. Analysis and application of high order implicit Runge-Kutta schemes for unsteady conjugate heat transfer: A strongly-coupled approach

    NASA Astrophysics Data System (ADS)

    Kazemi-Kamyab, V.; van Zuijlen, A. H.; Bijl, H.

    2014-09-01

    Thermal interaction of fluids and solids, or conjugate heat transfer (CHT), is encountered in many engineering applications. Since time-accurate computations of unsteady CHT can be computationally demanding, we consider the use of high order implicit time integration schemes which have the potential to be more efficient relative to the commonly used second order implicit schemes. We present a strongly-coupled solution algorithm where the high order L-stable explicit first-stage singly diagonally implicit Runge-Kutta (ESDIRK) schemes are used to advance the solution in time within each separate fluid and solid subdomains. Furthermore, the stability and rate of convergence of performing (Gauss-Seidel) subiterations at each stage of the ESDIRK schemes are analyzed. The results from solving a numerical example (an unsteady conjugate natural convection in an enclosure) show good agreement with the performed analytical stability analysis. In addition, the (computational) work-(temporal) precision character of several schemes in solving a strongly coupled CHT problem is compared over a range of accuracy requirements. From the efficiency investigation, it is observed that performing subiterations with the strongly-coupled ESDIRK algorithm is more efficient than lowering time-step size using a high order loosely-coupled IMEX algorithm. In addition, by using the ESDIRK schemes, gain in computational efficiency relative to Crank-Nicolson is observed for time-accurate solutions (a factor of 1.4 using the fourth order ESDIRK). The computational gain is higher for smaller tolerances.

  19. The Super Tuesday Outbreak: Forecast Sensitivities to Single-Moment Microphysics Schemes

    NASA Technical Reports Server (NTRS)

    Molthan, Andrew L.; Case, Jonathan L.; Dembek, Scott R.; Jedlovec, Gary J.; Lapenta, William M.

    2008-01-01

    Forecast precipitation and radar characteristics are used by operational centers to guide the issuance of advisory products. As operational numerical weather prediction is performed at increasingly finer spatial resolution, convective precipitation traditionally represented by sub-grid scale parameterization schemes is now being determined explicitly through single- or multi-moment bulk water microphysics routines. Gains in forecasting skill are expected through improved simulation of clouds and their microphysical processes. High resolution model grids and advanced parameterizations are now available through steady increases in computer resources. As with any parameterization, their reliability must be measured through performance metrics, with errors noted and targeted for improvement. Furthermore, the use of these schemes within an operational framework requires an understanding of limitations and an estimate of biases so that forecasters and model development teams can be aware of potential errors. The National Severe Storms Laboratory (NSSL) Spring Experiments have produced daily, high resolution forecasts used to evaluate forecast skill among an ensemble with varied physical parameterizations and data assimilation techniques. In this research, high resolution forecasts of the 5-6 February 2008 Super Tuesday Outbreak are replicated using the NSSL configuration in order to evaluate two components of simulated convection on a large domain: sensitivities of quantitative precipitation forecasts to assumptions within a single-moment bulk water microphysics scheme, and to determine if these schemes accurately depict the reflectivity characteristics of well-simulated, organized, cold frontal convection. As radar returns are sensitive to the amount of hydrometeor mass and the distribution of mass among variably sized targets, radar comparisons may guide potential improvements to a single-moment scheme. In addition, object-based verification metrics are evaluated for

  20. A flux splitting scheme with high-resolution and robustness for discontinuities

    NASA Technical Reports Server (NTRS)

    Wada, Yasuhiro; Liou, Meng-Sing

    1994-01-01

    A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

  1. Numerical Integration

    ERIC Educational Resources Information Center

    Sozio, Gerry

    2009-01-01

    Senior secondary students cover numerical integration techniques in their mathematics courses. In particular, students would be familiar with the "midpoint rule," the elementary "trapezoidal rule" and "Simpson's rule." This article derives these techniques by methods which secondary students may not be familiar with and an approach that…

  2. A Second-Order Accurate, Component-Wise TVD Scheme for Nonlinear, Hyperbolic Conservation Laws

    NASA Astrophysics Data System (ADS)

    Yu, Heng; Liu, Yu-Ping

    2001-10-01

    In this paper, we present a two-step, component-wise TVD scheme for nonlinear, hyperbolic conservation laws, which is obtained by combining the schemes of Mac Cormack and Warming-Beam. The scheme does not necessitate the characteristic decompositions of the usual TVD schemes. It employs component-wise limiting; hence the programming is much simpler, especially for complicated coupled systems. For Euler systems of conservation laws, we found the scheme is two times faster in computation than the usual TVD schemes based on field-by-field decomposition limiting. A lot of numerical results show primarily the value of the new method.

  3. Finite Volume TVD Schemes for Magnetohydrodynamics on Unstructered Grids

    NASA Astrophysics Data System (ADS)

    Tanaka, T.

    A three-dimensional (3-D) high-resolution magnetohydrodynamic (MHD) simulation scheme is developed on unstructured grid systems to solve the complex-system problems in space science and space weather in which numerical difficulties arise from inhomogeneity due to strong background potential fields, inclusion of multi-species ions, and formations of shocks and discontinuities. The ideal MHD equations are extended to the 9-component MHD equations for multi-component ions and modified soas to avoid a direct inclusion of background potential field in dependent variables through the use of new variables. The numerical scheme adopts the finite volume method (FVM) with an upwinding numerical flux based on the linearized Riemann solver. Upwindings on unstructured grid systems are realized from the fact that the MHD equations are symmetric with respect to the rotation of the space. Despite the modifications of the equation system, the eigenvectors in the mode-synthesis matrix necessary for the ev aluation of the upwinding numerical flux can still be written analytically. To get a higher order of accuracy, the upwinding flux is extended to the third-order total variation diminishing (TVD) numerical flux in the calculation of FVM, through the monotonic upstream scheme for conservation laws (MUSCL) approach and Van Leer's differentiable limiter. Three numerical examples are given in order to show the efficiency of the above scheme.

  4. Quantum messages with signatures forgeable in arbitrated quantum signature schemes

    NASA Astrophysics Data System (ADS)

    Kim, Taewan; Choi, Jeong Woon; Jho, Nam-Su; Lee, Soojoon

    2015-02-01

    Even though a method to perfectly sign quantum messages has not been known, the arbitrated quantum signature scheme has been considered as one of the good candidates. However, its forgery problem has been an obstacle to the scheme becoming a successful method. In this paper, we consider one situation, which is slightly different from the forgery problem, that we use to check whether at least one quantum message with signature can be forged in a given scheme, although all the messages cannot be forged. If there are only a finite number of forgeable quantum messages in the scheme, then the scheme can be secured against the forgery attack by not sending forgeable quantum messages, and so our situation does not directly imply that we check whether the scheme is secure against the attack. However, if users run a given scheme without any consideration of forgeable quantum messages, then a sender might transmit such forgeable messages to a receiver and in such a case an attacker can forge the messages if the attacker knows them. Thus it is important and necessary to look into forgeable quantum messages. We show here that there always exists such a forgeable quantum message-signature pair for every known scheme with quantum encryption and rotation, and numerically show that there are no forgeable quantum message-signature pairs that exist in an arbitrated quantum signature scheme.

  5. Explicit BCJ numerators of nonlinear simga model

    NASA Astrophysics Data System (ADS)

    Du, Yi-Jian; Fu, Chih-Hao

    2016-09-01

    In this paper, we investigate the color-kinematics duality in nonlinear sigma model (NLSM). We present explicit polynomial expressions for the kinematic numerators (BCJ numerators). The calculation is done separately in two parametrization schemes of the theory using Kawai-Lewellen-Tye relation inspired technique, both lead to polynomial numerators. We summarize the calculation in each case into a set of rules that generates BCJ numerators for all multilplicities. In Cayley parametrization we find the numerator is described by a particularly simple formula solely in terms of momentum kernel.

  6. ESCAP mobile training scheme.

    PubMed

    Yasas, F M

    1977-01-01

    In response to a United Nations resolution, the Mobile Training Scheme (MTS) was set up to provide training to the trainers of national cadres engaged in frontline and supervisory tasks in social welfare and rural development. The training is innovative in its being based on an analysis of field realities. The MTS team consisted of a leader, an expert on teaching methods and materials, and an expert on action research and evaluation. The country's trainers from different departments were sent to villages to work for a short period and to report their problems in fulfilling their roles. From these grass roots experiences, they made an analysis of the job, determining what knowledge, attitude and skills it required. Analysis of daily incidents and problems were used to produce indigenous teaching materials drawn from actual field practice. How to consider the problems encountered through government structures for policy making and decisions was also learned. Tasks of the students were to identify the skills needed for role performance by job analysis, daily diaries and project histories; to analyze the particular community by village profiles; to produce indigenous teaching materials; and to practice the role skills by actual role performance. The MTS scheme was tried in Nepal in 1974-75; 3 training programs trained 25 trainers and 51 frontline workers; indigenous teaching materials were created; technical papers written; and consultations were provided. In Afghanistan the scheme was used in 1975-76; 45 participants completed the training; seminars were held; and an ongoing Council was created. It is hoped that the training program will be expanded to other countries. PMID:12265562

  7. Entropy stable schemes for initial-boundary-value conservation laws

    NASA Astrophysics Data System (ADS)

    Svärd, Magnus; Mishra, Siddhartha

    2012-12-01

    We consider initial-boundary-value problems for systems of conservation laws and design entropy stable finite difference schemes to approximate them. The schemes are shown to be entropy stable for a large class of systems that are equipped with a symmetric splitting, derived from the entropy formulation. Numerical examples for the Euler equations of gas dynamics are presented to illustrate the robust performance of the proposed method.

  8. New LNG process scheme

    SciTech Connect

    Foglietta, J.H.

    1999-07-01

    A new LNG cycle has been developed for base load liquefaction facilities. This new design offers a different technical and economical solution comparing in efficiency with the classical technologies. The new LNG scheme could offer attractive business opportunities to oil and gas companies that are trying to find paths to monetize gas sources more effectively; particularly for remote or offshore locations where smaller scale LNG facilities might be applicable. This design offers also an alternative route to classic LNG projects, as well as alternative fuel sources. Conceived to offer simplicity and access to industry standard equipment, This design is a hybrid result of combining a standard refrigeration system and turboexpander technology.

  9. Receptivity of a TVD Scheme in Incompressible Flow Analysis

    NASA Astrophysics Data System (ADS)

    Shin, Byeong Rog

    A TVD upwind scheme originally designed for compressible flow is applied to the SMAC finite-difference method for incompressible flow analysis. The receptivity and validity of this application are investigated by an evaluation of the accuracy, stability and convergence rate for the SMAC method combined with the TVD scheme. Using this method, three-dimensional developing entry flows through a square-curved duct are calculated and compared with available experimental data as well as some computational results obtained by QUICKs and third-order upwind schemes. Such comparisons show that the numerical method applying the TVD scheme has the highest computational efficiency without a sharp loss of accuracy, resulting in confidence in the application this scheme to incompressible flow computations.

  10. Comparison of Several Dissipation Algorithms for Central Difference Schemes

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Radespiel, R.; Turkel, E.

    1997-01-01

    Several algorithms for introducing artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical results are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme.

  11. The construction of high-accuracy schemes for acoustic equations

    NASA Technical Reports Server (NTRS)

    Tang, Lei; Baeder, James D.

    1995-01-01

    An accuracy analysis of various high order schemes is performed from an interpolation point of view. The analysis indicates that classical high order finite difference schemes, which use polynomial interpolation, hold high accuracy only at nodes and are therefore not suitable for time-dependent problems. Thus, some schemes improve their numerical accuracy within grid cells by the near-minimax approximation method, but their practical significance is degraded by maintaining the same stencil as classical schemes. One-step methods in space discretization, which use piecewise polynomial interpolation and involve data at only two points, can generate a uniform accuracy over the whole grid cell and avoid spurious roots. As a result, they are more accurate and efficient than multistep methods. In particular, the Cubic-Interpolated Psuedoparticle (CIP) scheme is recommended for computational acoustics.

  12. On Approximate Factorization Schemes for Solving the Full Potential Equation

    NASA Technical Reports Server (NTRS)

    Holst, Terry L.

    1997-01-01

    An approximate factorization scheme based on the AF2 algorithm is presented for solving the three-dimensional full potential equation for the transonic flow about isolated wings. Two spatial discretization variations are presented, one using a hybrid first-order/second-order-accurate scheme and the second using a fully second-order-accurate scheme. The present algorithm utilizes a C-H grid topology to map the flow field about the wing. One version of the AF2 iteration scheme is used on the upper wing surface and another slightly modified version is used on the lower surface. These two algorithm variations are then connected at the wing leading edge using a local iteration technique. The resulting scheme has improved linear stability characteristics and improved time-like damping characteristics relative to previous implementations of the AF2 algorithm. The presentation is highlighted with a grid refinement study and a number of numerical results.

  13. Advanced Numerical Modeling of Turbulent Atmospheric Flows

    NASA Astrophysics Data System (ADS)

    Kühnlein, Christian; Dörnbrack, Andreas; Gerz, Thomas

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

  14. Handling geophysical flows: Numerical modelling using Graphical Processing Units

    NASA Astrophysics Data System (ADS)

    Garcia-Navarro, Pilar; Lacasta, Asier; Juez, Carmelo; Morales-Hernandez, Mario

    2016-04-01

    Computational tools may help engineers in the assessment of sediment transport during the decision-making processes. The main requirements are that the numerical results have to be accurate and simulation models must be fast. The present work is based on the 2D shallow water equations in combination with the 2D Exner equation [1]. The resulting numerical model accuracy was already discussed in previous work. Regarding the speed of the computation, the Exner equation slows down the already costly 2D shallow water model as the number of variables to solve is increased and the numerical stability is more restrictive. On the other hand, the movement of poorly sorted material over steep areas constitutes a hazardous environmental problem. Computational tools help in the predictions of such landslides [2]. In order to overcome this problem, this work proposes the use of Graphical Processing Units (GPUs) for decreasing significantly the simulation time [3, 4]. The numerical scheme implemented in GPU is based on a finite volume scheme. The mathematical model and the numerical implementation are compared against experimental and field data. In addition, the computational times obtained with the Graphical Hardware technology are compared against Single-Core (sequential) and Multi-Core (parallel) CPU implementations. References [Juez et al.(2014)] Juez, C., Murillo, J., & Garca-Navarro, P. (2014) A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed. Advances in Water Resources. 71 93-109. [Juez et al.(2013)] Juez, C., Murillo, J., & Garca-Navarro, P. (2013) . 2D simulation of granular flow over irregular steep slopes using global and local coordinates. Journal of Computational Physics. 225 166-204. [Lacasta et al.(2014)] Lacasta, A., Morales-Hernndez, M., Murillo, J., & Garca-Navarro, P. (2014) An optimized GPU implementation of a 2D free surface simulation model on unstructured meshes Advances in Engineering Software. 78 1-15. [Lacasta

  15. XFEM schemes for level set based structural optimization

    NASA Astrophysics Data System (ADS)

    Li, Li; Wang, Michael Yu; Wei, Peng

    2012-12-01

    In this paper, some elegant extended finite element method (XFEM) schemes for level set method structural optimization are proposed. Firstly, two-dimension (2D) and three-dimension (3D) XFEM schemes with partition integral method are developed and numerical examples are employed to evaluate their accuracy, which indicate that an accurate analysis result can be obtained on the structural boundary. Furthermore, the methods for improving the computational accuracy and efficiency of XFEM are studied, which include the XFEM integral scheme without quadrature sub-cells and higher order element XFEM scheme. Numerical examples show that the XFEM scheme without quadrature sub-cells can yield similar accuracy of structural analysis while prominently reducing the time cost and that higher order XFEM elements can improve the computational accuracy of structural analysis in the boundary elements, but the time cost is increasing. Therefore, the balance of time cost between FE system scale and the order of element needs to be discussed. Finally, the reliability and advantages of the proposed XFEM schemes are illustrated with several 2D and 3D mean compliance minimization examples that are widely used in the recent literature of structural topology optimization. All numerical results demonstrate that the proposed XFEM is a promising structural analysis approach for structural optimization with the level set method.

  16. The standard upwind compact difference schemes for incompressible flow simulations

    NASA Astrophysics Data System (ADS)

    Fan, Ping

    2016-10-01

    Compact difference schemes have been used extensively for solving the incompressible Navier-Stokes equations. However, the earlier formulations of the schemes are of central type (called central compact schemes, CCS), which are dispersive and susceptible to numerical instability. To enhance stability of CCS, the optimal upwind compact schemes (OUCS) are developed recently by adding high order dissipative terms to CCS. In this paper, it is found that OUCS are essentially not of the upwind type because they do not use upwind-biased but central type of stencils. Furthermore, OUCS are not the most optimal since orders of accuracy of OUCS are at least one order lower than the maximum achievable orders. New upwind compact schemes (called standard upwind compact schemes, SUCS) are developed in this paper. In contrast to OUCS, SUCS are constructed based completely on upwind-biased stencils and hence can gain adequate numerical dissipation with no need for introducing optimization calculations. Furthermore, SUCS can achieve the maximum achievable orders of accuracy and hence be more compact than OUCS. More importantly, SUCS have prominent advantages on combining the stable and high resolution properties which are demonstrated from the global spectral analyses and typical numerical experiments.

  17. The Impact of Microphysical Schemes on Intensity and Track of Hurricane

    NASA Technical Reports Server (NTRS)

    Tao, W. K.; Shi, J. J.; Chen, S. S.; Lang, S.; Lin, P.; Hong, S. Y.; Peters-Lidard, C.; Hou, A.

    2010-01-01

    During the past decade, both research and operational numerical weather prediction models [e.g. Weather Research and Forecasting Model (WRF)] have started using more complex microphysical schemes originally developed for high-resolution cloud resolving models (CRMs) with a 1-2 km or less horizontal resolutions. The WRF is a next-generation meso-scale forecast model and assimilation system that has incorporated a modern software framework, advanced dynamics, numeric and data assimilation techniques, a multiple moveable nesting capability, and improved physical packages. The WRF model can be used for a wide range of applications, from idealized research to operational forecasting, with an emphasis on horizontal grid sizes in the range of 1-10 km. The current WRF includes several different microphysics options. At Goddard, four different cloud microphysics schemes (warm rain only, two-class of ice, two three-class of ice with either graupel or hail) are implemented into the WRF. The performances of these schemes have been compared to those from other WRF microphysics scheme options for an Atlantic hurricane case. In addition, a brief review and comparison on the previous modeling studies on the impact of microphysics schemes and microphysical processes on intensity and track of hurricane will be presented. Generally, almost all modeling studies found that the microphysics schemes did not have major impacts on track forecast, but did have more effect on the intensity. All modeling studies found that the simulated hurricane has rapid deepening and/or intensification for the warm rain-only case. It is because all hydrometeors were very large raindrops, and they fell out quickly at and near the eye-wall region. This would hydrostatically produce the lowest pressure. In addition, these modeling studies suggested that the simulated hurricane becomes unrealistically strong by removing the evaporative cooling of cloud droplets and melting of ice particles. This is due to the

  18. AMR vs High Order Schemes Wavelets as a Guide

    SciTech Connect

    Jameson, L.

    2000-10-04

    The final goal behind any numerical method is give the smallest wall-clock time for a given final time error or, conversely, the smallest run-time error for a given wall clock time, etc. Here a comparison will be given between adaptive mesh refinement schemes and non-adaptive schemes of higher order. It will be shown that in three dimension calculations that in order for AMR schemes to be competitive that the finest scale must be restricted to an extremely, and unrealistic, small percentage of the computational domain.

  19. Weighted-mean scheme for solving incompressible viscous flow

    NASA Technical Reports Server (NTRS)

    Huynh, Q. Q.

    1981-01-01

    The problem of how a boundary layer responds to the motion of a convexed vortex on a porous wall was investigated. The wall velocity is approximately given by Darcy's law. The vorticity-stream function approach was adopted for solving Navier-Stokes equations of two dimensional incompressible viscous flows. The weighted-mean scheme was used for constructing finite difference approximations of spatial derivatives. Several test problems were solved and numerical results demonstrate clearly the accuracy, stability, and efficiency of the scheme. The weighted mean scheme then can be applied to the vortical flow problem.

  20. Multi-dimensional ENO schemes for general geometries

    NASA Technical Reports Server (NTRS)

    Harten, Ami; Chakravarthy, Sukumar R.

    1991-01-01

    A class of ENO schemes is presented for the numerical solution of multidimensional hyperbolic systems of conservation laws in structured and unstructured grids. This is a class of shock-capturing schemes which are designed to compute cell-averages to high order accuracy. The ENO scheme is composed of a piecewise-polynomial reconstruction of the solution form its given cell-averages, approximate evolution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is based on an adaptive selection of stencil for each cell so as to avoid spurious oscillations near discontinuities while achieving high order of accuracy away from them.

  1. Recent progress on essentially non-oscillatory shock capturing schemes

    NASA Technical Reports Server (NTRS)

    Osher, Stanley; Shu, Chi-Wang

    1989-01-01

    An account is given of the construction of efficient implementations of 'essentially nonoscillatory' (ENO) schemes that approximate systems of hyperbolic conservation laws. ENO schemes use a local adaptive stencil to automatically obtain information from regions of smoothness when the solution develops discontinuities. Approximations employing ENOs can thereby obtain uniformly high accuracy to the very onset of discontinuities, while retaining a sharp and essentially nonoscillatory shock transition. For ease of implementation, ENO schemes applying the adaptive stencil concept to the numerical fluxes and employing a TVD Runge-Kutta-type time discretization are constructed.

  2. Accurate Monotonicity - Preserving Schemes With Runge-Kutta Time Stepping

    NASA Technical Reports Server (NTRS)

    Suresh, A.; Huynh, H. T.

    1997-01-01

    A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented. The interface value in these schemes is obtained by limiting a higher-order polynominal reconstruction. The limiting is designed to preserve accuracy near extrema and to work well with Runge-Kutta time stepping. Computational efficiency is enhanced by a simple test that determines whether the limiting procedure is needed. For linear advection in one dimension, these schemes are shown as well as the Euler equations also confirm their high accuracy, good shock resolution, and computational efficiency.

  3. Large eddy simulations and direct numerical simulations of high speed turbulent reacting flows

    NASA Technical Reports Server (NTRS)

    Givi, Peyman; Madnia, Cyrus K.; Steinberger, Craig J.

    1990-01-01

    This research is involved with the implementation of advanced computational schemes based on large eddy simulations (LES) and direct numerical simulations (DNS) to study the phenomenon of mixing and its coupling with chemical reactions in compressible turbulent flows. In the efforts related to LES, a research program to extend the present capabilities of this method was initiated for the treatment of chemically reacting flows. In the DNS efforts, the focus is on detailed investigations of the effects of compressibility, heat release, and non-equilibrium kinetics modelings in high speed reacting flows. Emphasis was on the simulations of simple flows, namely homogeneous compressible flows, and temporally developing high speed mixing layers.

  4. A certification scheme for the boson sampler

    NASA Astrophysics Data System (ADS)

    Liu, Kai; Lund, Austin Peter; Gu, Yong-Jian; Ralph, Timothy Cameron

    2016-09-01

    Boson sampling can provide strong evidence that the computational power of a quantum computer outperforms a classical one via currently feasible linear optics experiments. However, how to identify an actual boson sampling device against any classical computing imposters is an ambiguous problem due to the computational complexity class in which boson sampling lies. The certification protocol based on bosonic bunching fails to rule out the so-called mean-field sampling. We propose a certification scheme to distinguish the boson sampling from the mean-field sampling for any random scattering matrices chosen via the Harr-measure. We numerically analyze our scheme and the influence of imperfect input states caused by non-simultaneous arrival photons.

  5. Iterated upwind schemes for gas dynamics

    SciTech Connect

    Smolarkiewicz, Piotr K. Szmelter, Joanna

    2009-01-10

    A class of high-resolution schemes established in integration of anelastic equations is extended to fully compressible flows, and documented for unsteady (and steady) problems through a span of Mach numbers from zero to supersonic. The schemes stem from iterated upwind technology of the multidimensional positive definite advection transport algorithm (MPDATA). The derived algorithms employ standard and modified forms of the equations of gas dynamics for conservation of mass, momentum and either total or internal energy as well as potential temperature. Numerical examples from elementary wave propagation, through computational aerodynamics benchmarks, to atmospheric small- and large-amplitude acoustics with intricate wave-flow interactions verify the approach for both structured and unstructured meshes, and demonstrate its flexibility and robustness.

  6. Robust Neighboring Optimal Guidance for the Advanced Launch System

    NASA Technical Reports Server (NTRS)

    Hull, David G.

    1993-01-01

    In recent years, optimization has become an engineering tool through the availability of numerous successful nonlinear programming codes. Optimal control problems are converted into parameter optimization (nonlinear programming) problems by assuming the control to be piecewise linear, making the unknowns the nodes or junction points of the linear control segments. Once the optimal piecewise linear control (suboptimal) control is known, a guidance law for operating near the suboptimal path is the neighboring optimal piecewise linear control (neighboring suboptimal control). Research conducted under this grant has been directed toward the investigation of neighboring suboptimal control as a guidance scheme for an advanced launch system.

  7. Finite-difference schemes for anisotropic diffusion

    SciTech Connect

    Es, Bram van; Koren, Barry; Blank, Hugo J. de

    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.

  8. A Comparison of three high-precision quadrature schemes

    SciTech Connect

    Bailey, David H.; Li, Xiaoye S.

    2003-07-01

    The authors have implemented three numerical quadrature schemes, using the new Arbitrary Precision (ARPREC) software package, with the objective of seeking a completely ''automatic'' arbitrary precision quadrature facility, namely one that does not rely on a priori information of the function to be integrated. Such a facility is required, for example, to permit the experimental identification of definite integrals based on their numerical values. The performance and accuracy of these three quadrature schemes are compared using a suite of 15 integrals, ranging from continuous, well-behaved functions on finite intervals to functions with vertical derivatives and integrable singularities at endpoints, as well as several integrals on an infinite interval.

  9. A rotationally biased upwind difference scheme for the Euler equations

    NASA Technical Reports Server (NTRS)

    Davis, S. F.

    1983-01-01

    The upwind difference schemes of Godunov, Osher, Roe and van Leer are able to resolve one dimensional steady shocks for the Euler equations within one or two mesh intervals. Unfortunately, this resolution is lost in two dimensions when the shock crosses the computing grid at an oblique angle. To correct this problem, a numerical scheme was developed which automatically locates the angle at which a shock might be expected to cross the computing grid and then constructs separate finite difference formulas for the flux components normal and tangential to this direction. Numerical results which illustrate the ability of this method to resolve steady oblique shocks are presented.

  10. A rotationally biased upwind difference scheme for the Euler equations

    NASA Technical Reports Server (NTRS)

    Davis, S. F.

    1984-01-01

    The upwind difference schemes of Godunov, Osher, Roe and van Leer are able to resolve one dimensional steady shocks for the Euler equations within one or two mesh intervals. Unfortunately, this resolution is lost in two dimensions when the shock crosses the computing grid at an oblique angle. To correct this problem, a numerical scheme was developed which automatically locates the angle at which a shock might be expected to cross the computing grid and then constructs separate finite difference formulas for the flux components normal and tangential to this direction. Numerical results which illustrate the ability of this method to resolve steady oblique shocks are presented.

  11. Accelerating development of advanced inverters :

    SciTech Connect

    Neely, Jason C.; Gonzalez, Sigifredo; Ropp, Michael; Schutz, Dustin

    2013-11-01

    The high penetration of utility interconnected photovoltaic (PV) systems is causing heightened concern over the effect that variable renewable generation will have on the electrical power system (EPS). These concerns have initiated the need to amend the utility interconnection standard to allow advanced inverter control functionalities that provide: (1) reactive power control for voltage support, (2) real power control for frequency support and (3) better tolerance of grid disturbances. These capabilities are aimed at minimizing the negative impact distributed PV systems may have on EPS voltage and frequency. Unfortunately, these advanced control functions may interfere with island detection schemes, and further development of advanced inverter functions requires a study of the effect of advanced functions on the efficacy of antiislanding schemes employed in industry. This report summarizes the analytical, simulation and experimental work to study interactions between advanced inverter functions and anti-islanding schemes being employed in distributed PV systems.

  12. Recent Advances in Vibroacoustics

    NASA Technical Reports Server (NTRS)

    Hughes, William O.; McNelis, Mark E.

    2002-01-01

    Numerous vibroacoustics advances and impacts in the aerospace industry have occurred over the last 15 years. This article addresses some of these that developed from engineering programmatic task-work at the NASA Glenn Research Center at Lewis Field.

  13. A triple-moment hail bulk microphysics scheme. Part II: Verification and comparison with two-moment bulk microphysics

    NASA Astrophysics Data System (ADS)

    Loftus, A. M.; Cotton, W. R.

    2014-12-01

    Microphysical parameterizations in numerical cloud models continue to grow in complexity as our capability to represent microphysical processes increases owing to greater knowledge of these processes as well as advances in computing power. In Part I of this study, a new triple-moment bulk hail microphysics scheme (3MHAIL) that predicts the spectral shape parameter of the hail size distribution was presented and evaluated against lower order-moment schemes. In this paper, the 3MHAIL scheme is verified in simulations of a well-observed supercell storm that occurred over northwest Kansas on 29 June 2000 during the Severe Thunderstorm and Electrification and Precipitation Study (STEPS). Comparisons of the simulation results with the observations for this case, as well as with results of simulations using two different two-moment (2M) configurations of the RAMS microphysics schemes, suggest a significant improvement of the simulated storm structure and evolution is achieved with the 3MHAIL scheme. The generation of large hail and subsequent fallout in the simulation using 3MHAIL microphysics show particularly good agreement with surface hail reports for this storm as well as with previous studies of hail-producing supercell storms. On the other hand, the simulation with 2M microphysics produces only small hail aloft and virtually no hail at the surface, whereas a 2M version of the 3MHAIL scheme (with a fixed spectral shape parameter) produces unrealistically high amounts of large hail at low levels as a result of artificial shifts in the hail size spectra towards larger diameter hail during the melting process.

  14. Front tracking in the numerical simulation of binary alloy solidification

    NASA Astrophysics Data System (ADS)

    Simpson, James Edward

    2000-12-01

    A model for directional solidification in dilute binary alloys is presented. The energy equation is solved for the temperature field, while the species equation is solved for the solute distribution. Either the vorticity-vector potential formulation or the pressure-velocity formulation is used to solve the governing equations for the velocity field. The constitutive equations are solved using a fully transient scheme. A variety of fast numerical schemes for solving sparse systems are used in the solution procedure. A single domain approach is used for the solution scheme for the energy and concentration equations. The effects of phase-change (energy equation) and solute rejection at the advancing solid/liquid interface (concentration equation) are handled via the introduction of appropriate source terms. The numerical approach was validated by comparing numerical results to data from a series of experiments of the Bridgman growth of pure succinonitrile. These experiments were performed as part of this work and are explained in detail. The numerical results agree well with the experimental data in terms of interface shape, temperature and velocity data. The key contribution of this work is the investigation of the Bridgman crystal growth of bismuth-tin in support of NASA's MEPHISTO project. The simulations reported in this work are among the first fully transient simulations of the process; no simplifying steady state approximations were used. Results are obtained for Bi-Sn alloys at a variety of initial concentrations and gravity levels. For most of the work, the solid/liquid interface temperature is assumed to be constant. For the richer alloy (Bi-1.0 at.% Sn) the results indicate that a secondary convective cell, driven by solutal gradients, forms near the interface. The magnitude of the velocities in this cell increases with time, causing increasing solute segregation at the solid/liquid interface. At lower gravity levels, convection-induced segregation is

  15. Accuracy study of the IDO scheme by Fourier analysis

    NASA Astrophysics Data System (ADS)

    Imai, Yohsuke; Aoki, Takayuki

    2006-09-01

    The numerical accuracy of the Interpolated Differential Operator (IDO) scheme is studied with Fourier analysis for the solutions of Partial Differential Equations (PDEs): advection, diffusion, and Poisson equations. The IDO scheme solves governing equations not only for physical variable but also for first-order spatial derivative. Spatial discretizations are based on Hermite interpolation functions with both of them. In the Fourier analysis for the IDO scheme, the Fourier coefficients of the physical variable and the first-order derivative are coupled by the equations derived from the governing equations. The analysis shows the IDO scheme resolves all the wavenumbers with higher accuracy than the fourth-order Finite Difference (FD) and Compact Difference (CD) schemes for advection equation. In particular, for high wavenumbers, the accuracy is superior to that of the sixth-order Combined Compact Difference (CCD) scheme. The diffusion and Poisson equations are also more accurately solved in comparison with the FD and CD schemes. These results show that the IDO scheme guarantees highly resolved solutions for all the terms of fluid flow equations.

  16. Resolution-optimised nonlinear scheme for secondary derivatives

    NASA Astrophysics Data System (ADS)

    Li, Li; Yu, Changping; Chen, Zhe; Li, Xinliang

    2016-02-01

    A 5-point-stencil optimised nonlinear scheme with spectral-like resolution within the whole wave number range for secondary derivatives is devised. The proposed scheme can compensate for the dissipation deficiency of traditional linear schemes and suppress the spurious energy accumulation that occurs at high wave numbers, both of which are frequently encountered in large eddy simulation. The new scheme is composed of a linear fourth-order central scheme term and an artificial viscosity term. These two terms are connected by a nonlinear weight. The proposed nonlinear weight is designed based on Fourier analysis, rather than Taylor analysis, to guarantee a spectral-like resolution. Moreover, the accuracy is not affected by the optimisation, and the new scheme reaches fourth-order accuracy. The new scheme is tested numerically using the one-dimensional diffusion problem, one-dimensional steady viscous Burger's shock, two-dimensional vortex decaying, three-dimensional isotropic decaying turbulence and fully developed turbulent channel flow. All the tests confirm that the new scheme has spectral-like resolution and can improve the accuracy of the energy spectrum, dissipation rate and high-order statistics of turbulent flows.

  17. Numerical analysis of turbulent coaxial flow with internal heat generation

    NASA Technical Reports Server (NTRS)

    Lin, A.; Weinstein, H.

    1981-01-01

    A computational method with which to obtain a physical understanding of the turbulent field of two coaxial jets entering an axisymmetric chamber is developed. Even the laminar field of this flow is quite complicated. This is due to the many different domains which exist in the field especially in the entrance region. Physically, three regions may be identified: the wall region, the initial region near the axis of symmetry and the mixing region. Advancing downstream, these regions change relative size with the ratio of the two jets' mass fluxes as the main parameter. The turbulent field of these flows is much more complicated due to the difference in the effective transport coefficients and turbulence level from region to region. However, being aware beforehand of the complications and the different regions of this field, the appropriate turbulence model and numerical scheme can be adjusted to treat the problem.

  18. Advanced geometries and regimes

    SciTech Connect

    Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Margarone, D.; Korn, G.

    2013-07-26

    We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.

  19. Entropy Splitting and Numerical Dissipation

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Vinokur, M.; Djomehri, M. J.

    1999-01-01

    A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock

  20. LHC INTERACTION REGION CORRECTION SCHEME STUDIES

    SciTech Connect

    FISCHER,W.; PTITSIN,V.; WEI,J.

    1999-09-07

    In a companion paper the authors showed that the performance of the Large Hadron Collider (LHC) at collision energy is limited by the field quality of the interaction region quadrupoles and dipoles. In this situation, the dynamic aperture can be increased through local multipole correctors. Since the betatron phase advance is well defined for magnets that are located in regions of large beta functions, local corrections can be very effective and robust. They compare possible compensation schemes and propose a corrector layout to meet the required dynamic aperture performance.

  1. Generalized formulation of a class of explicit and implicit TVD schemes

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1985-01-01

    A one parameter family of second order explicit and implicit total variation diminishing (TVD) schemes is reformulated so that a simpler and wider group of limiters is included. The resulting scheme can be viewed as a symmetrical algorithm with a variety of numerical dissipation terms that are designed for weak solutions of hyperbolic problems. This is a generalization of Roe and Davis's recent works to a wider class of symmetric schemes other than Lax-Wendroff. The main properties of the present class of schemes are that they can be implicit, and when steady state calculations are sought, the numerical solution is independent of the time step.

  2. A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

    NASA Astrophysics Data System (ADS)

    Chernogorova, Tatiana; Vulkov, Lubin

    2009-11-01

    This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

  3. A modified symplectic scheme for seismic wave modeling

    NASA Astrophysics Data System (ADS)

    Liu, Shaolin; Li, Xiaofan; Wang, Wenshuai; Xu, Ling; Li, Bingfei

    2015-05-01

    Symplectic integrators are well known for their excellent performance in solving partial differential equation of dynamical systems because they are capable of preserving some conservative properties of dynamic equations. However, there are not enough high-order, for example third-order symplectic schemes, which are suitable for seismic wave equations. Here, we propose a strategy to construct a symplectic scheme that is based on a so-called high-order operator modification method. We first employ a conventional two-stage Runge-Kutta-Nyström (RKN) method to solve the ordinary differential equations, which are derived from the spatial discretization of the seismic wave equations. We then add a high-order term to the RKN method. Finally, we obtain a new third-order symplectic scheme with all positive symplectic coefficients, and it is defined based on the order condition, the symplectic condition, the stability condition and the dispersion relation. It is worth noting that the new scheme is independent of the spatial discretization type used, and we simply apply some finite difference operators to approximate the spatial derivatives of the isotropic elastic equations for a straightforward discussion. For the theoretical analysis, we obtain the semi-analytic stability conditions of our scheme with various orders of spatial approximation. The stability and dispersion properties of our scheme are also compared with conventional schemes to illustrate the favorable numerical behaviors of our scheme in terms of precision, stability and dispersion characteristics. Finally, three numerical experiments are employed to further demonstrate the validity of our method. The modified strategy that is proposed in this paper can be used to construct other explicit symplectic schemes.

  4. Final Progress Report submitted via the DOE Energy Link (E-Link) in June 2009 [Collaborative Research: Decadal-to-Centennial Climate & Climate Change Studies with Enhanced Variable and Uniform Resolution GCMs Using Advanced Numerical Techniques

    SciTech Connect

    Fox-Rabinovitz, M; Cote, J

    2009-10-09

    The joint U.S-Canadian project has been devoted to: (a) decadal climate studies using developed state-of-the-art GCMs (General Circulation Models) with enhanced variable and uniform resolution; (b) development and implementation of advanced numerical techniques; (c) research in parallel computing and associated numerical methods; (d) atmospheric chemistry experiments related to climate issues; (e) validation of regional climate modeling strategies for nested- and stretched-grid models. The variable-resolution stretched-grid (SG) GCMs produce accurate and cost-efficient regional climate simulations with mesoscale resolution. The advantage of the stretched grid approach is that it allows us to preserve the high quality of both global and regional circulations while providing consistent interactions between global and regional scales and phenomena. The major accomplishment for the project has been the successful international SGMIP-1 and SGMIP-2 (Stretched-Grid Model Intercomparison Project, phase-1 and phase-2) based on this research developments and activities. The SGMIP provides unique high-resolution regional and global multi-model ensembles beneficial for regional climate modeling and broader modeling community. The U.S SGMIP simulations have been produced using SciDAC ORNL supercomputers. The results of the successful SGMIP multi-model ensemble simulations of the U.S. climate are available at the SGMIP web site (http://essic.umd.edu/~foxrab/sgmip.html) and through the link to the WMO/WCRP/WGNE web site: http://collaboration.cmc.ec.gc.ca/science/wgne. Collaborations with other international participants M. Deque (Meteo-France) and J. McGregor (CSIRO, Australia) and their centers and groups have been beneficial for the strong joint effort, especially for the SGMIP activities. The WMO/WCRP/WGNE endorsed the SGMIP activities in 2004-2008. This project reflects a trend in the modeling and broader communities to move towards regional and sub-regional assessments and

  5. Numerical simulation of electrospray in the cone-jet mode.

    PubMed

    Herrada, M A; López-Herrera, J M; Gañán-Calvo, A M; Vega, E J; Montanero, J M; Popinet, S

    2012-08-01

    We present a robust and computationally efficient numerical scheme for simulating steady electrohydrodynamic atomization processes (electrospray). The main simplification assumed in this scheme is that all the free electrical charges are distributed over the interface. A comparison of the results with those calculated with a volume-of-fluid method showed that the numerical scheme presented here accurately describes the flow pattern within the entire liquid domain. Experiments were performed to partially validate the numerical predictions. The simulations reproduced accurately the experimental shape of the liquid cone jet, providing correct values of the emitted electric current even for configurations very close to the cone-jet stability limit. PMID:23005852

  6. Numerical simulation of electrospray in the cone-jet mode.

    PubMed

    Herrada, M A; López-Herrera, J M; Gañán-Calvo, A M; Vega, E J; Montanero, J M; Popinet, S

    2012-08-01

    We present a robust and computationally efficient numerical scheme for simulating steady electrohydrodynamic atomization processes (electrospray). The main simplification assumed in this scheme is that all the free electrical charges are distributed over the interface. A comparison of the results with those calculated with a volume-of-fluid method showed that the numerical scheme presented here accurately describes the flow pattern within the entire liquid domain. Experiments were performed to partially validate the numerical predictions. The simulations reproduced accurately the experimental shape of the liquid cone jet, providing correct values of the emitted electric current even for configurations very close to the cone-jet stability limit.

  7. Comparison of the AUSM(+) and H-CUSP Schemes for Turbomachinery Applications

    NASA Technical Reports Server (NTRS)

    Chima, Rodrick V.; Liou, Meng-Sing

    2003-01-01

    Many turbomachinery CFD codes use second-order central-difference (C-D) schemes with artificial viscosity to control point decoupling and to capture shocks. While C-D schemes generally give accurate results, they can also exhibit minor numerical problems including overshoots at shocks and at the edges of viscous layers, and smearing of shocks and other flow features. In an effort to improve predictive capability for turbomachinery problems, two C-D codes developed by Chima, RVCQ3D and Swift, were modified by the addition of two upwind schemes: the AUSM+ scheme developed by Liou, et al., and the H-CUSP scheme developed by Tatsumi, et al. Details of the C-D scheme and the two upwind schemes are described, and results of three test cases are shown. Results for a 2-D transonic turbine vane showed that the upwind schemes eliminated viscous layer overshoots. Results for a 3-D turbine vane showed that the upwind schemes gave improved predictions of exit flow angles and losses, although the HCUSP scheme predicted slightly higher losses than the other schemes. Results for a 3-D supersonic compressor (NASA rotor 37) showed that the AUSM+ scheme predicted exit distributions of total pressure and temperature that are not generally captured by C-D codes. All schemes showed similar convergence rates, but the upwind schemes required considerably more CPU time per iteration.

  8. Involution and Difference Schemes for the Navier-Stokes Equations

    NASA Astrophysics Data System (ADS)

    Gerdt, Vladimir P.; Blinkov, Yuri A.

    In the present paper we consider the Navier-Stokes equations for the two-dimensional viscous incompressible fluid flows and apply to these equations our earlier designed general algorithmic approach to generation of finite-difference schemes. In doing so, we complete first the Navier-Stokes equations to involution by computing their Janet basis and discretize this basis by its conversion into the integral conservation law form. Then we again complete the obtained difference system to involution with eliminating the partial derivatives and extracting the minimal Gröbner basis from the Janet basis. The elements in the obtained difference Gröbner basis that do not contain partial derivatives of the dependent variables compose a conservative difference scheme. By exploiting arbitrariness in the numerical integration approximation we derive two finite-difference schemes that are similar to the classical scheme by Harlow and Welch. Each of the two schemes is characterized by a 5×5 stencil on an orthogonal and uniform grid. We also demonstrate how an inconsistent difference scheme with a 3×3 stencil is generated by an inappropriate numerical approximation of the underlying integrals.

  9. A new flux splitting scheme for Euler equations of gas dynamics

    SciTech Connect

    Li, Xindong; Hu, Zongmin; Jiang, Zonglin

    2015-03-10

    A new flux splitting method named K-CUSP scheme is proposed in the paper. The major difference between K-CUSP and two traditional CUSP schemes (H-CUSP and E-CUSP) is that all kinematic quantities and all thermodynamic quantities in total enthalpy will be separately split into convective term and pressure term. The present scheme adopts the cell-face Mach number splitting method of AUSM+ scheme and the interface flux of pressure term is given a new way in the subsonic regime. Numerical solutions demonstrate that the new scheme inherits the simplicity and robustness of FVS schemes, which overcomes the shortcomings of pressure overshoot of shock wave in H-CUSP and E-CUSP schemes, but also retains the high-resolution of FDS schemes, which achieves the high accuracy of contact discontinuity and shock discontinuity.

  10. Three discontinuous Galerkin schemes for the anisotropic heat conduction equation on non-aligned grids

    NASA Astrophysics Data System (ADS)

    Held, M.; Wiesenberger, M.; Stegmeir, A.

    2016-02-01

    We present and discuss three discontinuous Galerkin (dG) discretizations for the anisotropic heat conduction equation on non-aligned cylindrical grids. Our non-aligned scheme relies on a self-adjoint local dG (LDG) discretization of the elliptic operator. It conserves the energy exactly and converges with arbitrary order. The pollution by numerical perpendicular heat fluxes decreases with superconvergence rates. We compare this scheme with aligned schemes that are based on the flux-coordinate independent approach for the discretization of parallel derivatives. Here, the dG method provides the necessary interpolation. The first aligned discretization can be used in an explicit time-integrator. However, the scheme violates conservation of energy and shows up stagnating convergence rates for very high resolutions. We overcome this partly by using the adjoint of the parallel derivative operator to construct a second self-adjoint aligned scheme. This scheme preserves energy, but reveals unphysical oscillations in the numerical tests, which result in a decreased order of convergence. Both aligned schemes exhibit low numerical heat fluxes into the perpendicular direction and are superior for flute-modes with finite parallel gradients. We build our argumentation on various numerical experiments on all three schemes for a general axisymmetric magnetic field, which is closed by a comparison to the aligned finite difference (FD) schemes of Stegmeir et al. (2014) and Stegmeir et al. (submitted for publication).

  11. Numerical simulation of shock wave propagation in flows

    NASA Astrophysics Data System (ADS)

    Rénier, Mathieu; Marchiano, Régis; Gaudard, Eric; Gallin, Louis-Jonardan; Coulouvrat, François

    2012-09-01

    Acoustical shock waves propagate through flows in many situations. The sonic boom produced by a supersonic aircraft influenced by winds, or the so-called Buzz-Saw-Noise produced by turbo-engine fan blades when rotating at supersonic speeds, are two examples of such a phenomenon. In this work, an original method called FLHOWARD, acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction, is presented. It relies on a scalar nonlinear wave equation, which takes into account propagation in a privileged direction (one-way approach), with diffraction, flow, heterogeneous and nonlinear effects. Theoretical comparison of the dispersion relations between that equation and parabolic equations (standard or wide angle) shows that this approach is more precise than the parabolic approach because there are no restrictions about the angle of propagation. A numerical procedure based on the standard split-step technique is used. It consists in splitting the nonlinear wave equation into simpler equations. Each of these equations is solved thanks to an analytical solution when it is possible, and a finite differences scheme in other cases. The advancement along the propagation direction is done with an implicit scheme. The validity of that numerical procedure is assessed by comparisons with analytical solutions of the Lilley's equation in waveguides for uniform or shear flows in linear regime. Attention is paid to the advantages and drawbacks of that method. Finally, the numerical code is used to simulate the propagation of sonic boom through a piece of atmosphere with flows and heterogeneities. The effects of the various parameters are analysed.

  12. Numerical Propulsion System Simulation

    NASA Technical Reports Server (NTRS)

    Naiman, Cynthia

    2006-01-01

    The NASA Glenn Research Center, in partnership with the aerospace industry, other government agencies, and academia, is leading the effort to develop an advanced multidisciplinary analysis environment for aerospace propulsion systems called the Numerical Propulsion System Simulation (NPSS). NPSS is a framework for performing analysis of complex systems. The initial development of NPSS focused on the analysis and design of airbreathing aircraft engines, but the resulting NPSS framework may be applied to any system, for example: aerospace, rockets, hypersonics, power and propulsion, fuel cells, ground based power, and even human system modeling. NPSS provides increased flexibility for the user, which reduces the total development time and cost. It is currently being extended to support the NASA Aeronautics Research Mission Directorate Fundamental Aeronautics Program and the Advanced Virtual Engine Test Cell (AVETeC). NPSS focuses on the integration of multiple disciplines such as aerodynamics, structure, and heat transfer with numerical zooming on component codes. Zooming is the coupling of analyses at various levels of detail. NPSS development includes capabilities to facilitate collaborative engineering. The NPSS will provide improved tools to develop custom components and to use capability for zooming to higher fidelity codes, coupling to multidiscipline codes, transmitting secure data, and distributing simulations across different platforms. These powerful capabilities extend NPSS from a zero-dimensional simulation tool to a multi-fidelity, multidiscipline system-level simulation tool for the full development life cycle.

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

    NASA Technical Reports Server (NTRS)

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

    1993-01-01

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

  14. Direct numerical simulations of a spatially developing plane wake

    NASA Technical Reports Server (NTRS)

    Maekawa, Hiroshi; Mansour, Nagi N.

    1992-01-01

    In the present paper, direct numerical methods by which to simulate the spatially developing free shear flows in the transitional region are described and the numerical results of a spatially developing plane wake are presented. The incompressible time-dependent Navier-Stokes equations were solved using Pade finite difference approximations in the streamwise direction, a mapped pseudospectral Fourier method in the cross-stream direction, and a third-order compact Runge-Kutta scheme for time advancement. The unstable modes of the Orr-Sommerfeld equations were used to perturb the inlet of the wake. Statistical analyses were performed and some numerical results were compared with experimental measurements. When only the fundamental mode is forced, the energy spectra show amplification of the fundamental and its higher harmonics. In this case, unperturbed alternate vortices develop in the saturation region of the wake. The phase jitter around the fundamental frequency plays a critical role in generating vortices of random shape and spacing. Large- and small-scale distortions of the fundamental structure are observed. Pairing of vortices of the same sign is observed, as well as vortex coupling of vortices of the opposite sign.

  15. An Improved Lattice Kinetic Scheme for Incompressible Viscous Fluid Flows

    NASA Astrophysics Data System (ADS)

    Suzuki, Kosuke; Inamuro, Takaji

    2014-01-01

    The lattice Boltzmann method (LBM) is an explicit numerical scheme for the incompressible Navier-Stokes equations (INSE) without integrating the Poisson equation for the pressure. In spite of its merit, the LBM has some drawbacks in accuracy. First, we review drawbacks for three numerical methods based on the LBM. The three methods are the LBM with the Bhatnagar-Gross-Krook model (LBGK), the lattice kinetic scheme (LKS) and the link-wise artificial compressibility method (LWACM). Second, in order to remedy the drawbacks, we propose an improved LKS. The present method incorporates (i) the scheme used in the LWACM for determining the kinematic viscosity, (ii) an iterative calculation of the pressure and (iii) a semi-implicit algorithm, while preserving the simplicity of the algorithm of the original LKS. Finally, in simulations of test problems, we find that the improved LKS eliminates the drawbacks and gives more accurate and stable results than LBGK, LKS and LWACM.

  16. The design and application of upwind schemes on unstructured meshes

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Jespersen, Dennis C.

    1989-01-01

    Solution and mesh generation algorithms for solving the Euler equations on unstructured meshes consisting of triangle and quadrilateral control volumes are presented. Cell-centered and mesh-vertex upwind finite-volume schemes are developed which utilize multi-dimensional monotone linear reconstruction procedures. These algorithms differ from existing algorithms (even on structured meshes). Numerical results in two dimensions are presented.

  17. Analysis of synchronous digital-modulation schemes for satellite communication

    NASA Technical Reports Server (NTRS)

    Takhar, G. S.; Gupta, S. C.

    1975-01-01

    The multipath communication channel for space communications is modeled as a multiplicative channel. This paper discusses the effects of multiplicative channel processes on the symbol error rate for quadrature modulation (QM) digital modulation schemes. An expression for the upper bound on the probability of error is derived and numerically evaluated. The results are compared with those obtained for additive channels.

  18. Plotting and Scheming

    NASA Technical Reports Server (NTRS)

    2004-01-01

    [figure removed for brevity, see original site] Figure 1 [figure removed for brevity, see original site] Figure 2 Click for larger view

    These two graphics are planning tools used by Mars Exploration Rover engineers to plot and scheme the perfect location to place the rock abrasion tool on the rock collection dubbed 'El Capitan' near Opportunity's landing site. 'El Capitan' is located within a larger outcrop nicknamed 'Opportunity Ledge.'

    The rover visualization team from NASA Ames Research Center, Moffett Field, Calif., initiated the graphics by putting two panoramic camera images of the 'El Capitan' area into their three-dimensional model. The rock abrasion tool team from Honeybee Robotics then used the visualization tool to help target and orient their instrument on the safest and most scientifically interesting locations. The blue circle represents one of two current targets of interest, chosen because of its size, lack of dust, and most of all its distinct and intriguing geologic features. To see the second target location, see the image titled 'Plotting and Scheming.'

    The rock abrasion tool is sensitive to the shape and texture of a rock, and must safely sit within the 'footprint' indicated by the blue circles. The rock area must be large enough to fit the contact sensor and grounding mechanism within the area of the outer blue circle, and the rock must be smooth enough to get an even grind within the abrasion area of the inner blue circle. If the rock abrasion tool were not grounded by its support mechanism or if the surface were uneven, it could 'run away' from its target. The rock abrasion tool is location on the rover's instrument deployment device, or arm.

    Over the next few martian days, or sols, the rover team will use these and newer, similar graphics created with more recent, higher-resolution panoramic camera images and super-spectral data from the miniature thermal emission spectrometer. These data will be used to pick the best

  19. A no-key-exchange secure image sharing scheme based on Shamir's three-pass cryptography protocol and the multiple-parameter fractional Fourier transform.

    PubMed

    Lang, Jun

    2012-01-30

    In this paper, we propose a novel secure image sharing scheme based on Shamir's three-pass protocol and the multiple-parameter fractional Fourier transform (MPFRFT), which can safely exchange information with no advance distribution of either secret keys or public keys between users. The image is encrypted directly by the MPFRFT spectrum without the use of phase keys, and information can be shared by transmitting the encrypted image (or message) three times between users. Numerical simulation results are given to verify the performance of the proposed algorithm.

  20. Comparison of two schemes for derivation of atmospheric motion vectors

    NASA Astrophysics Data System (ADS)

    Xu, J.; Holmlund, K.; Zhang, Q.; Schmetz, J.

    2002-07-01

    This paper presents the operational scheme of the National Satellite Meteorological Center (NSMC) of the China Meteorological Administration (CMA) to derive atmospheric motion vectors. The NSMC scheme is compared with a method developed at the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) in preparation for Meteosat Second Generation. Both schemes employ similar basic principles in terms of feature tracking and height assignment, however there are also some important differences. Furthermore, the EUMETSAT scheme assigns quality indicators to each wind vector at the end of the processing chain, whereas the NMSC scheme has inbuilt quality checking at different processing steps allowing for reinstatement of winds rejected by a first quality check. The evaluation of the performance is gained from two periods: a week in January and a week in July 1999. European Centre for Medium-Range Weather Forecast analyses and radiosonde data are used as independent data for evaluation of the two schemes. It is shown that correlating infrared image data with water vapor data before height adjustment, as performed in the NSMC scheme, has a great potential to better distinguish high and low cloud and to provide high-density wind fields. The utilization of radiative transfer calculations for the estimation of the height of thin clouds in the EUMETSAT scheme is shown to be imperative for good quality wind fields. Finally, the feature of the EUMETSAT scheme to assign quality indicators improves the utility of the wind vectors for use in numerical weather prediction models. It is suggested that a combination of the different features of both schemes potentially provide highly increased spatial density in the wind field with improved quality.

  1. Adaptive Numerical Dissipation Controls for High Order Methods

    NASA Technical Reports Server (NTRS)

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

    2001-01-01

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

  2. Numerical noise in ocean and estuarine models

    USGS Publications Warehouse

    Walters, R.; Carey, G.F.

    1984-01-01

    Approximate methods for solving the shallow water equations may lead to solutions exhibiting large fictitious, numerically-induced oscillations. The analysis of the discrete dispersion relation and modal solutions of small wavelengths provides a powerful technique for assessing the sensitivity of alternative numerical schemes to irregular data which may lead to such oscillatory numerical noise. For those schemes where phase speed vanishes at a finite wavenumber or there are multiple roots for wavenumber, oscillation modes can exist which are uncoupled from the dynamics of the problem. The discrete modal analysis approach is used here to identify two classes of spurious oscillation modes associated respectively with the two different asymptotic limits corresponding to estuarine and large scale ocean models. The analysis provides further insight into recent numerical results for models which include large spatial scales and Coriolis acceleration. ?? 1984.

  3. TVD scheme for computing open channel wave flows

    NASA Astrophysics Data System (ADS)

    Buntina, M. V.; Ostapenko, V. V.

    2008-12-01

    For the shallow water equations in the first approximation (Saint-Venant equations), a TVD scheme is developed for shock-capturing computations of open channel flows with discontinuous waves. The scheme is based on a special nondivergence approximation of the total momentum equation that does not involve integrals related to the cross-section pressure force and the channel wall reaction. In standard divergence difference schemes, most of the CPU time is spent on the computation of these integrals. Test computations demonstrate that the discontinuity relations reproduced by the scheme are accurate enough for actual discontinuous wave propagation to be numerically simulated. All the qualitatively distinct solutions for a dam collapsing in a trapezoidal channel with a contraction in the tailwater area are constructed as an example.

  4. Progress with multigrid schemes for hypersonic flow problems

    NASA Technical Reports Server (NTRS)

    Radespiel, R.; Swanson, R. C.

    1991-01-01

    Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm uses 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(exp 6) and Mach numbers up to 25.

  5. Interpolated Differential Operator (IDO) scheme for solving partial differential equations

    NASA Astrophysics Data System (ADS)

    Aoki, Takayuki

    1997-05-01

    We present a numerical scheme applicable to a wide variety of partial differential equations (PDEs) in space and time. The scheme is based on a high accurate interpolation of the profile for the independent variables over a local area and repetitive differential operations regarding PDEs as differential operators. We demonstrate that the scheme is uniformly applicable to hyperbolic, ellipsoidal and parabolic equations. The equations are solved in terms of the primitive independent variables, so that the scheme has flexibility for various types of equations including source terms. We find out that the conservation holds accurate when a Hermite interpolation is used. For compressible fluid problems, the shock interface is found to be sharply described by adding an artificial viscosity term.

  6. Conservative properties of finite difference schemes for incompressible flow

    NASA Technical Reports Server (NTRS)

    Morinishi, Youhei

    1995-01-01

    The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.

  7. Progress with multigrid schemes for hypersonic flow problems

    SciTech Connect

    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{sup 6} and Mach numbers up to 25. 32 refs., 31 figs., 1 tab.

  8. Efficient scheme for parametric fitting of data in arbitrary dimensions.

    PubMed

    Pang, Ning-Ning; Tzeng, Wen-Jer; Kao, Hisen-Ching

    2008-07-01

    We propose an efficient scheme for parametric fitting expressed in terms of the Legendre polynomials. For continuous systems, our scheme is exact and the derived explicit expression is very helpful for further analytical studies. For discrete systems, our scheme is almost as accurate as the method of singular value decomposition. Through a few numerical examples, we show that our algorithm costs much less CPU time and memory space than the method of singular value decomposition. Thus, our algorithm is very suitable for a large amount of data fitting. In addition, the proposed scheme can also be used to extract the global structure of fluctuating systems. We then derive the exact relation between the correlation function and the detrended variance function of fluctuating systems in arbitrary dimensions and give a general scaling analysis.

  9. Dispersion-relation-preserving finit difference schemes for computational acoustics

    SciTech Connect

    Tam, C.K.W.; Webb, J.C. )

    1993-08-01

    Acoustics problems are governed by the linearized Euler equations. According to wave propagation theory, the number of wave modes and their wave propagation characteristics are all encoded in the dispersion relation of the governing equations. Thus one is assured that the numerical solutions of high order finite difference scheme will have the same number of wave modes (namely, the acoustic, vorticity, and entropy waves), the same wave propagation characteristics (namely, nondispersive, nondissipative, and isotropic) and the same wave speeds as those of the solutions of the Euler equations if both systems of equations have the same dispersion relations. Finite difference schemes which have the same dispersion relations as the original partial differential equations are referred to as dispersion-relation-preserving (DRP) schemes. A way to construct time marching DRP schemes by optimizing the finite difference approximations of the space and time derivatives in the wave number and frequency space is proposed. The stability of these schemes is analyzed and a sufficient condition for numerical stability is established. A set of radiation and outflow boundary conditions compatible with the DRP schemes is constructed. These conditions are derived from the asymptotic solutions of the governing equations. The asymptotic solutions are found by the use of Fourier-Laplace transforms and the method of stationary phase. A sequence of numerical simulations has been carried out. These simulation are designed to test the effectiveness of the DRP schemes and the radiation and outflow boundary conditions. The computed solutions agree very favorably with the exact solutions. The radiation boundary conditions perform satisfactorily causing little acoustic reflections. The outflow boundary conditions are found to be quite transparent to outgoing disturbances even when the disturbances are made up of a combination of acoustic, vorticity, and entropy waves. 26 refs., 14 figs.

  10. Action Learning in Action: The Teaching Company Scheme.

    ERIC Educational Resources Information Center

    Peattie, Ken

    1996-01-01

    Examines the Teaching Company Scheme, which aims to raise the level of industrial performance by effective use of academic resources, improve industrial methods by effective implementation of advanced technology and new ideas, help graduates with careers for industry, and give academic staff broad and direct involvement with industry in order to…

  11. An Analysis of the Robustness of Composition Scoring Schemes.

    ERIC Educational Resources Information Center

    Perkins, Kyle

    Various claims have been made about the efficiency of different composition scoring schemes. This paper reports the results of a systematic analysis of the robustness of holistic scoring, analytical scoring, and an obective diagnostic test, Davidson's "Test of the Ability to Subordinate." Compositions from an advanced English as a Second Language…

  12. Efficient Semi-numerical Implementation of Global and Local Hybrid Functionals for Time-Dependent Density Functional Theory.

    PubMed

    Maier, Toni M; Bahmann, Hilke; Kaupp, Martin

    2015-09-01

    Local hybrid functionals with position-dependent exact-exchange admixture offer increased flexibility compared to global hybrids. For sufficiently advanced functionals of this type, this is expected to hold also for a wide range of electronic excitations within time-dependent density functional theory (TDDFT). Following a recent semi-numerical implementation of local hybrid functionals for ground-state self-consistent-field calculations (Bahmann, H.; Kaupp, M. J. Chem. Theory Comput. 2015, 11, 1540-1548), the first linear-response TDDFT implementation of local hybrids is reported, using a semi-numerical integration technique. The timings and accuracy of the semi-numerical implementation are evaluated by comparison with analytical schemes for time-dependent Hartree-Fock (TDHF) and for the TPSSh global hybrid. In combination with the RI approximation to the Coulomb part of the kernel, the semi-numerical implementation is faster than the existing analytical TDDFT/TDHF implementation of global hybrid functionals in the TURBOMOLE code, even for small systems and moderate basis sets. Moreover, timings for global and local hybrids are practically equal for the semi-numerical scheme. The way to TDDFT calculations with local hybrid functionals for large systems is thus now open, and more sophisticated parametrizations of local hybrids may be evaluated.

  13. Periastron advance in black-hole binaries.

    PubMed

    Le Tiec, Alexandre; Mroué, Abdul H; Barack, Leor; Buonanno, Alessandra; Pfeiffer, Harald P; Sago, Norichika; Taracchini, Andrea

    2011-09-30

    The general relativistic (Mercury-type) periastron advance is calculated here for the first time with exquisite precision in full general relativity. We use accurate numerical relativity simulations of spinless black-hole binaries with mass ratios 1/8≤m(1)/m(2)≤1 and compare with the predictions of several analytic approximation schemes. We find the effective-one-body model to be remarkably accurate and, surprisingly, so also the predictions of self-force theory [replacing m(1)/m(2)→m(1)m(2)/(m(1)+m(2))(2)]. Our results can inform a universal analytic model of the two-body dynamics, crucial for ongoing and future gravitational-wave searches. PMID:22107182

  14. Periastron advance in black-hole binaries.

    PubMed

    Le Tiec, Alexandre; Mroué, Abdul H; Barack, Leor; Buonanno, Alessandra; Pfeiffer, Harald P; Sago, Norichika; Taracchini, Andrea

    2011-09-30

    The general relativistic (Mercury-type) periastron advance is calculated here for the first time with exquisite precision in full general relativity. We use accurate numerical relativity simulations of spinless black-hole binaries with mass ratios 1/8≤m(1)/m(2)≤1 and compare with the predictions of several analytic approximation schemes. We find the effective-one-body model to be remarkably accurate and, surprisingly, so also the predictions of self-force theory [replacing m(1)/m(2)→m(1)m(2)/(m(1)+m(2))(2)]. Our results can inform a universal analytic model of the two-body dynamics, crucial for ongoing and future gravitational-wave searches.

  15. High order WENO scheme for computational cosmology

    NASA Astrophysics Data System (ADS)

    Roy, Ishani

    2010-11-01

    This doctoral dissertation is concerned with the formulation and application of a high order accurate numerical algorithm suitable in solving complex multi dimensional equations and the application of this algorithm to a problem in Astrophysics. The algorithm is designed with the aim of resolving solutions of partial differential equations with sharp fronts propagating with time. This high order accurate class of numerical technique is called a Weighted Essentially Non Oscillatory (WENO) method and is well suited for shock capturing in solving conservation laws. The numerical approximation method, in the algorithm, is coupled with high order time marching as well as integration techniques designed to reduce computational cost. This numerical algorithm is used in several applications in computational cosmology to help understand questions about certain physical phenomena which occurred during the formation and evolution of first generation stars. The thesis is divided broadly in terms of the algorithm and its application to the different galactic processes. The first chapter deals with the astrophysical problem and offers an introduction to the numerical algorithm. In chapter 2 we outline the mathematical model and the various functions and parameters associated with the model. We also give a brief description of the relevant physical phenomena and the conservation laws associated with them. In chapter 3, we give a detailed description of the higher order algorithm and its formulation. We also highlight the special techniques incorporated in the algorithm in order to make it more suitable for handling cases which are computationally intensive. In the later chapters, 4-7, we explore in detail the physical processes and the different applications of our numerical scheme. We calculate different results such as the time scale of a temperature coupling mechanism, radiation and intensity changes etc. Different tests are also performed to illustrate the stability and

  16. On smoothing of the Crank-Nicolson scheme and higher order schemes for pricing barrier options

    NASA Astrophysics Data System (ADS)

    Wade, B. A.; Khaliq, A. Q. M.; Yousuf, M.; Vigo-Aguiar, J.; Deininger, R.

    2007-07-01

    Most option pricing problems have nonsmooth payoffs or discontinuous derivatives at the exercise price. Discrete barrier options have not only nonsmooth payoffs but also time dependent discontinuities. In pricing barrier options, certain aspects are triggered if the asset price becomes too high or too low. Standard smoothing schemes used to solve problems with nonsmooth payoff do not work well for discrete barrier options because of discontinuities introduced in the time domain when each barrier is applied. Moreover, these unwanted oscillations become worse when estimating the hedging parameters, e.g., Delta and Gamma. We have an improved smoothing strategy for the Crank-Nicolson method which is unique in achieving optimal order convergence for barrier option problems. Numerical experiments are discussed for one asset and two asset problems. Time evolution graphs are obtained for one asset problems to show how option prices change with respect to time. This smoothing strategy is then extended to higher order methods using diagonal (m,m)--Pade main schemes under a smoothing strategy of using as damping schemes the (0,2m-1) subdiagonal Pade schemes.

  17. Ferrofluids: Modeling, numerical analysis, and scientific computation

    NASA Astrophysics Data System (ADS)

    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

  18. r-modified Crank-Nicholson difference schemes for one dimensional nonlinear viscous Burgers' equation for an incompressible flow

    NASA Astrophysics Data System (ADS)

    Ashyralyev, Allaberen; Gambo, Yusuf Ya'u.

    2016-08-01

    The nonlocal boundary value problem for viscous Burgers' equation is considered. Solutions to the 1-D equation are presented numerically by Rothe, Crank-Nicholson and r-modified Crank-Nicholson difference schemes. Matlab codes for all the three schemes are designed based on the idea of fixed-point iteration procedure and modified Gauss elimination method. The numerical results are compared.

  19. The simulation of dam-break flows by an improved predictor-corrector TVD scheme

    NASA Astrophysics Data System (ADS)

    Tseng, Ming Hseng; Chu, Chia R.

    This paper reports a finite difference predictor-corrector TVD (total variation diminishing) scheme for the computation of unsteady one-dimensional dam-break flows. The algorithm modified the widely used MacCormack scheme by implementing a conservative dissipation step to avoid any unphysical oscillation in the vicinity of strong gradients in the numerical solution. A general treatment for satisfying the entropy inequality condition is incorporated. The accuracy and robustness of the numerical scheme are verified with an analytic solution and experimental data. Furthermore, a sensitivity study is carried out to investigate the accuracy of four different versions of the predictor-corrector schemes. It is found that the numerical scheme will have less computational error and higher efficiency when the direction of the predictor-corrector step is the same as the direction of the shock wave propagation.

  20. Implicit total variation diminishing (TVD) schemes for steady-state calculations

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Warming, R. F.; Harten, A.

    1983-01-01

    The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme. Previously announced in STAR as N83-23085

  1. Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Warming, R. F.; Harten, A.

    1983-01-01

    The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

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

    NASA Astrophysics Data System (ADS)

    Bistrian, Diana Alina

    2013-10-01

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

  3. A second-order characteristic line scheme for solving a juvenile-adult model of amphibians.

    PubMed

    Deng, Keng; Wang, Yi

    2015-01-01

    In this paper, we develop a second-order characteristic line scheme for a nonlinear hierarchical juvenile-adult population model of amphibians. The idea of the scheme is not to follow the characteristics from the initial data, but for each time step to find the origins of the grid nodes at the previous time level. Numerical examples are presented to demonstrate the accuracy of the scheme and its capability to handle solutions with singularity.

  4. Classification schemes for arteriovenous malformations.

    PubMed

    Davies, Jason M; Kim, Helen; Young, William L; Lawton, Michael T

    2012-01-01

    The wide variety of arteriovenous malformation (AVM) anatomy, size, location, and clinical presentation makes patient selection for surgery a difficult process. Neurosurgeons have identified key factors that determine the risks of surgery and then devised classification schemes that integrate these factors, predict surgical results, and help select patients for surgery. These classification schemes have value because they transform complex decisions into simpler algorithms. In this review, the important grading schemes that have contributed to management of patients with brain AVMs are described, and our current approach to patient selection is outlined.

  5. A NON-OSCILLATORY SCHEME FOR OPEN CHANNEL FLOWS. (R825200)

    EPA Science Inventory

    In modeling shocks in open channel flows, the traditional finite difference schemes become inefficient and warrant special numerical treatment for smooth computations. This paper provides a general introduction to the non-oscillatory high-resolution methodology, coupled with the ...

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

    NASA Astrophysics Data System (ADS)

    Zagorodnov, Igor; Weiland, Thomas

    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.

  7. Well-balanced Component-wise Scheme for Shallow Water System

    SciTech Connect

    Louaked, M.; Tounsi, H.

    2010-11-25

    This paper presents a well-balanced numerical scheme for solving free surface flows involving wetting and drying. The proposed algorithm combines a component-wise approach with hydrostatic reconstruction strategy to compute flows over wet or dry surfaces and to satisfy the steady state condition of still water. The robustness of the proposed scheme is verified under several benchmark hydraulic tests.

  8. Round-off error propagation in four generally applicable, recursive, least-squares-estimation schemes

    NASA Technical Reports Server (NTRS)

    Verhaegen, M. H.

    1987-01-01

    The numerical robustness of four generally applicable, recursive, least-squares-estimation schemes is analyzed by means of a theoretical round-off propagation study. This study highlights a number of practical, interesting insights of widely used recursive least-squares schemes. These insights have been confirmed in an experimental study as well.

  9. WENO schemes on arbitrary unstructured meshes for laminar, transitional and turbulent flows

    SciTech Connect

    Tsoutsanis, Panagiotis Antoniadis, Antonios Foivos Drikakis, Dimitris

    2014-01-01

    This paper presents the development and implementation of weighted-essentially-non-oscillatory (WENO) schemes for viscous flows on arbitrary unstructured grids. WENO schemes up to fifth-order accurate have been implemented in conjunction with hybrid and non-hybrid unstructured grids. The schemes are investigated with reference to numerical and experimental results for the Taylor–Green vortex, as well as for laminar and turbulent flows around a sphere, and the turbulent shock-wave boundary layer interaction flow problem. The results show that the accuracy of the schemes depends on the arbitrariness of shape and orientation of the unstructured mesh elements, as well as the compactness of directional stencils. The WENO schemes provide a more accurate numerical framework compared to second-order and third-order total variation diminishing (TVD) methods, however, the fifth-order version of the schemes is computationally too expensive to make the schemes practically usable. On the other hand, the third-order variant offers an excellent numerical framework in terms of accuracy and computational cost compared to the fifth-order WENO and second-order TVD schemes. Parallelisation of the CFD code (henceforth labelled as UCNS3D), where the schemes have been implemented, shows that the present methods offer very good scalable performance.

  10. Unconditionally stable time marching scheme for Reynolds stress models

    NASA Astrophysics Data System (ADS)

    Mor-Yossef, Y.

    2014-11-01

    Progress toward a stable and efficient numerical treatment for the compressible Favre-Reynolds-averaged Navier-Stokes equations with a Reynolds-stress model (RSM) is presented. The mean-flow and the Reynolds stress model equations are discretized using finite differences on a curvilinear coordinates mesh. The convective flux is approximated by a third-order upwind biased MUSCL scheme. The diffusive flux is approximated using second-order central differencing, based on a full-viscous stencil. The novel time-marching approach relies on decoupled, implicit time integration, that is, the five mean-flow equations are solved separately from the seven Reynolds-stress closure equations. The key idea is the use of the unconditionally positive-convergent implicit scheme (UPC), originally developed for two-equation turbulence models. The extension of the UPC scheme for RSM guarantees the positivity of the normal Reynolds-stress components and the turbulence (specific) dissipation rate for any time step. Thanks to the UPC matrix-free structure and the decoupled approach, the resulting computational scheme is very efficient. Special care is dedicated to maintain the implicit operator compact, involving only nearest neighbor grid points, while fully supporting the larger discretized residual stencil. Results obtained from two- and three-dimensional numerical simulations demonstrate the significant progress achieved in this work toward optimally convergent solution of Reynolds stress models. Furthermore, the scheme is shown to be unconditionally stable and positive.

  11. Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

    NASA Technical Reports Server (NTRS)

    Yu, Sheng-Tao

    1992-01-01

    Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples

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

    NASA Astrophysics Data System (ADS)

    Liu, Fang; Lin, Lin; Vigil-Fowler, Derek; Lischner, Johannes; Kemper, Alexander F.; Sharifzadeh, Sahar; da Jornada, Felipe H.; Deslippe, Jack; Yang, Chao; Neaton, Jeffrey B.; Louie, Steven G.

    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.

  13. Design and Analysis of a Dynamic Mobility Management Scheme for Wireless Mesh Network

    PubMed Central

    Roy, Sudipta

    2013-01-01

    Seamless mobility management of the mesh clients (MCs) in wireless mesh network (WMN) has drawn a lot of attention from the research community. A number of mobility management schemes such as mesh network with mobility management (MEMO), mesh mobility management (M3), and wireless mesh mobility management (WMM) have been proposed. The common problem with these schemes is that they impose uniform criteria on all the MCs for sending route update message irrespective of their distinct characteristics. This paper proposes a session-to-mobility ratio (SMR) based dynamic mobility management scheme for handling both internet and intranet traffic. To reduce the total communication cost, this scheme considers each MC's session and mobility characteristics by dynamically determining optimal threshold SMR value for each MC. A numerical analysis of the proposed scheme has been carried out. Comparison with other schemes shows that the proposed scheme outperforms MEMO, M3, and WMM with respect to total cost. PMID:24311982

  14. High-Order Central WENO Schemes for Multi-Dimensional Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

    2002-01-01

    We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional Central WENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multi-dimensional fifth-order scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes.

  15. Assessment of Two Planetary Boundary Layer Schemes (ACM2 and YSU) within the Weather Research and Forecasting (WRF) Model

    NASA Astrophysics Data System (ADS)

    Wolff, J.; Harrold, M.; Xu, M.

    2014-12-01

    The Weather Research and Forecasting (WRF) model is a highly configurable numerical weather prediction system used in both research and operational forecasting applications. Rigorously testing select configurations and evaluating the performance for specific applications is necessary due to the flexibility offered by the system. The Developmental Testbed Center (DTC) performed extensive testing and evaluation with the Advanced Research WRF (ARW) dynamic core for two physics suite configurations with a goal of assessing the impact that the planetary boundary layer (PBL) scheme had on the final forecast performance. The baseline configuration was run with the Air Force Weather Agency's physics suite, which includes the Yonsei University PBL scheme, while the second configuration was substituted with the Asymmetric Convective Model (ACM2) PBL scheme. This presentation will focus on assessing the forecast performance of the two configurations; both configurations were run over the same set of cases, allowing for a direct comparison of performance. The evaluation was performed over a 15 km CONUS domain for a testing period from September 2013 through August 2014. Simulations were initialized every 36 hours and run out to 48 hours; a 6-hour "warm start" spin-up, including data assimilation using the Gridpoint Statistical Interpolation system preceded each simulation. The extensive testing period allows for robust results as well as the ability to investigate seasonal and regional differences between the two configurations. Results will focus on the evaluation of traditional verification metrics for surface and upper air variables, along with an assessment of statistical and practical significance.

  16. On large time step TVD scheme for hyperbolic conservation laws and its efficiency evaluation

    NASA Astrophysics Data System (ADS)

    Qian, ZhanSen; Lee, Chun-Hian

    2012-08-01

    A large time step (LTS) TVD scheme originally proposed by Harten is modified and further developed in the present paper and applied to Euler equations in multidimensional problems. By firstly revealing the drawbacks of Harten's original LTS TVD scheme, and reasoning the occurrence of the spurious oscillations, a modified formulation of its characteristic transformation is proposed and a high resolution, strongly robust LTS TVD scheme is formulated. The modified scheme is proven to be capable of taking larger number of time steps than the original one. Following the modified strategy, the LTS TVD schemes for Yee's upwind TVD scheme and Yee-Roe-Davis's symmetric TVD scheme are constructed. The family of the LTS schemes is then extended to multidimensional by time splitting procedure, and the associated boundary condition treatment suitable for the LTS scheme is also imposed. The numerical experiments on Sod's shock tube problem, inviscid flows over NACA0012 airfoil and ONERA M6 wing are performed to validate the developed schemes. Computational efficiencies for the respective schemes under different CFL numbers are also evaluated and compared. The results reveal that the improvement is sizable as compared to the respective single time step schemes, especially for the CFL number ranging from 1.0 to 4.0.

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

    PubMed

    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.

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

    PubMed

    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. PMID:27646969

  19. Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

    NASA Technical Reports Server (NTRS)

    Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)

    2000-01-01

    This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

  20. Extension of Low Dissipative High Order Hydrodynamics Schemes for MHD Equations

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sjoegreen, Bjoern; Mansour, Nagi (Technical Monitor)

    2002-01-01

    The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD (magnetohydrodynamic) equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvi-linear grids. The three features of the present MHD scheme over existing schemes in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion magnetized flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike existing schemes for the conservative MHD equations which suffer from ill-conditioned eigen-decompositions, the present scheme makes use of a well-conditioned eigen-decomposition to solve the conservative form of the MHD equations. This is due to, partly. the fact that the divergence of the magnetic field condition is a different type of constraint from its incompressible Navier-Stokes cousin. Third, a new approach to minimize the numerical error of the divergence free magnetic condition for high order scheme is introduced.

  1. Efficient implementation of essentially non-oscillatory shock capturing schemes

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang; Osher, Stanley

    1987-01-01

    In the computation of discontinuous solutions of hyperbolic conservation laws, TVD (total-variation-diminishing), TVB (total-variation-bounded) and the recently developed ENO (essentially non-oscillatory) schemes have proven to be very useful. In this paper two improvements are discussed: a simple TVD Runge-Kutta type time discretization, and an ENO construction procedure based on fluxes rather than on cell averages. These improvements simplify the schemes considerably -- especially for multi-dimensional problems or problems with forcing terms. Preliminary numerical results are also given.

  2. Fourier analysis of finite element preconditioned collocation schemes

    NASA Technical Reports Server (NTRS)

    Deville, Michel O.; Mund, Ernest H.

    1990-01-01

    The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

  3. Crab Crossing Schemes and Studies for Electron Ion Collider

    SciTech Connect

    S. Ahmed, Y. Derbenev, V. Morozov, A. Castilla, G.A. Krafft, B. Yunn, Y. Zhang, J.R. Delayen

    2011-09-01

    This report shows our progress in crab crossing consideration for future electron-ion collider envisioned at JLab. In this design phase, we are evaluating two crabbing schemes viz., the deflecting and dispersive. The mathematical formulations and lattice design for these schemes are discussed in this paper. Numerical simulations involving particle tracking through a realistic deflecting RF cavity and optics illustrate the desired crab tilt of 25 mrad for 1.35 MV. Evolution of beam propagation are shown which provides the physical insight of the crabbing phenomenon.

  4. Iterative schemes for nonsymmetric and indefinite elliptic boundary value problems

    SciTech Connect

    Bramble, J.H.; Leyk, Z.; Pasciak, J.E.

    1993-01-01

    The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space H ([Omega]) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right half of the complex plane. In fact, for symmetric indefinite problems, the iteration is reduced to a well-conditioned symmetric positive definite system which can be solved by conjugate gradient interation. Applications of the general theory as well as numerical examples are given. 20 refs., 8 tabs.

  5. On the application and extension of Harten's high resolution scheme

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Warming, R. F.; Harten, A.

    1982-01-01

    Extensions of a second order high resolution explicit method for the numerical computation of weak solutions of one dimensonal hyperbolic conservation laws are discussed. The main objectives were (1) to examine the shock resoluton of Harten's method for a two dimensional shock reflection problem, (2) to study the use of a high resolution scheme as a post-processor to an approximate steady state solution, and (3) to construct an implicit in the delta-form using Harten's scheme for the explicit operator and a simplified iteration matrix for the implicit operator.

  6. Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Harten, A.

    1985-01-01

    The Harten (1983, 1984) total variation-diminishing (TVD) schemes, constituting a one-parameter explicit and implicit, second-order-accurate family, have the property of not generating spurious oscillations when applied to one-dimensional, nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. These methods are presently extended to the multidimensional hyperbolic conservation laws in curvilinear coordinates. Means by which to linearize the implicit operator and solution strategies, in order to improve the computation efficiency of the implicit algorithm, are discussed. Numerical experiments with steady state airfoil calculations indicate that the proposed linearized implicit TVD schemes are accurate and robust.

  7. Grid and Zone Selection for AMR and ALE Schemes

    SciTech Connect

    Jameson, L; Johnson, J; Bihari, B; Eliason, D; Peyser, T

    2002-09-11

    Numerical algorithms are based fundamentally on polynomial interpolation. In regions of the computational domain where a low order polynomial fits the data well one will find small errors in the computed quantities. Therefore, in order to design robust methods for grid selection for AMR schemes or zone selection for ALE schemes, one needs some information on the local polynomial structure of the fields being computed. We provide here algorithms and software for selecting zones based on local estimates of polynomial interpolation error. The algorithms are based on multiresolution and wavelet analysis.

  8. A Gas-Kinetic Scheme for Reactive Flows

    NASA Technical Reports Server (NTRS)

    Lian,Youg-Sheng; Xu, Kun

    1998-01-01

    In this paper, the gas-kinetic BGK scheme for the compressible flow equations is extended to chemical reactive flow. The mass fraction of the unburnt gas is implemented into the gas kinetic equation by assigning a new internal degree of freedom to the particle distribution function. The new variable can be also used to describe fluid trajectory for the nonreactive flows. Due to the gas-kinetic BGK model, the current scheme basically solves the Navier-Stokes chemical reactive flow equations. Numerical tests validate the accuracy and robustness of the current kinetic method.

  9. Software Partitioning Schemes for Advanced Simulation Computer Systems. Final Report.

    ERIC Educational Resources Information Center

    Clymer, S. J.

    Conducted to design software partitioning techniques for use by the Air Force to partition a large flight simulator program for optimal execution on alternative configurations, this study resulted in a mathematical model which defines characteristics for an optimal partition, and a manually demonstrated partitioning algorithm design which…

  10. [Hypofractionation in locally advanced breast cancer: "flash" scheme].

    PubMed

    Padilha, Marisa; Gonçalves, Sara; Fardilha, Carlos; Melo, Gilberto; Miranda, Cristina; Alves, Paula

    2013-01-01

    Introdução: O carcinoma da mama é uma das principais causas de morte no nosso país. No Serviço de Radioterapia do Instituto Português de Oncologia de Coimbra de Coimbra utilizamos, desde há mais de 30 anos, um esquema de hipofraccionamento de radioterapia, denominado “Flash”, como opção terapêutica em doentes idosos ou com baixo Performance Status, portadores de carcinoma da mama localmente avançado ou com estádios IIb ou IV, com intenção neoadjuvante ou paliativa. Objectivos: Avaliar a resposta ao tratamento, nomeadamente sobrevivência global aos três anos, resposta local e toxicidades aguda e crónica, no grupo de doentes seleccionados submetidos a esquema de hipofraccionamento, em estudo retrospectivo. Metodologia: Entre Janeiro de 2006 e Dezembro de 2008, um total de 83 doentes com diagnóstico de Carcinoma da Mama Localmente Avançado ou com estádios IIb ou IV, foi submetido a “Flash” mamário. A dose de radioterapia prescrita foi de 13Gy / 2Fr / 3 dias (em 23 doentes - 27,7%) e 26Gy / 4Fr / 2,5 semanas (em 60 doentes - 72,3%), com fotões de 4 MV, sobre a mama afectada. Foi avaliada sobrevivência global segundo o método de Kaplan-Meier. A análise estatística foi efectuada através da aplicação SPSS, versão 17.0 e os testes estatísticos foram avaliados ao nível de significância de 5%. Resultados: 80 doentes (96,4%) que efectuaram “Flash” mamário eram do género feminino, com idades compreendidas entre os 59 e os 93 anos (idade média 80,72 + 5,87 anos) e Performance Status (Karnosfsky: 0 - 100) entre 90 e 50%. Em 72 doentes (86,7%) o diagnóstico histológico foi Carcinoma Ductal Invasivo. A cirurgia após a realização do “Flash” Mamário foi realizada em 44 doentes (53%) após evidência de resposta local à radioterapia, sendo a Mastectomia Radical Modificada a técnica cirúrgica mais frequente. Efectuou-se o diagnóstico de metastização óssea em 10 doentes (12%), sendo que a taxa de sobrevivência global foi de 68,7% (57 doentes), em quatro anos. Dez doentes (12%) morreram por progressão da doença ou persistência tumoral Em 42 doentes (50,6%) não se verificaram evidência ou progressão de doença e três doentes (3,6%) apresentaram melhoria clínica. Conclusões:O “Flash Mamário” é uma modalidade de tratamento segura, relativamente aos efeitos secundários, e opção terapêutica válida para doentes idosos ou com baixo Performance Status, com o diagnóstico de carcinoma localmente avançado ou estádio IIb ou IV, a título neoadjuvante ou paliativo. Há menor risco de recidiva/progressão, nos doentes com melhor estado geral, sendo a taxa de sobrevivência global maior.

  11. Numerical Considerations for Lagrangian Stochastic Dispersion Models: Eliminating Rogue Trajectories, and the Importance of Numerical Accuracy

    NASA Astrophysics Data System (ADS)

    Bailey, Brian N.

    2016-07-01

    When Lagrangian stochastic models for turbulent dispersion are applied to complex atmospheric flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behaviour in the numerical solution. Here we discuss numerical strategies for solving the non-linear Langevin-based particle velocity evolution equation that eliminate such unphysical behaviour in both Reynolds-averaged and large-eddy simulation applications. Extremely large or `rogue' particle velocities are caused when the numerical integration scheme becomes unstable. Such instabilities can be eliminated by using a sufficiently small integration timestep, or in cases where the required timestep is unrealistically small, an unconditionally stable implicit integration scheme can be used. When the generalized anisotropic turbulence model is used, it is critical that the input velocity covariance tensor be realizable, otherwise unphysical behaviour can become problematic regardless of the integration scheme or size of the timestep. A method is presented to ensure realizability, and thus eliminate such behaviour. It was also found that the numerical accuracy of the integration scheme determined the degree to which the second law of thermodynamics or `well-mixed condition' was satisfied. Perhaps more importantly, it also determined the degree to which modelled Eulerian particle velocity statistics matched the specified Eulerian distributions (which is the ultimate goal of the numerical solution). It is recommended that future models be verified by not only checking the well-mixed condition, but perhaps more importantly by checking that computed Eulerian statistics match the Eulerian statistics specified as inputs.

  12. Control Scheme of Tether Drag Deorbit System in Orbital Plane

    NASA Astrophysics Data System (ADS)

    Cui, Wei-Dong; Sun, Liang; Zhao, Guo-Wei

    In this paper, based on a dumbbell model of tethered satellite, a tension control scheme and a thrust control scheme of tether drag deorbit system in orbital plane are respectively proposed. In the tension control scheme, the tether tension can be measured by tension sensor and controlled by adjusting the tether length with a certain windlass mechanism, so that the librational angles could track the expected value; meanwhile, the tether could come back to the initial value. Because of the windlass mechanism, the slackness of tether can be avoided. In the thrust control scheme, the tether drag deorbit system is with a short tether in orbital maneuvering and the thrust acceleration imposed on the base satellite can be adjusted to avoid the slackness of tether and damp out the librational angles; besides, it is required that the regulation value of thrust acceleration meets with accuracy trajectory in practical engineering. Afterwards, a reasonable deorbit case of an abandoned GEO satellite is studied, in which the control of base satellite is considered; then, the advantages and disadvantages of two control schemes are analyzed and an improved control strategy is given. Numerical simulation results indicate that the slackness of tether can be eliminated and the librational angles are damped out according to the designed controllers, and the stability of the attitude of abandoned satellite is also guaranteed during flight. The proposed control schemes are feasible, which is useful for the flight safety.

  13. High resolution finite volume scheme for the quantum hydrodynamic equations

    NASA Astrophysics Data System (ADS)

    Lin, Chin-Tien; Yeh, Jia-Yi; Chen, Jiun-Yeu

    2009-03-01

    The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10 -5 to 10 -12. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10 -4. To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were

  14. High resolution finite volume scheme for the quantum hydrodynamic equations

    SciTech Connect

    Lin, C.-T. Yeh, J.-Y. Chen, J.-Y.

    2009-03-20

    The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10{sup -5} to 10{sup -12}. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10{sup -4}. To check the QFD finite difference numerical computations, one- and two-dimensional particle

  15. A review of thrust-vectoring schemes for fighter applications

    NASA Technical Reports Server (NTRS)

    Berrier, B. L.; Re, R. J.

    1978-01-01

    This paper presents a review of thrust vectoring schemes for advanced fighter applications. Results are presented from wind tunnel and system integration studies on thrust vectoring nozzle concepts. Vectoring data are presented from wind tunnel tests of axisymmetric C-D (convergent-divergent) and nonaxisymmetric wedge, C-D, single ramp and USB (upper-surface blowing) nozzle concepts. Results from recent airframe/nozzle integration studies on the impact of thrust vectoring on weight, cooling and performance characteristics are discussed. This review indicates that the aircraft designer has, at his disposal, a wide range of thrust vectoring schemes which offer potential for added or improved aircraft capability.

  16. A low-order coupled chemistry meteorology model for testing online and offline data assimilation schemes: L95-GRS (v1.0)

    NASA Astrophysics Data System (ADS)

    Haussaire, J.-M.; Bocquet, M.

    2016-01-01

    Bocquet and Sakov (2013) introduced a low-order model based on the coupling of the chaotic Lorenz-95 (L95) model, which simulates winds along a mid-latitude circle, with the transport of a tracer species advected by this zonal wind field. This model, named L95-T, can serve as a playground for testing data assimilation schemes with an online model. Here, the tracer part of the model is extended to a reduced photochemistry module. This coupled chemistry meteorology model (CCMM), the L95-GRS (generic reaction set) model, mimics continental and transcontinental transport and the photochemistry of ozone, volatile organic compounds and nitrogen oxides. Its numerical implementation is described. The model is shown to reproduce the major physical and chemical processes being considered. L95-T and L95-GRS are specifically designed and useful for testing advanced data assimilation schemes, such as the iterative ensemble Kalman smoother (IEnKS), which combines the best of ensemble and variational methods. These models provide useful insights prior to the implementation of data assimilation methods into larger models. We illustrate their use with data assimilation schemes on preliminary yet instructive numerical experiments. In particular, online and offline data assimilation strategies can be conveniently tested and discussed with this low-order CCMM. The impact of observed chemical species concentrations on the wind field estimate can be quantitatively assessed. The impacts of the wind chaotic dynamics and of the chemical species non-chaotic but highly nonlinear dynamics on the data assimilation strategies are illustrated.

  17. Numerical solution for option pricing with stochastic volatility model

    NASA Astrophysics Data System (ADS)

    Mariani, Andi; Nugrahani, Endar H.; Lesmana, Donny C.

    2016-01-01

    The option pricing equations derived from stochatic volatility models in finance are often cast in the form of nonlinear partial differential equations. To solve the equations, we used the upwind finite difference scheme for the spatial discretisation and a fully implicit time-stepping scheme. The result of this scheme is a matrix system in the form of an M-Matrix and we proof that the approximate solution converges to the viscosity solution to the equation by showing that the scheme is monotone, consistent and stable. Numerical experiments are implemented to show that the behavior and the order of convergence of upwind finite difference method.

  18. An operational phenological model for numerical pollen prediction

    NASA Astrophysics Data System (ADS)

    Scheifinger, Helfried

    2010-05-01

    The general prevalence of seasonal allergic rhinitis is estimated to be about 15% in Europe, and still increasing. Pre-emptive measures require both the reliable assessment of production and release of various pollen species and the forecasting of their atmospheric dispersion. For this purpose numerical pollen prediction schemes are being developed by a number of European weather services in order to supplement and improve the qualitative pollen prediction systems by state of the art instruments. Pollen emission is spatially and temporally highly variable throughout the vegetation period and not directly observed, which precludes a straightforward application of dispersion models to simulate pollen transport. Even the beginning and end of flowering, which indicates the time period of potential pollen emission, is not (yet) available in real time. One way to create a proxy for the beginning, the course and the end of the pollen emission is its simulation as function of real time temperature observations. In this work the European phenological data set of the COST725 initiative forms the basis of modelling the beginning of flowering of 15 species, some of which emit allergic pollen. In order to keep the problem as simple as possible for the sake of spatial interpolation, a 3 parameter temperature sum model was implemented in a real time operational procedure, which calculates the spatial distribution of the entry dates for the current day and 24, 48 and 72 hours in advance. As stand alone phenological model and combined with back trajectories it is thought to support the qualitative pollen prediction scheme at the Austrian national weather service. Apart from that it is planned to incorporate it in a numerical pollen dispersion model. More details, open questions and first results of the operation phenological model will be discussed and presented.

  19. A Study of Failure Events in Drinking Water Systems As a Basis for Comparison and Evaluation of the Efficacy of Potable Reuse Schemes

    PubMed Central

    Onyango, Laura A.; Quinn, Chloe; Tng, Keng H.; Wood, James G.; Leslie, Greg

    2015-01-01

    Potable reuse is implemented in several countries around the world to augment strained water supplies. This article presents a public health perspective on potable reuse by comparing the critical infrastructure and institutional capacity characteristics of two well-established potable reuse schemes with conventional drinking water schemes in developed nations that have experienced waterborne outbreaks. Analysis of failure events in conventional water systems between 2003 and 2013 showed that despite advances in water treatment technologies, drinking water outbreaks caused by microbial contamination were still frequent in developed countries and can be attributed to failures in infrastructure or institutional practices. Numerous institutional failures linked to ineffective treatment protocols, poor operational practices, and negligence were detected. In contrast, potable reuse schemes that use multiple barriers, online instrumentation, and operational measures were found to address the events that have resulted in waterborne outbreaks in conventional systems in the past decade. Syndromic surveillance has emerged as a tool in outbreak detection and was useful in detecting some outbreaks; increases in emergency department visits and GP consultations being the most common data source, suggesting potential for an increasing role in public health surveillance of waterborne outbreaks. These results highlight desirable characteristics of potable reuse schemes from a public health perspective with potential for guiding policy on surveillance activities. PMID:27053920

  20. Advances in Doppler OCT

    PubMed Central

    Liu, Gangjun; Chen, Zhongping

    2014-01-01

    We review the principle and some recent applications of Doppler optical coherence tomography (OCT). The advances of the phase-resolved Doppler OCT method are described. Functional OCT algorithms which are based on an extension of the phase-resolved scheme are also introduced. Recent applications of Doppler OCT for quantification of flow, imaging of microvasculature and vocal fold vibration, and optical coherence elastography are briefly discussed. PMID:24443649

  1. New parallelizable schemes for integrating the Dissipative Particle Dynamics with Energy conservation.

    PubMed

    Homman, Ahmed-Amine; Maillet, Jean-Bernard; Roussel, Julien; Stoltz, Gabriel

    2016-01-14

    This work presents new parallelizable numerical schemes for the integration of dissipative particle dynamics with energy conservation. So far, no numerical scheme introduced in the literature is able to correctly preserve the energy over long times and give rise to small errors on average properties for moderately small time steps, while being straightforwardly parallelizable. We present in this article two new methods, both straightforwardly parallelizable, allowing to correctly preserve the total energy of the system. We illustrate the accuracy and performance of these new schemes both on equilibrium and nonequilibrium parallel simulations. PMID:26772559

  2. New parallelizable schemes for integrating the Dissipative Particle Dynamics with Energy conservation

    NASA Astrophysics Data System (ADS)

    Homman, Ahmed-Amine; Maillet, Jean-Bernard; Roussel, Julien; Stoltz, Gabriel

    2016-01-01

    This work presents new parallelizable numerical schemes for the integration of dissipative particle dynamics with energy conservation. So far, no numerical scheme introduced in the literature is able to correctly preserve the energy over long times and give rise to small errors on average properties for moderately small time steps, while being straightforwardly parallelizable. We present in this article two new methods, both straightforwardly parallelizable, allowing to correctly preserve the total energy of the system. We illustrate the accuracy and performance of these new schemes both on equilibrium and nonequilibrium parallel simulations.

  3. Advances in Solar Power Forecasting

    NASA Astrophysics Data System (ADS)

    Haupt, S. E.; Kosovic, B.; Drobot, S.

    2014-12-01

    The National Center for Atmospheric Research and partners are building a blended SunCast Solar Power Forecasting system. This system includes several short-range nowcasting models and improves upon longer range numerical weather prediction (NWP) models as part of the "Public-Private-Academic Partnership to Advance Solar Power Forecasting." The nowcasting models being built include statistical learning models that include cloud regime prediction, multiple sky imager-based advection models, satellite image-based advection models, and rapid update NWP models with cloud assimilation. The team has also integrated new modules into the Weather Research and Forecasting Model (WRF) to better predict clouds, aerosols, and irradiance. The modules include a new shallow convection scheme; upgraded physics parameterizations of clouds; new radiative transfer modules that specify GHI, DNI, and DIF prediction; better satellite assimilation methods; and new aerosol estimation methods. These new physical models are incorporated into WRF-Solar, which is then integrated with publically available NWP models via the Dynamic Integrated Forecast (DICast) system as well as the Nowcast Blender to provide seamless forecasts at partner utility and balancing authority commercial solar farms. The improvements will be described and results to date discussed.

  4. Numerical simulation of heat exchanger

    SciTech Connect

    Sha, W.T.

    1985-01-01

    Accurate and detailed knowledge of the fluid flow field and thermal distribution inside a heat exchanger becomes invaluable as a large, efficient, and reliable unit is sought. This information is needed to provide proper evaluation of the thermal and structural performance characteristics of a heat exchanger. It is to be noted that an analytical prediction method, when properly validated, will greatly reduce the need for model testing, facilitate interpolating and extrapolating test data, aid in optimizing heat-exchanger design and performance, and provide scaling capability. Thus tremendous savings of cost and time are realized. With the advent of large digital computers and advances in the development of computational fluid mechanics, it has become possible to predict analytically, through numerical solution, the conservation equations of mass, momentum, and energy for both the shellside and tubeside fluids. The numerical modeling technique will be a valuable, cost-effective design tool for development of advanced heat exchangers.

  5. Numerical solution of the stochastic parabolic equation with the dependent operator coefficient

    SciTech Connect

    Ashyralyev, Allaberen; Okur, Ulker

    2015-09-18

    In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

  6. The upgraded scheme of Hefei Light Source

    SciTech Connect

    Li Weimin; Xu Hongliang; Wang Lin; Feng Guangyao; Zhang Shancai; Hao Hao

    2010-06-23

    To enhance the performance of Hefei Light Source, which was designed and constructed two decades ago, an upgrade project would be carried out in the near future. The detail upgrade scheme was described in this paper. Firstly, the magnet lattice of storage ring should be reconstructed with 4 DBA cells, whose advantages are lower beam emittance and more straight section available for insertion devices. Secondly, the beam diagnostics, main power supply, transverse and longitudinal multi-bunch feedback, beam control and manipulation system would be upgrade to improve the beam orbit stability. Finally, the injection system of storage ring and injector, which is composed of electron linac and beam transfer line, would be updated in order to assure smooth beam accumulation process under new low emittance lattice. With above improvement, it is hopeful to increase the brilliance of Hefei Light Source by two orders approximately. After three-year upgrade project, the performance of HLS would meet the demands of advanced SR users.

  7. Energy partitioning schemes: a dilemma.

    PubMed

    Mayer, I

    2007-01-01

    Two closely related energy partitioning schemes, in which the total energy is presented as a sum of atomic and diatomic contributions by using the "atomic decomposition of identity", are compared on the example of N,N-dimethylformamide, a simple but chemically rich molecule. Both schemes account for different intramolecular interactions, for instance they identify the weak C-H...O intramolecular interactions, but give completely different numbers. (The energy decomposition scheme based on the virial theorem is also considered.) The comparison of the two schemes resulted in a dilemma which is especially striking when these schemes are applied for molecules distorted from their equilibrium structures: one either gets numbers which are "on the chemical scale" and have quite appealing values at the equilibrium molecular geometries, but exhibiting a counter-intuitive distance dependence (the two-center energy components increase in absolute value with the increase of the interatomic distances)--or numbers with too large absolute values but "correct" distance behaviour. The problem is connected with the quick decay of the diatomic kinetic energy components.

  8. Nonlinear secret image sharing scheme.

    PubMed

    Shin, Sang-Ho; Lee, Gil-Je; Yoo, Kee-Young

    2014-01-01

    Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2 m⌉ bit-per-pixel (bpp), respectively.

  9. Nonlinear secret image sharing scheme.

    PubMed

    Shin, Sang-Ho; Lee, Gil-Je; Yoo, Kee-Young

    2014-01-01

    Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2 m⌉ bit-per-pixel (bpp), respectively. PMID:25140334

  10. Energy partitioning schemes: a dilemma.

    PubMed

    Mayer, I

    2007-01-01

    Two closely related energy partitioning schemes, in which the total energy is presented as a sum of atomic and diatomic contributions by using the "atomic decomposition of identity", are compared on the example of N,N-dimethylformamide, a simple but chemically rich molecule. Both schemes account for different intramolecular interactions, for instance they identify the weak C-H...O intramolecular interactions, but give completely different numbers. (The energy decomposition scheme based on the virial theorem is also considered.) The comparison of the two schemes resulted in a dilemma which is especially striking when these schemes are applied for molecules distorted from their equilibrium structures: one either gets numbers which are "on the chemical scale" and have quite appealing values at the equilibrium molecular geometries, but exhibiting a counter-intuitive distance dependence (the two-center energy components increase in absolute value with the increase of the interatomic distances)--or numbers with too large absolute values but "correct" distance behaviour. The problem is connected with the quick decay of the diatomic kinetic energy components. PMID:17328441

  11. Nonlinear Secret Image Sharing Scheme

    PubMed Central

    Shin, Sang-Ho; Yoo, Kee-Young

    2014-01-01

    Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2⁡m⌉ bit-per-pixel (bpp), respectively. PMID:25140334

  12. Numerical Modeling of Weakly Ionized Plasmas

    NASA Astrophysics Data System (ADS)

    O'Sullivan, S.; Downes, T. P.

    2006-12-01

    Numerical investigations of astrophysical plasma flows often rely on the ideal magnetohydrodynamic (MHD) approximation. In the case of weakly ionized plasmas the most questionable assumption of this is that the gas may be adequately approximated as a perfectly conducting single fluid. In direct consequence, the field lines are frozen into the bulk flow and may exert unrealistic forces on the gas in situations where magnetic diffusion should be important. A more appropriate treatment under these conditions is to discard the flux-freezing approximation by allowing charged species (i.e. electrons, ions, charge carrying dust grains) to have relative motions and compete in their interactions with the neutral gas component and the magnetic field. Taking such a multifluid approach admits ambipolar and Hall diffusion effects which can have a significant influence on the dynamics of the plasma. Conventional explicit numerical schemes have been shown to have a vanishing stable time step limit as the Hall effect becomes large and implicit schemes are, by nature, difficult to implement on distributed architectures, particularly when adaptive mesh refinement (AMR) is used. We present a novel explicit numerical scheme which allows a very significant claw-back of the deficit in efficiency when compared with implicit techniques. In addition, given that the scheme is explicit, it is straightforward to plug into existing AMR packages.

  13. Really TVD advection schemes for the depth-integrated transport equation

    NASA Astrophysics Data System (ADS)

    Mercier, Ch.; Delhez, E. J. M.

    This paper explores the use of TVD advection schemes to solve the depth-integrated transport equation for tracers in finite volume marine models. Numerical experiments show that the blind application of the usual TVD schemes and associated flux limiters can lead to non-TVD solutions when applied in complex geometries. Spatial and/or temporal variations of the local bathymetry can indeed break the TVD property of the usual schemes. Really TVD schemes can be recovered by taking into account the local depth and its variations in the formulation of the flux limiters. Using this approach, a generalized superbee limiter is introduced and validated.

  14. Second order finite volume scheme for Maxwell's equations with discontinuous electromagnetic properties on unstructured meshes

    SciTech Connect

    Ismagilov, Timur Z.

    2015-02-01

    This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.

  15. A new class of high accuracy TVD schemes for hyperbolic conservation laws. [Total Variation Diminishing

    NASA Technical Reports Server (NTRS)

    Chakravarthy, S. R.; Osher, S.

    1985-01-01

    A new family of high accuracy Total Variation Diminishing (TVD) schemes has been developed. Members of the family include the conventional second-order TVD upwind scheme, various other second-order accurate TVD schemes with lower truncation error, and even a third-order accurate TVD approximation. All the schemes are defined with a five-point grid bandwidth. In this paper, the new algorithms are described for scalar equations, systems, and arbitrary coordinates. Selected numerical results are provided to illustrate the new algorithms and their properties.

  16. Numerical simulations of cryogenic cavitating flows

    NASA Astrophysics Data System (ADS)

    Kim, Hyunji; Kim, Hyeongjun; Min, Daeho; Kim, Chongam

    2015-12-01

    The present study deals with a numerical method for cryogenic cavitating flows. Recently, we have developed an accurate and efficient baseline numerical scheme for all-speed water-gas two-phase flows. By extending such progress, we modify the numerical dissipations to be properly scaled so that it does not show any deficiencies in low Mach number regions. For dealing with cryogenic two-phase flows, previous EOS-dependent shock discontinuity sensing term is replaced with a newly designed EOS-free one. To validate the proposed numerical method, cryogenic cavitating flows around hydrofoil are computed and the pressure and temperature depression effect in cryogenic cavitation are demonstrated. Compared with Hord's experimental data, computed results are turned out to be satisfactory. Afterwards, numerical simulations of flow around KARI turbopump inducer in liquid rocket are carried out under various flow conditions with water and cryogenic fluids, and the difference in inducer flow physics depending on the working fluids are examined.

  17. A family of high-order targeted ENO schemes for compressible-fluid simulations

    NASA Astrophysics Data System (ADS)

    Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.

    2016-01-01

    Although classical WENO schemes have achieved great success and are widely accepted, they exhibit several shortcomings. They are too dissipative for direct simulations of turbulence and lack robustness when very-high-order versions are applied to complex flows. In this paper, we propose a family of high-order targeted ENO schemes which are applicable for compressible-fluid simulations involving a wide range of flow scales. In order to increase the numerical robustness as compared to very-high-order classical WENO schemes, the reconstruction dynamically assembles a set of low-order candidate stencils with incrementally increasing width. While discontinuities and small-scale fluctuations are efficiently separated, the numerical dissipation is significantly diminished by an ENO-like stencil selection, which either applies a candidate stencil with its original linear weight, or removes its contribution when it is crossed by a discontinuity. The background linear scheme is optimized under the constraint of preserving an approximate dispersion-dissipation relation. By means of quasi-linear analyses and practical numerical experiments, a set of case-independent parameters is determined. The general formulation of arbitrarily high-order schemes is presented in a straightforward way. A variety of benchmark-test problems, including broadband waves, strong shock and contact discontinuities are studied. Compared to well-established classical WENO schemes, the present schemes exhibit significantly improved robustness, low numerical dissipation and sharp discontinuity capturing. They are particularly suitable for DNS and LES of shock-turbulence interactions.

  18. Fourth-Order Accurate IDO Scheme Using Gradient-Staggered Interpolation

    NASA Astrophysics Data System (ADS)

    Imai, Yohsuke; Aoki, Takayuki

    An Interpolated Differential Operator (IDO) scheme using a new interpolation function is proposed. The gradient of the dependent variable is calculated at the position shifted by a half grid size from that of the physical value. A fourth-order Hermite-interpolation function is constructed locally using both the value and the gradient defined at staggered positions. The numerical solutions for the Poisson, diffusion, advection and wave equations have fourth-order accuracy in space. In particular, for the Poisson and diffusion equations, the Gradient-Staggered (G-S) IDO scheme shows better accuracy than the original IDO scheme. As a practical application, the Direct Numerical Simulation (DNS) for two-dimensional isotropic homogeneous turbulence is examined and a comparable result with that of the original IDO scheme is obtained. The G-S IDO scheme clearly contributes to high-accurate computations for solving partial differential equations in computational mechanics.

  19. Analysis of Finite Difference Discretization Schemes for Diffusion in Spheres with Variable Diffusivity

    PubMed Central

    Versypt, Ashlee N. Ford; Braatz, Richard D.

    2014-01-01

    Two finite difference discretization schemes for approximating the spatial derivatives in the diffusion equation in spherical coordinates with variable diffusivity are presented and analyzed. The numerical solutions obtained by the discretization schemes are compared for five cases of the functional form for the variable diffusivity: (I) constant diffusivity, (II) temporally-dependent diffusivity, (III) spatially-dependent diffusivity, (IV) concentration-dependent diffusivity, and (V) implicitly-defined, temporally- and spatially-dependent diffusivity. Although the schemes have similar agreement to known analytical or semi-analytical solutions in the first four cases, in the fifth case for the variable diffusivity, one scheme produces a stable, physically reasonable solution, while the other diverges. We recommend the adoption of the more accurate and stable of these finite difference discretization schemes to numerically approximate the spatial derivatives of the diffusion equation in spherical coordinates for any functional form of variable diffusivity, especially cases where the diffusivity is a function of position. PMID:25642003

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

    SciTech Connect

    Sha, Wei . E-mail: ws108@ahu.edu.cn; Huang, Zhixiang; Wu, Xianliang; Chen, Mingsheng

    2007-07-01

    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.