Oligomeric Amyloid-β Peptide on Sialylic Lewisx-Selectin Bonding at Cerebral Endothelial Surface.

PubMed

Askarova, Sholpan; Sun, Grace Y; Meininger, Gerald A; Lee, James

2014-01-01

Alzheimer's disease (AD) is a chronic neurodegenerative disorder, which affects approximately 10% of the population aged 65 and 40% of people over the age 80. Currently, AD is on the list of diseases with no effective treatment. Thus, the study of molecular and cellular mechanisms of AD progression is of high scientific and practical importance. In fact, dysfunction of the blood-brain barrier (BBB) plays an important role in the onset and progression of the disease. Increased deposition of amyloid b peptide (Aβ) in cerebral vasculature and enhanced transmigration of monocytes across the BBB are frequently observed in AD brains and are some of the pathological hallmarks of the diseases. Since the transmigration of monocytes across the BBB is both a mechanical and a biochemical process, the expression of adhesion molecules and mechanical properties of endothelial cells are the critical factors that require investigation. Because of recent advances in the biological applications of atomic force microscopy (AFM), we applied AFM with cantilever tips bio-functionalized by sLe x in combination with the advanced immunofluorescent microscopy (QIM) to study the direct effects of Aβ 42 oligomers on the selectins expression, actin polymerization, and cellular mechanical and adhesion properties in cerebral endothelial cells (mouse bEnd3 line and primary human CECs) and find a possible way to attenuate these effects. QIM results showed that Aβ 42 increased the expressions of P-selectin on the cell surface and enhanced actin polymerization. Consistent with our QIM results, AFM data showed that Aβ 42 increased the probability of cell adhesion with sLe x -coated cantilever and cell stiffness. These effects were counteracted by lovstatin, a cholesterol-lowering drug. Surprisingly, the apparent rupture force of sLe x -selectin bonding was significantly lower after treatment with Aβ 42 , as compared with the control (i.e. no treatment). Similar results were also obtained when cells were treated with latruculin A (F-actin-disrupting drug). These results suggest that the decrease in the apparent rupture force of sLe x -selectin bonding is the consequence of the dissociation of adhesion between the cytoskeleton and the bilayer membrane induced by Aβ 42 . The major causes of excess mortality in the first group were neoplams (30.6%), hypertension (23.8%), and myocardial infarction (22.6%). The effects of radiation influenced mortality in the second group were 2-2.5 times lower than the first group. The studies of the effects of Aβ 42 on the adhesion properties of cerebral endothelial cells and how pharmacological agents (e.g. statin) counteract these effects should prove to provide insights into the mechanism of inflammation in Alzheimer's brains and the design of therapeutic treatments of the disease.

Freshness assessments of Moroccan sardine (Sardina pilchardus): comparison of overall sensory changes to instrumentally determined volatiles.

PubMed

Triqui, Réda; Bouchriti, Nourredine

2003-12-17

Freshness of ice-stored sardine was assessed by two sensory methods, the quality index method (QIM) and the European Union freshness grading system, and by instrumental means using the method of aroma extract dilution analysis. Screening of sardine potent volatiles was carried out at three freshness stages. In the very fresh state, the plant-like fresh volatiles dominated the odor pattern, with the exception of methional. Overall odor changes in sardine throughout storage correlated with changes in the concentration of some potent volatiles: after 2 days of ice storage, (Z)-4-heptenal, (Z)-1,5-octadien-3-one, and methional imparted an overall "fishy" odor character to sardine, whereas at a lower sensory grade (B), the compounds (E)-2-nonenal and (E,Z)-2,6-nonadienal could be, in part, associated with the slightly rancid aroma top notes. Trimethylamine was detected as a highly volatile odorant using solid-phase microextraction (SPME) headspace analysis of refrigerator-stored sardine. Intensity and sensory characteristics of some SPME determined volatiles, for example, 3-methylnonane-2,4-dione, were closely related to overall odor changes. SPME headspace analysis may be useful in the characterization of off-flavors in fish.

Amyloid-β peptide on sialyl-Lewis(X)-selectin-mediated membrane tether mechanics at the cerebral endothelial cell surface.

PubMed

Askarova, Sholpan; Sun, Zhe; Sun, Grace Y; Meininger, Gerald A; Lee, James C-M

2013-01-01

Increased deposition of amyloid-β peptide (Aβ) at the cerebral endothelial cell (CEC) surface has been implicated in enhancement of transmigration of monocytes across the brain blood barrier (BBB) in Alzheimer's disease (AD). In this study, quantitative immunofluorescence microscopy (QIM) and atomic force microscopy (AFM) with cantilevers biofunctionalized by sialyl-Lewis(x) (sLe(x)) were employed to investigate Aβ-altered mechanics of membrane tethers formed by bonding between sLe(x) and p-selectin at the CEC surface, the initial mechanical step governing the transmigration of monocytes. QIM results indicated the ability for Aβ to increase p-selectin expression at the cell surface and promote actin polymerization in both bEND3 cells (immortalized mouse CECs) and human primary CECs. AFM data also showed the ability for Aβ to increase cell stiffness and adhesion probability in bEND3 cells. On the contrary, Aβ lowered the overall force of membrane tether formation (Fmtf ), and produced a bimodal population of Fmtf , suggesting subcellular mechanical alterations in membrane tethering. The lower Fmtf population was similar to the results obtained from cells treated with an F-actin-disrupting drug, latrunculin A. Indeed, AFM results also showed that both Aβ and latrunculin A decreased membrane stiffness, suggesting a lower membrane-cytoskeleton adhesion, a factor resulting in lower Fmtf . In addition, these cerebral endothelial alterations induced by Aβ were abrogated by lovastatin, consistent with its anti-inflammatory effects. In sum, these results demonstrated the ability for Aβ to enhance p-selectin expression at the CEC surface and induce cytoskeleton reorganization, which in turn, resulted in changes in membrane-cytoskeleton adhesion and membrane tethering, mechanical factors important in transmigration of monocytes through the BBB.

Amyloid-β Peptide on Sialyl-LewisX-Selectin-Mediated Membrane Tether Mechanics at the Cerebral Endothelial Cell Surface

PubMed Central

Askarova, Sholpan; Sun, Zhe; Sun, Grace Y.; Meininger, Gerald A.; Lee, James C-M.

2013-01-01

Increased deposition of amyloid-β peptide (Aβ) at the cerebral endothelial cell (CEC) surface has been implicated in enhancement of transmigration of monocytes across the brain blood barrier (BBB) in Alzheimer's disease (AD). In this study, quantitative immunofluorescence microscopy (QIM) and atomic force microscopy (AFM) with cantilevers biofunctionalized by sialyl-Lewisx (sLex) were employed to investigate Aβ-altered mechanics of membrane tethers formed by bonding between sLex and p-selectin at the CEC surface, the initial mechanical step governing the transmigration of monocytes. QIM results indicated the ability for Aβ to increase p-selectin expression at the cell surface and promote actin polymerization in both bEND3 cells (immortalized mouse CECs) and human primary CECs. AFM data also showed the ability for Aβ to increase cell stiffness and adhesion probability in bEND3 cells. On the contrary, Aβ lowered the overall force of membrane tether formation (Fmtf), and produced a bimodal population of Fmtf, suggesting subcellular mechanical alterations in membrane tethering. The lower Fmtf population was similar to the results obtained from cells treated with an F-actin-disrupting drug, latrunculin A. Indeed, AFM results also showed that both Aβ and latrunculin A decreased membrane stiffness, suggesting a lower membrane-cytoskeleton adhesion, a factor resulting in lower Fmtf. In addition, these cerebral endothelial alterations induced by Aβ were abrogated by lovastatin, consistent with its anti-inflammatory effects. In sum, these results demonstrated the ability for Aβ to enhance p-selectin expression at the CEC surface and induce cytoskeleton reorganization, which in turn, resulted in changes in membrane-cytoskeleton adhesion and membrane tethering, mechanical factors important in transmigration of monocytes through the BBB. PMID:23593361

Culturally competent health care from the immigrant lens: a qualitative interpretive meta-synthesis (QIMS).

PubMed

Maleku, Arati; Aguirre, Regina T P

2014-01-01

Immigrant groups comprise a large segment of ethnic minorities in the United States. Although the literature is rich with strategies to deliver culturally and linguistically appropriate services to eliminate health inequities, studies addressing cultural competence from the immigrant's perspective are limited. Further research is needed to build knowledge of the predictors and needs of this population, and to influence health care policy and practice. Using qualitative interpretive meta-synthesis, this study describes the lived experience of immigrants accessing health care to understand the essence of cultural competence in health care through their lens. Findings provide insight on expanding the definition of culturally competent health care beyond language, behaviors, attitudes, and policies.

VizieR Online Data Catalog: Stellar yields and the initial mass function (Molla+, 2015)

NASA Astrophysics Data System (ADS)

Molla, M.; Cavichia, O.; Gavilan, M.; Gibson, B. K.

2017-10-01

These tables give the theoretical chemical evolution models applied for the Milky Way Galaxy (MWG) from the cited paper. Basically give tables 2, 4 of stellar yields used and results of table 6 for the 144 models computed that work. Tables 2 and 4 give the stellar yields q_i(m) and remmnant mass for low and intermediate stars and massive stars, respectively, in a similar format for all authors. Table 6 gives the value of Chi2 for the 144 models computed for MWG using those stellar yields and different Initial Mass Function (see paper). Moreover, we give the table with results of the present time state of the Galactic disk for these 144 models. (12 data files).

Color change of the snapper (Pagrus auratus) and Gurnard (Chelidonichthys kumu) skin and eyes during storage: effect of light polarization and contact with ice.

PubMed

Balaban, Murat O; Stewart, Kelsie; Fletcher, Graham C; Alçiçek, Zayde

2014-12-01

Ten gurnard and 10 snapper were stored on ice. One side always contacted the ice; the other side was always exposed to air. At different intervals for up to 12 d, the fish were placed in a light box, and the images of both sides were taken using polarized and nonpolarized illumination. Image analysis resulted in average L*, a*, and b* values of skin, and average L* values of the eyes. The skin L* value of gurnard changed significantly over time while that of snapper was substantially constant. The a* and b* values of both fish decreased over time. The L* values of eyes were significantly lower for polarized images, and significantly lower for the side of fish exposed to air only. This may be a concern in quality evaluation methods such as QIM. The difference of colors between the polarized and nonpolarized images was calculated to quantify the reflection off the surface of fish. For accurate measurement of surface color and eye color, use of polarized light is recommended. © 2014 Institute of Food Technologists®

Quantum-Inspired Maximizer

NASA Technical Reports Server (NTRS)

Zak, Michail

2008-01-01

A report discusses an algorithm for a new kind of dynamics based on a quantum- classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen 'computational' potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear. Special attention is paid to simulation of integer programming and NP-complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum- classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).

Drift-free MPEG-4 AVC semi-fragile watermarking

NASA Astrophysics Data System (ADS)

Hasnaoui, M.; Mitrea, M.

2014-02-01

While intra frame drifting is a concern for all types of MPEG-4 AVC compressed-domain video processing applications, it has a particular negative impact in watermarking. In order to avoid the drift drawbacks, two classes of solutions are currently considered in the literature. They try either to compensate the drift distortions at the expense of complex decoding/estimation algorithms or to restrict the insertion to the blocks which are not involved in the prediction, thus reducing the data payload. The present study follows a different approach. First, it algebraically models the drift distortion spread problem by considering the analytic expressions of the MPEG-4 AVC encoding operations. Secondly, it solves the underlying algebraic system under drift-free constraints. Finally, the advanced solution is adapted to take into account the watermarking peculiarities. The experiments consider an m-QIM semi-fragile watermarking method and a video surveillance corpus of 80 minutes. For prescribed data payload (100 bit/s), robustness (BER < 0.1 against transcoding at 50% in stream size), fragility (frame modification detection with accuracies of 1/81 from the frame size and 3s) and complexity constraints, the modified insertion results in gains in transparency of 2 dB in PSNR, of 0.4 in AAD, of 0.002 in IF, of 0.03 in SC, of 0.017 NCC and 22 in DVQ.

MPEG-4 AVC saliency map computation

NASA Astrophysics Data System (ADS)

Ammar, M.; Mitrea, M.; Hasnaoui, M.

2014-02-01

A saliency map provides information about the regions inside some visual content (image, video, ...) at which a human observer will spontaneously look at. For saliency maps computation, current research studies consider the uncompressed (pixel) representation of the visual content and extract various types of information (intensity, color, orientation, motion energy) which are then fusioned. This paper goes one step further and computes the saliency map directly from the MPEG-4 AVC stream syntax elements with minimal decoding operations. In this respect, an a-priori in-depth study on the MPEG-4 AVC syntax elements is first carried out so as to identify the entities appealing the visual attention. Secondly, the MPEG-4 AVC reference software is completed with software tools allowing the parsing of these elements and their subsequent usage in objective benchmarking experiments. This way, it is demonstrated that an MPEG-4 saliency map can be given by a combination of static saliency and motion maps. This saliency map is experimentally validated under a robust watermarking framework. When included in an m-QIM (multiple symbols Quantization Index Modulation) insertion method, PSNR average gains of 2.43 dB, 2.15dB, and 2.37 dB are obtained for data payload of 10, 20 and 30 watermarked blocks per I frame, i.e. about 30, 60, and 90 bits/second, respectively. These quantitative results are obtained out of processing 2 hours of heterogeneous video content.

Some results on numerical methods for hyperbolic conservation laws

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang Huanan.

1989-01-01

This dissertation contains some results on the numerical solutions of hyperbolic conservation laws. (1) The author introduced an artificial compression method as a correction to the basic ENO schemes. The method successfully prevents contact discontinuities from being smeared. This is achieved by increasing the slopes of the ENO reconstructions in such a way that the essentially non-oscillatory property of the schemes is kept. He analyzes the non-oscillatory property of the new artificial compression method by applying it to the UNO scheme which is a second order accurate ENO scheme, and proves that the resulting scheme is indeed non-oscillatory. Extensive 1-Dmore » numerical results and some preliminary 2-D ones are provided to show the strong performance of the method. (2) He combines the ENO schemes and the centered difference schemes into self-adjusting hybrid schemes which will be called the localized ENO schemes. At or near the jumps, he uses the ENO schemes with the field by field decompositions, otherwise he simply uses the centered difference schemes without the field by field decompositions. The method involves a new interpolation analysis. In the numerical experiments on several standard test problems, the quality of the numerical results of this method is close to that of the pure ENO results. The localized ENO schemes can be equipped with the above artificial compression method. In this way, he dramatically improves the resolutions of the contact discontinuities at very little additional costs. (3) He introduces a space-time mesh refinement method for time dependent problems.« less

Air Force Office of Scientific Research Technical Report Summaries January - March 1991.

DTIC Science & Technology

1991-04-01

SUS 4SU Uc m W1( -W 0x t - 030 L O F-C-UC W QIMS O-UC tN -C 0 Lo - in 4 LC 4--- 41 UU 00W142 U4 (a 4- C- L 0) -0*-LU0 u ZaW inUi x& Ii- .0 5C4 L US)-L...C 3 L4-in > L 1 4 0 0 4) - DUC 0 L -0M Li nnU 0 3O> C U 0IX 9 z L f -) i- njo e CL .-- w* 1- - .I& - tUn I-. (A in 0 CQ4O 3 041 M -CC 0- LO A A L0...0 ’ 1- - -4-0 -V40 A -- 0 -- W;z a-a 0 Sn C’) 4A OLD tun , z 1’.S oEV mmU OW =3 ) ml > 23 S3 N S 01 1 54 V -0 a0 5 -0 .<Z - 0 4U.~ >jI~S𔃺~.C 42 r - C

Focus on China: should clinicians engage in research? and lessons from other countries

PubMed Central

Zhang, Zhongheng; Winston, Gavin P.; Zhao, Hai-Tao; Oei, Edwin H.G.; Ai, Qiyong; Loffroy, Romaric; Lin, Ting; Shen, Yaxing; Ng, Chin K.; Liu, Hua; Civelek, A. Cahid; Han, Zhijun; He, Yong-Ming; Ji, Ling-Yan

2014-01-01

Following tremendous economic progress, society in China is also undergoing fundamental changes, as is the healthcare system. Currently the training of Chinese young doctors and their future work placement are all undergoing re-structuring. We compiled some thoughts and opinions on the topic of ‘should clinicians in China engage in research?’, and publish them as a special report in this issue of Quantitative Imaging in Medicine and Surgery (QIMS). The contributors included some editorial members of this journal, and a few personal friends. Besides a few minor linguistic corrections, opinions from the contributors have not been edited, as we want authors’ to write their own independent views. However, it is possible there is a selection bias of the contributors of this paper; more likely those who are interested in the medical research are selected and therefore the views of the contributors may not be generalizable. To compare the structure and funding of China with other countries, authors from UK, The Netherlands, France, and USA are also invited. PMID:25392826

Vectorized schemes for conical potential flow using the artificial density method

NASA Technical Reports Server (NTRS)

Bradley, P. F.; Dwoyer, D. L.; South, J. C., Jr.; Keen, J. M.

1984-01-01

A method is developed to determine solutions to the full-potential equation for steady supersonic conical flow using the artificial density method. Various update schemes used generally for transonic potential solutions are investigated. The schemes are compared for speed and robustness. All versions of the computer code have been vectorized and are currently running on the CYBER-203 computer. The update schemes are vectorized, where possible, either fully (explicit schemes) or partially (implicit schemes). Since each version of the code differs only by the update scheme and elements other than the update scheme are completely vectorizable, comparisons of computational effort and convergence rate among schemes are a measure of the specific scheme's performance. Results are presented for circular and elliptical cones at angle of attack for subcritical and supercritical crossflows.

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

PubMed

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

2017-04-01

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

A Review of High-Order and Optimized Finite-Difference Methods for Simulating Linear Wave Phenomena

NASA Technical Reports Server (NTRS)

Zingg, David W.

1996-01-01

This paper presents a review of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, or elastic waves. The spatial operators reviewed include compact schemes, non-compact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods discussed include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fourth-order fully-discrete finite-difference methods are considered: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method studied, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. Recommendations are made with respect to the suitability of the methods for specific problems and practical aspects of their use, such as appropriate Courant numbers and grid densities. Avenues for future research are suggested.

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

NASA Astrophysics Data System (ADS)

Yang, Lei; Yan, Hongyong; Liu, Hong

2017-03-01

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

A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Jameson, Antony

1986-01-01

A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Comparison of three explicit multigrid methods for the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chima, Rodrick V.; Turkel, Eli; Schaffer, Steve

1987-01-01

Three explicit multigrid methods, Ni's method, Jameson's finite-volume method, and a finite-difference method based on Brandt's work, are described and compared for two model problems. All three methods use an explicit multistage Runge-Kutta scheme on the fine grid, and this scheme is also described. Convergence histories for inviscid flow over a bump in a channel for the fine-grid scheme alone show that convergence rate is proportional to Courant number and that implicit residual smoothing can significantly accelerate the scheme. Ni's method was slightly slower than the implicitly-smoothed scheme alone. Brandt's and Jameson's methods are shown to be equivalent in form but differ in their node versus cell-centered implementations. They are about 8.5 times faster than Ni's method in terms of CPU time. Results for an oblique shock/boundary layer interaction problem verify the accuracy of the finite-difference code. All methods slowed considerably on the stretched viscous grid but Brandt's method was still 2.1 times faster than Ni's method.

Optimal rotated staggered-grid finite-difference schemes for elastic wave modeling in TTI media

NASA Astrophysics Data System (ADS)

Yang, Lei; Yan, Hongyong; Liu, Hong

2015-11-01

The rotated staggered-grid finite-difference (RSFD) is an effective approach for numerical modeling to study the wavefield characteristics in tilted transversely isotropic (TTI) media. But it surfaces from serious numerical dispersion, which directly affects the modeling accuracy. In this paper, we propose two different optimal RSFD schemes based on the sampling approximation (SA) method and the least-squares (LS) method respectively to overcome this problem. We first briefly introduce the RSFD theory, based on which we respectively derive the SA-based RSFD scheme and the LS-based RSFD scheme. Then different forms of analysis are used to compare the SA-based RSFD scheme and the LS-based RSFD scheme with the conventional RSFD scheme, which is based on the Taylor-series expansion (TE) method. The contrast in numerical accuracy analysis verifies the greater accuracy of the two proposed optimal schemes, and indicates that these schemes can effectively widen the wavenumber range with great accuracy compared with the TE-based RSFD scheme. Further comparisons between these two optimal schemes show that at small wavenumbers, the SA-based RSFD scheme performs better, while at large wavenumbers, the LS-based RSFD scheme leads to a smaller error. Finally, the modeling results demonstrate that for the same operator length, the SA-based RSFD scheme and the LS-based RSFD scheme can achieve greater accuracy than the TE-based RSFD scheme, while for the same accuracy, the optimal schemes can adopt shorter difference operators to save computing time.

On High-Order Upwind Methods for Advection

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2017-01-01

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom ?? per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2??-1, which is higher than the expected order of ??.

Projection methods for incompressible flow problems with WENO finite difference schemes

NASA Astrophysics Data System (ADS)

de Frutos, Javier; John, Volker; Novo, Julia

2016-03-01

Weighted essentially non-oscillatory (WENO) finite difference schemes have been recommended in a competitive study of discretizations for scalar evolutionary convection-diffusion equations [20]. This paper explores the applicability of these schemes for the simulation of incompressible flows. To this end, WENO schemes are used in several non-incremental and incremental projection methods for the incompressible Navier-Stokes equations. Velocity and pressure are discretized on the same grid. A pressure stabilization Petrov-Galerkin (PSPG) type of stabilization is introduced in the incremental schemes to account for the violation of the discrete inf-sup condition. Algorithmic aspects of the proposed schemes are discussed. The schemes are studied on several examples with different features. It is shown that the WENO finite difference idea can be transferred to the simulation of incompressible flows. Some shortcomings of the methods, which are due to the splitting in projection schemes, become also obvious.

A splitting scheme based on the space-time CE/SE method for solving multi-dimensional hydrodynamical models of semiconductor devices

NASA Astrophysics Data System (ADS)

Nisar, Ubaid Ahmed; Ashraf, Waqas; Qamar, Shamsul

2016-08-01

Numerical solutions of the hydrodynamical model of semiconductor devices are presented in one and two-space dimension. The model describes the charge transport in semiconductor devices. Mathematically, the models can be written as a convection-diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a splitting scheme based on the conservation element and solution element (CE/SE) method for hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results of the suggested scheme are compared with the splitting scheme based on Nessyahu-Tadmor (NT) central scheme for convection step and the same semi-implicit scheme for the relaxation step. The effects of various parameters such as low field mobility, device length, lattice temperature and voltages for one-space dimensional hydrodynamic model are explored to further validate the generic applicability of the CE/SE method for the current model equations. A two dimensional simulation is also performed by CE/SE method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.

Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

2017-04-01

Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

High-Order Semi-Discrete Central-Upwind 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 the first fifth order, semi-discrete central upwind method for approximating solutions of multi-dimensional Hamilton-Jacobi equations. Unlike most of the commonly used high order upwind schemes, our scheme is formulated as a Godunov-type scheme. The scheme is based on the fluxes of Kurganov-Tadmor and Kurganov-Tadmor-Petrova, and is derived for an arbitrary number of space dimensions. A theorem establishing the monotonicity of these fluxes is provided. The spacial discretization is based on a weighted essentially non-oscillatory reconstruction of the derivative. The accuracy and stability properties of our scheme are demonstrated in a variety of examples. A comparison between our method and other fifth-order schemes for Hamilton-Jacobi equations shows that our method exhibits smaller errors without any increase in the complexity of the computations.

Voltage Drop Compensation Method for Active Matrix Organic Light Emitting Diode Displays

NASA Astrophysics Data System (ADS)

Choi, Sang-moo; Ryu, Do-hyung; Kim, Keum-nam; Choi, Jae-beom; Kim, Byung-hee; Berkeley, Brian

2011-03-01

In this paper, the conventional voltage drop compensation methods are reviewed and the novel design and driving scheme, the advanced power de-coupled (aPDC) driving method, is proposed to effectively compensate the voltage IR drop of active matrix light emitting diode (AMOLED) displays. The advanced PDC driving scheme can be applied to general AMOLED pixel circuits that have been developed with only minor modification or without requiring modification in pixel circuit. A 14-in. AMOLED panel with the aPDC driving scheme was fabricated. Long range uniformity (LRU) of the 14-in. AMOLED panel was improved from 43% without the aPDC driving scheme, to over 87% at the same brightness by using the scheme and the layout complexity of the panel with new design scheme is less than that of the panel with the conventional design scheme.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

NASA Technical Reports Server (NTRS)

Slack, David C.; Whitaker, D. L.; Walters, Robert W.

1994-01-01

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Neural-Dynamic-Method-Based Dual-Arm CMG Scheme With Time-Varying Constraints Applied to Humanoid Robots.

PubMed

Zhang, Zhijun; Li, Zhijun; Zhang, Yunong; Luo, Yamei; Li, Yuanqing

2015-12-01

We propose a dual-arm cyclic-motion-generation (DACMG) scheme by a neural-dynamic method, which can remedy the joint-angle-drift phenomenon of a humanoid robot. In particular, according to a neural-dynamic design method, first, a cyclic-motion performance index is exploited and applied. This cyclic-motion performance index is then integrated into a quadratic programming (QP)-type scheme with time-varying constraints, called the time-varying-constrained DACMG (TVC-DACMG) scheme. The scheme includes the kinematic motion equations of two arms and the time-varying joint limits. The scheme can not only generate the cyclic motion of two arms for a humanoid robot but also control the arms to move to the desired position. In addition, the scheme considers the physical limit avoidance. To solve the QP problem, a recurrent neural network is presented and used to obtain the optimal solutions. Computer simulations and physical experiments demonstrate the effectiveness and the accuracy of such a TVC-DACMG scheme and the neural network solver.

Development of a new flux splitting scheme

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Steffen, Christopher J., Jr.

1991-01-01

The use of a new splitting scheme, the advection upstream splitting method, for model aerodynamic problems where Van Leer and Roe schemes had failed previously is discussed. The present scheme is based on splitting in which the convective and pressure terms are separated and treated differently depending on the underlying physical conditions. The present method is found to be both simple and accurate.

Development of a new flux splitting scheme

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Steffen, Christopher J., Jr.

1991-01-01

The successful use of a novel splitting scheme, the advection upstream splitting method, for model aerodynamic problems where Van Leer and Roe schemes had failed previously is discussed. The present scheme is based on splitting in which the convective and pressure terms are separated and treated differently depending on the underlying physical conditions. The present method is found to be both simple and accurate.

Numerical experiments with a symmetric high-resolution shock-capturing scheme

NASA Technical Reports Server (NTRS)

Yee, H. C.

1986-01-01

Characteristic-based explicit and implicit total variation diminishing (TVD) schemes for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD schemes other than Lax-Wendroff. The Roe and Davis schemes can be viewed as a subset of the class of explicit methods. 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. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD scheme with an implicit upwind TVD scheme originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more numerical experiments are being conducted on time-accurate calculations and on the effect of grid topology, numerical boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of scheme and give guidelines for its use.

Application of kinetic flux vector splitting scheme for solving multi-dimensional hydrodynamical models of semiconductor devices

NASA Astrophysics Data System (ADS)

Nisar, Ubaid Ahmed; Ashraf, Waqas; Qamar, Shamsul

In this article, one and two-dimensional hydrodynamical models of semiconductor devices are numerically investigated. The models treat the propagation of electrons in a semiconductor device as the flow of a charged compressible fluid. It plays an important role in predicting the behavior of electron flow in semiconductor devices. Mathematically, the governing equations form a convection-diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a splitting scheme based on the kinetic flux-vector splitting (KFVS) method for the hyperbolic step, and a semi-implicit Runge-Kutta method for the relaxation step. The KFVS method is based on the direct splitting of macroscopic flux functions of the system on the cell interfaces. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Several case studies are considered. For validation, the results of current scheme are compared with those obtained from the splitting scheme based on the NT central scheme. The effects of various parameters such as low field mobility, device length, lattice temperature and voltage are analyzed. The accuracy, efficiency and simplicity of the proposed KFVS scheme validates its generic applicability to the given model equations. A two dimensional simulation is also performed by KFVS method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.

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.

Multigrid method for the equilibrium equations of elasticity using a compact scheme

NASA Technical Reports Server (NTRS)

Taasan, S.

1986-01-01

A compact difference scheme is derived for treating the equilibrium equations of elasticity. The scheme is inconsistent and unstable. A multigrid method which takes into account these properties is described. The solution of the discrete equations, up to the level of discretization errors, is obtained by this method in just two multigrid cycles.

Reduction of bias and variance for evaluation of computer-aided diagnostic schemes.

PubMed

Li, Qiang; Doi, Kunio

2006-04-01

Computer-aided diagnostic (CAD) schemes have been developed to assist radiologists in detecting various lesions in medical images. In addition to the development, an equally important problem is the reliable evaluation of the performance levels of various CAD schemes. It is good to see that more and more investigators are employing more reliable evaluation methods such as leave-one-out and cross validation, instead of less reliable methods such as resubstitution, for assessing their CAD schemes. However, the common applications of leave-one-out and cross-validation evaluation methods do not necessarily imply that the estimated performance levels are accurate and precise. Pitfalls often occur in the use of leave-one-out and cross-validation evaluation methods, and they lead to unreliable estimation of performance levels. In this study, we first identified a number of typical pitfalls for the evaluation of CAD schemes, and conducted a Monte Carlo simulation experiment for each of the pitfalls to demonstrate quantitatively the extent of bias and/or variance caused by the pitfall. Our experimental results indicate that considerable bias and variance may exist in the estimated performance levels of CAD schemes if one employs various flawed leave-one-out and cross-validation evaluation methods. In addition, for promoting and utilizing a high standard for reliable evaluation of CAD schemes, we attempt to make recommendations, whenever possible, for overcoming these pitfalls. We believe that, with the recommended evaluation methods, we can considerably reduce the bias and variance in the estimated performance levels of CAD schemes.

Embedded WENO: A design strategy to improve existing WENO schemes

NASA Astrophysics Data System (ADS)

van Lith, Bart S.; ten Thije Boonkkamp, Jan H. M.; IJzerman, Wilbert L.

2017-02-01

Embedded WENO methods utilise all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu [1] and on the WENO-Z scheme of Borges et al. [2] are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts.

High-Order Implicit-Explicit Multi-Block Time-stepping Method for Hyperbolic PDEs

NASA Technical Reports Server (NTRS)

Nielsen, Tanner B.; Carpenter, Mark H.; Fisher, Travis C.; Frankel, Steven H.

2014-01-01

This work seeks to explore and improve the current time-stepping schemes used in computational fluid dynamics (CFD) in order to reduce overall computational time. A high-order scheme has been developed using a combination of implicit and explicit (IMEX) time-stepping Runge-Kutta (RK) schemes which increases numerical stability with respect to the time step size, resulting in decreased computational time. The IMEX scheme alone does not yield the desired increase in numerical stability, but when used in conjunction with an overlapping partitioned (multi-block) domain significant increase in stability is observed. To show this, the Overlapping-Partition IMEX (OP IMEX) scheme is applied to both one-dimensional (1D) and two-dimensional (2D) problems, the nonlinear viscous Burger's equation and 2D advection equation, respectively. The method uses two different summation by parts (SBP) derivative approximations, second-order and fourth-order accurate. The Dirichlet boundary conditions are imposed using the Simultaneous Approximation Term (SAT) penalty method. The 6-stage additive Runge-Kutta IMEX time integration schemes are fourth-order accurate in time. An increase in numerical stability 65 times greater than the fully explicit scheme is demonstrated to be achievable with the OP IMEX method applied to 1D Burger's equation. Results from the 2D, purely convective, advection equation show stability increases on the order of 10 times the explicit scheme using the OP IMEX method. Also, the domain partitioning method in this work shows potential for breaking the computational domain into manageable sizes such that implicit solutions for full three-dimensional CFD simulations can be computed using direct solving methods rather than the standard iterative methods currently used.

A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chaudhry, Jehanzeb H.; Collins, J. B.; Shadid, John N.

Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error inmore » a quantity-of-interest.« less

A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes

DOE PAGES

Chaudhry, Jehanzeb H.; Collins, J. B.; Shadid, John N.

2017-02-05

Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error inmore » a quantity-of-interest.« less

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

DOE PAGES

Finn, John M.

2015-03-01

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a 'special divergence-free' property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. Wemore » also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Ref. [11], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Ref. [35], appears to work very well.« less

Higher-order accurate space-time schemes for computational astrophysics—Part I: finite volume methods

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.

2017-12-01

As computational astrophysics comes under pressure to become a precision science, there is an increasing need to move to high accuracy schemes for computational astrophysics. The algorithmic needs of computational astrophysics are indeed very special. The methods need to be robust and preserve the positivity of density and pressure. Relativistic flows should remain sub-luminal. These requirements place additional pressures on a computational astrophysics code, which are usually not felt by a traditional fluid dynamics code. Hence the need for a specialized review. The focus here is on weighted essentially non-oscillatory (WENO) schemes, discontinuous Galerkin (DG) schemes and PNPM schemes. WENO schemes are higher order extensions of traditional second order finite volume schemes. At third order, they are most similar to piecewise parabolic method schemes, which are also included. DG schemes evolve all the moments of the solution, with the result that they are more accurate than WENO schemes. PNPM schemes occupy a compromise position between WENO and DG schemes. They evolve an Nth order spatial polynomial, while reconstructing higher order terms up to Mth order. As a result, the timestep can be larger. Time-dependent astrophysical codes need to be accurate in space and time with the result that the spatial and temporal accuracies must be matched. This is realized with the help of strong stability preserving Runge-Kutta schemes and ADER (Arbitrary DERivative in space and time) schemes, both of which are also described. The emphasis of this review is on computer-implementable ideas, not necessarily on the underlying theory.

Parallelization of implicit finite difference schemes in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel

1990-01-01

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

A Computer Oriented Scheme for Coding Chemicals in the Field of Biomedicine.

ERIC Educational Resources Information Center

Bobka, Marilyn E.; Subramaniam, J.B.

The chemical coding scheme of the Medical Coding Scheme (MCS), developed for use in the Comparative Systems Laboratory (CSL), is outlined and evaluated in this report. The chemical coding scheme provides a classification scheme and encoding method for drugs and chemical terms. Using the scheme complicated chemical structures may be expressed…

Factorized Runge-Kutta-Chebyshev Methods

NASA Astrophysics Data System (ADS)

O'Sullivan, Stephen

2017-05-01

The second-order extended stability Factorized Runge-Kutta-Chebyshev (FRKC2) explicit schemes for the integration of large systems of PDEs with diffusive terms are presented. The schemes are simple to implement through ordered sequences of forward Euler steps with complex stepsizes, and easily parallelised for large scale problems on distributed architectures. Preserving 7 digits for accuracy at 16 digit precision, the schemes are theoretically capable of maintaining internal stability for acceleration factors in excess of 6000 with respect to standard explicit Runge-Kutta methods. The extent of the stability domain is approximately the same as that of RKC schemes, and a third longer than in the case of RKL2 schemes. Extension of FRKC methods to fourth-order, by both complex splitting and Butcher composition techniques, is also discussed. A publicly available implementation of FRKC2 schemes may be obtained from maths.dit.ie/frkc

A Novel WA-BPM Based on the Generalized Multistep Scheme in the Propagation Direction in the Waveguide

NASA Astrophysics Data System (ADS)

Ji, Yang; Chen, Hong; Tang, Hongwu

2017-06-01

A highly accurate wide-angle scheme, based on the generalized mutistep scheme in the propagation direction, is developed for the finite difference beam propagation method (FD-BPM). Comparing with the previously presented method, the simulation shows that our method results in a more accurate solution, and the step size can be much larger

Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness

NASA Astrophysics Data System (ADS)

Mengaldo, Gianmarco; De Grazia, Daniele; Moura, Rodrigo C.; Sherwin, Spencer J.

2018-04-01

This study focuses on the dispersion and diffusion characteristics of high-order energy-stable flux reconstruction (ESFR) schemes via the spatial eigensolution analysis framework proposed in [1]. The analysis is performed for five ESFR schemes, where the parameter 'c' dictating the properties of the specific scheme recovered is chosen such that it spans the entire class of ESFR methods, also referred to as VCJH schemes, proposed in [2]. In particular, we used five values of 'c', two that correspond to its lower and upper bounds and the others that identify three schemes that are linked to common high-order methods, namely the ESFR recovering two versions of discontinuous Galerkin methods and one recovering the spectral difference scheme. The performance of each scheme is assessed when using different numerical intercell fluxes (e.g. different levels of upwinding), ranging from "under-" to "over-upwinding". In contrast to the more common temporal analysis, the spatial eigensolution analysis framework adopted here allows one to grasp crucial insights into the diffusion and dispersion properties of FR schemes for problems involving non-periodic boundary conditions, typically found in open-flow problems, including turbulence, unsteady aerodynamics and aeroacoustics.

An implicit spatial and high-order temporal finite difference scheme for 2D acoustic modelling

NASA Astrophysics Data System (ADS)

Wang, Enjiang; Liu, Yang

2018-01-01

The finite difference (FD) method exhibits great superiority over other numerical methods due to its easy implementation and small computational requirement. We propose an effective FD method, characterised by implicit spatial and high-order temporal schemes, to reduce both the temporal and spatial dispersions simultaneously. For the temporal derivative, apart from the conventional second-order FD approximation, a special rhombus FD scheme is included to reach high-order accuracy in time. Compared with the Lax-Wendroff FD scheme, this scheme can achieve nearly the same temporal accuracy but requires less floating-point operation times and thus less computational cost when the same operator length is adopted. For the spatial derivatives, we adopt the implicit FD scheme to improve the spatial accuracy. Apart from the existing Taylor series expansion-based FD coefficients, we derive the least square optimisation based implicit spatial FD coefficients. Dispersion analysis and modelling examples demonstrate that, our proposed method can effectively decrease both the temporal and spatial dispersions, thus can provide more accurate wavefields.

Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

NASA Astrophysics Data System (ADS)

Su, Bo; Tuo, Xianguo; Xu, Ling

2017-08-01

Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

Evaluation of the CPU time for solving the radiative transfer equation with high-order resolution schemes applying the normalized weighting-factor method

NASA Astrophysics Data System (ADS)

Xamán, J.; Zavala-Guillén, I.; Hernández-López, I.; Uriarte-Flores, J.; Hernández-Pérez, I.; Macías-Melo, E. V.; Aguilar-Castro, K. M.

2018-03-01

In this paper, we evaluated the convergence rate (CPU time) of a new mathematical formulation for the numerical solution of the radiative transfer equation (RTE) with several High-Order (HO) and High-Resolution (HR) schemes. In computational fluid dynamics, this procedure is known as the Normalized Weighting-Factor (NWF) method and it is adopted here. The NWF method is used to incorporate the high-order resolution schemes in the discretized RTE. The NWF method is compared, in terms of computer time needed to obtain a converged solution, with the widely used deferred-correction (DC) technique for the calculations of a two-dimensional cavity with emitting-absorbing-scattering gray media using the discrete ordinates method. Six parameters, viz. the grid size, the order of quadrature, the absorption coefficient, the emissivity of the boundary surface, the under-relaxation factor, and the scattering albedo are considered to evaluate ten schemes. The results showed that using the DC method, in general, the scheme that had the lowest CPU time is the SOU. In contrast, with the results of theDC procedure the CPU time for DIAMOND and QUICK schemes using the NWF method is shown to be, between the 3.8 and 23.1% faster and 12.6 and 56.1% faster, respectively. However, the other schemes are more time consuming when theNWFis used instead of the DC method. Additionally, a second test case was presented and the results showed that depending on the problem under consideration, the NWF procedure may be computationally faster or slower that the DC method. As an example, the CPU time for QUICK and SMART schemes are 61.8 and 203.7%, respectively, slower when the NWF formulation is used for the second test case. Finally, future researches to explore the computational cost of the NWF method in more complex problems are required.

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.

A comparison of two multi-variable integrator windup protection schemes

NASA Technical Reports Server (NTRS)

Mattern, Duane

1993-01-01

Two methods are examined for limit and integrator wind-up protection for multi-input, multi-output linear controllers subject to actuator constraints. The methods begin with an existing linear controller that satisfies the specifications for the nominal, small perturbation, linear model of the plant. The controllers are formulated to include an additional contribution to the state derivative calculations. The first method to be examined is the multi-variable version of the single-input, single-output, high gain, Conventional Anti-Windup (CAW) scheme. Except for the actuator limits, the CAW scheme is linear. The second scheme to be examined, denoted the Modified Anti-Windup (MAW) scheme, uses a scalar to modify the magnitude of the controller output vector while maintaining the vector direction. The calculation of the scalar modifier is a nonlinear function of the controller outputs and the actuator limits. In both cases the constrained actuator is tracked. These two integrator windup protection methods are demonstrated on a turbofan engine control system with five measurements, four control variables, and four actuators. The closed-loop responses of the two schemes are compared and contrasted during limit operation. The issue of maintaining the direction of the controller output vector using the Modified Anti-Windup scheme is discussed and the advantages and disadvantages of both of the IWP methods are presented.

Generalized energy and potential enstrophy conserving finite difference schemes for the shallow water equations

NASA Technical Reports Server (NTRS)

Abramopoulos, Frank

1988-01-01

The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.

New coherent laser communication detection scheme based on channel-switching method.

PubMed

Liu, Fuchuan; Sun, Jianfeng; Ma, Xiaoping; Hou, Peipei; Cai, Guangyu; Sun, Zhiwei; Lu, Zhiyong; Liu, Liren

2015-04-01

A new coherent laser communication detection scheme based on the channel-switching method is proposed. The detection front end of this scheme comprises a 90° optical hybrid and two balanced photodetectors which outputs the in-phase (I) channel and quadrature-phase (Q) channel signal current, respectively. With this method, the ultrahigh speed analog/digital transform of the signal of the I or Q channel is not required. The phase error between the signal and local lasers is obtained by simple analog circuit. Using the phase error signal, the signals of the I/Q channel are switched alternately. The principle of this detection scheme is presented. Moreover, the comparison of the sensitivity of this scheme with that of homodyne detection with an optical phase-locked loop is discussed. An experimental setup was constructed to verify the proposed detection scheme. The offline processing procedure and results are presented. This scheme could be realized through simple structure and has potential applications in cost-effective high-speed laser communication.

Equivalence of internal and external mixture schemes of single scattering properties in vector radiative transfer

PubMed Central

Mukherjee, Lipi; Zhai, Peng-Wang; Hu, Yongxiang; Winker, David M.

2018-01-01

Polarized radiation fields in a turbid medium are influenced by single-scattering properties of scatterers. It is common that media contain two or more types of scatterers, which makes it essential to properly mix single-scattering properties of different types of scatterers in the vector radiative transfer theory. The vector radiative transfer solvers can be divided into two basic categories: the stochastic and deterministic methods. The stochastic method is basically the Monte Carlo method, which can handle scatterers with different scattering properties explicitly. This mixture scheme is called the external mixture scheme in this paper. The deterministic methods, however, can only deal with a single set of scattering properties in the smallest discretized spatial volume. The single-scattering properties of different types of scatterers have to be averaged before they are input to deterministic solvers. This second scheme is called the internal mixture scheme. The equivalence of these two different mixture schemes of scattering properties has not been demonstrated so far. In this paper, polarized radiation fields for several scattering media are solved using the Monte Carlo and successive order of scattering (SOS) methods and scattering media contain two types of scatterers: Rayleigh scatterers (molecules) and Mie scatterers (aerosols). The Monte Carlo and SOS methods employ external and internal mixture schemes of scatterers, respectively. It is found that the percentage differences between radiances solved by these two methods with different mixture schemes are of the order of 0.1%. The differences of Q/I, U/I, and V/I are of the order of 10−5 ~ 10−4, where I, Q, U, and V are the Stokes parameters. Therefore, the equivalence between these two mixture schemes is confirmed to the accuracy level of the radiative transfer numerical benchmarks. This result provides important guidelines for many radiative transfer applications that involve the mixture of different scattering and absorptive particles. PMID:29047543

An extended GS method for dense linear systems

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi

2009-09-01

Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.

Improving multivariate Horner schemes with Monte Carlo tree search

NASA Astrophysics Data System (ADS)

Kuipers, J.; Plaat, A.; Vermaseren, J. A. M.; van den Herik, H. J.

2013-11-01

Optimizing the cost of evaluating a polynomial is a classic problem in computer science. For polynomials in one variable, Horner's method provides a scheme for producing a computationally efficient form. For multivariate polynomials it is possible to generalize Horner's method, but this leaves freedom in the order of the variables. Traditionally, greedy schemes like most-occurring variable first are used. This simple textbook algorithm has given remarkably efficient results. Finding better algorithms has proved difficult. In trying to improve upon the greedy scheme we have implemented Monte Carlo tree search, a recent search method from the field of artificial intelligence. This results in better Horner schemes and reduces the cost of evaluating polynomials, sometimes by factors up to two.

Symplectic partitioned Runge-Kutta scheme for Maxwell's equations

NASA Astrophysics Data System (ADS)

Huang, Zhi-Xiang; Wu, Xian-Liang

Using the symplectic partitioned Runge-Kutta (PRK) method, we construct a new scheme for approximating the solution to infinite dimensional nonseparable Hamiltonian systems of Maxwell's equations for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Several numerical examples are presented to verify the efficiency of the scheme.

A classification scheme for risk assessment methods.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stamp, Jason Edwin; Campbell, Philip LaRoche

2004-08-01

This report presents a classification scheme for risk assessment methods. This scheme, like all classification schemes, provides meaning by imposing a structure that identifies relationships. Our scheme is based on two orthogonal aspects--level of detail, and approach. The resulting structure is shown in Table 1 and is explained in the body of the report. Each cell in the Table represent a different arrangement of strengths and weaknesses. Those arrangements shift gradually as one moves through the table, each cell optimal for a particular situation. The intention of this report is to enable informed use of the methods so that amore » method chosen is optimal for a situation given. This report imposes structure on the set of risk assessment methods in order to reveal their relationships and thus optimize their usage.We present a two-dimensional structure in the form of a matrix, using three abstraction levels for the rows and three approaches for the columns. For each of the nine cells in the matrix we identify the method type by name and example. The matrix helps the user understand: (1) what to expect from a given method, (2) how it relates to other methods, and (3) how best to use it. Each cell in the matrix represent a different arrangement of strengths and weaknesses. Those arrangements shift gradually as one moves through the table, each cell optimal for a particular situation. The intention of this report is to enable informed use of the methods so that a method chosen is optimal for a situation given. The matrix, with type names in the cells, is introduced in Table 2 on page 13 below. Unless otherwise stated we use the word 'method' in this report to refer to a 'risk assessment method', though often times we use the full phrase. The use of the terms 'risk assessment' and 'risk management' are close enough that we do not attempt to distinguish them in this report. The remainder of this report is organized as follows. In Section 2 we provide context for this report--what a 'method' is and where it fits. In Section 3 we present background for our classification scheme--what other schemes we have found, the fundamental nature of methods and their necessary incompleteness. In Section 4 we present our classification scheme in the form of a matrix, then we present an analogy that should provide an understanding of the scheme, concluding with an explanation of the two dimensions and the nine types in our scheme. In Section 5 we present examples of each of our classification types. In Section 6 we present conclusions.« less

A new family of high-order compact upwind difference schemes with good spectral resolution

NASA Astrophysics Data System (ADS)

Zhou, Qiang; Yao, Zhaohui; He, Feng; Shen, M. Y.

2007-12-01

This paper presents a new family of high-order compact upwind difference schemes. Unknowns included in the proposed schemes are not only the values of the function but also those of its first and higher derivatives. Derivative terms in the schemes appear only on the upwind side of the stencil. One can calculate all the first derivatives exactly as one solves explicit schemes when the boundary conditions of the problem are non-periodic. When the proposed schemes are applied to periodic problems, only periodic bi-diagonal matrix inversions or periodic block-bi-diagonal matrix inversions are required. Resolution optimization is used to enhance the spectral representation of the first derivative, and this produces a scheme with the highest spectral accuracy among all known compact schemes. For non-periodic boundary conditions, boundary schemes constructed in virtue of the assistant scheme make the schemes not only possess stability for any selective length scale on every point in the computational domain but also satisfy the principle of optimal resolution. Also, an improved shock-capturing method is developed. Finally, both the effectiveness of the new hybrid method and the accuracy of the proposed schemes are verified by executing four benchmark test cases.

A gas-kinetic BGK scheme for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Xu, Kun

2000-01-01

This paper presents an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the compressible Navier-Stokes equations. The current method extends the previous gas-kinetic Navier-Stokes solver developed by Xu and Prendergast by implementing a general nonequilibrium state to represent the gas distribution function at the beginning of each time step. As a result, the requirement in the previous scheme, such as the particle collision time being less than the time step for the validity of the BGK Navier-Stokes solution, is removed. Therefore, the applicable regime of the current method is much enlarged and the Navier-Stokes solution can be obtained accurately regardless of the ratio between the collision time and the time step. The gas-kinetic Navier-Stokes solver developed by Chou and Baganoff is the limiting case of the current method, and it is valid only under such a limiting condition. Also, in this paper, the appropriate implementation of boundary condition for the kinetic scheme, different kinetic limiting cases, and the Prandtl number fix are presented. The connection among artificial dissipative central schemes, Godunov-type schemes, and the gas-kinetic BGK method is discussed. Many numerical tests are included to validate the current method.

A modified symplectic PRK scheme for seismic wave modeling

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Ma, Jian

2017-02-01

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

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Nielsen, Eric J.; Nishikawa, Hiroaki; White, Jeffery A.

2010-01-01

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes - a node-averaging scheme and two schemes with nearest-neighbor and adaptive compact stencils for least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Tests from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The tests of the second class are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes may degenerate on mixed grids, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to that of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping based on a distance function commonly available in practical schemes or modifying the scheme stencil to reflect the direction of strong coupling. The major conclusion is that accuracies of the node centered and the best cell-centered schemes are comparable at equivalent number of degrees of freedom.

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Noiseless Vlasov-Poisson simulations with linearly transformed particles

DOE PAGES

Pinto, Martin C.; Sonnendrucker, Eric; Friedman, Alex; ...

2014-06-25

We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development ofmore » Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Lastly, benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.« less

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

DOE Office of Scientific and Technical Information (OSTI.GOV)

Finn, John M., E-mail: finn@lanl.gov

2015-03-15

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a “special divergence-free” (SDF) property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint.more » We also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Feng and Shang [Numer. Math. 71, 451 (1995)], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Richardson and Finn [Plasma Phys. Controlled Fusion 54, 014004 (2012)], appears to work very well.« less

On Richardson extrapolation for low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes

NASA Astrophysics Data System (ADS)

Havasi, Ágnes; Kazemi, Ehsan

2018-04-01

In the modeling of wave propagation phenomena it is necessary to use time integration methods which are not only sufficiently accurate, but also properly describe the amplitude and phase of the propagating waves. It is not clear if amending the developed schemes by extrapolation methods to obtain a high order of accuracy preserves the qualitative properties of these schemes in the perspective of dissipation, dispersion and stability analysis. It is illustrated that the combination of various optimized schemes with Richardson extrapolation is not optimal for minimal dissipation and dispersion errors. Optimized third-order and fourth-order methods are obtained, and it is shown that the proposed methods combined with Richardson extrapolation result in fourth and fifth orders of accuracy correspondingly, while preserving optimality and stability. The numerical applications include the linear wave equation, a stiff system of reaction-diffusion equations and the nonlinear Euler equations with oscillatory initial conditions. It is demonstrated that the extrapolated third-order scheme outperforms the recently developed fourth-order diagonally implicit Runge-Kutta scheme in terms of accuracy and stability.

An exponential time-integrator scheme for steady and unsteady inviscid flows

NASA Astrophysics Data System (ADS)

Li, Shu-Jie; Luo, Li-Shi; Wang, Z. J.; Ju, Lili

2018-07-01

An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve multi-dimensional nonlinear partial differential equations pertaining to fluid dynamics. The effective and efficient implementation of PCEXP is realized by means of the Krylov method. The linear stability and truncation error are analyzed through a one-dimensional model equation. The proposed PCEXP scheme is applied to the Euler equations discretized with a discontinuous Galerkin method in both two and three dimensions. The effectiveness and efficiency of the PCEXP scheme are demonstrated for both steady and unsteady inviscid flows. The accuracy and efficiency of the PCEXP scheme are verified and validated through comparisons with the explicit third-order total variation diminishing Runge-Kutta scheme (TVDRK3), the implicit backward Euler (BE) and the implicit second-order backward difference formula (BDF2). For unsteady flows, the PCEXP scheme generates a temporal error much smaller than the BDF2 scheme does, while maintaining the expected acceleration at the same time. Moreover, the PCEXP scheme is also shown to achieve the computational efficiency comparable to the implicit schemes for steady flows.

Optimization of the scheme for natural ecology planning of urban rivers based on ANP (analytic network process) model.

PubMed

Zhang, Yichuan; Wang, Jiangping

2015-07-01

Rivers serve as a highly valued component in ecosystem and urban infrastructures. River planning should follow basic principles of maintaining or reconstructing the natural landscape and ecological functions of rivers. Optimization of planning scheme is a prerequisite for successful construction of urban rivers. Therefore, relevant studies on optimization of scheme for natural ecology planning of rivers is crucial. In the present study, four planning schemes for Zhaodingpal River in Xinxiang City, Henan Province were included as the objects for optimization. Fourteen factors that influenced the natural ecology planning of urban rivers were selected from five aspects so as to establish the ANP model. The data processing was done using Super Decisions software. The results showed that important degree of scheme 3 was highest. A scientific, reasonable and accurate evaluation of schemes could be made by ANP method on natural ecology planning of urban rivers. This method could be used to provide references for sustainable development and construction of urban rivers. ANP method is also suitable for optimization of schemes for urban green space planning and design.

Assessing the Resolution Adaptability of the Zhang-McFarlane Cumulus Parameterization With Spatial and Temporal Averaging: RESOLUTION ADAPTABILITY OF ZM SCHEME

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yun, Yuxing; Fan, Jiwen; Xiao, Heng

Realistic modeling of cumulus convection at fine model resolutions (a few to a few tens of km) is problematic since it requires the cumulus scheme to adapt to higher resolution than they were originally designed for (~100 km). To solve this problem, we implement the spatial averaging method proposed in Xiao et al. (2015) and also propose a temporal averaging method for the large-scale convective available potential energy (CAPE) tendency in the Zhang-McFarlane (ZM) cumulus parameterization. The resolution adaptability of the original ZM scheme, the scheme with spatial averaging, and the scheme with both spatial and temporal averaging at 4-32more » km resolution is assessed using the Weather Research and Forecasting (WRF) model, by comparing with Cloud Resolving Model (CRM) results. We find that the original ZM scheme has very poor resolution adaptability, with sub-grid convective transport and precipitation increasing significantly as the resolution increases. The spatial averaging method improves the resolution adaptability of the ZM scheme and better conserves the total transport of moist static energy and total precipitation. With the temporal averaging method, the resolution adaptability of the scheme is further improved, with sub-grid convective precipitation becoming smaller than resolved precipitation for resolution higher than 8 km, which is consistent with the results from the CRM simulation. Both the spatial distribution and time series of precipitation are improved with the spatial and temporal averaging methods. The results may be helpful for developing resolution adaptability for other cumulus parameterizations that are based on quasi-equilibrium assumption.« less

Nonequilibrium scheme for computing the flux of the convection-diffusion equation in the framework of the lattice Boltzmann method.

PubMed

Chai, Zhenhua; Zhao, T S

2014-07-01

In this paper, we propose a local nonequilibrium scheme for computing the flux of the convection-diffusion equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibrium scheme and the conventional second-order central-difference scheme indicates that, although both schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than the central-difference scheme. In addition, the flux computation rendered by the present scheme also preserves the parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the convection-diffusion equation and in computing the flux.

On Space-Time Inversion Invariance and its Relation to Non-Dissipatedness of a CESE Core Scheme

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

2006-01-01

The core motivating ideas of the space-time CESE method are clearly presented and critically analyzed. It is explained why these ideas result in all the simplifying and enabling features of the CESE method. A thorough discussion of the a scheme, a two-level non-dissipative CESE solver of a simple advection equation with two independent mesh variables and two equations per mesh point is also presented. It is shown that the scheme possesses some rather intriguing properties such as: (i) its two independent mesh variables separately satisfy two decoupled three-level leapfrog schemes and (ii) it shares with the leapfrog scheme the same amplification factors, even though the a scheme and the leapfrog scheme have completely different origins and structures. It is also explained why the leapfrog scheme is not as robust as the a scheme. The amplification factors/matrices of several non-dissipative schemes are carefully studied and the key properties that contribute to their non-dissipatedness are clearly spelled out. Finally we define and establish space-time inversion (STI) invariance for several non-dissipative schemes and show that their non-dissipatedness is a result of their STI invariance.

Dynamic Restarting Schemes for Eigenvalue Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.

Study of Velocity and Materials on Tribocharging of Polymer Powders for Powder Coating Applications

NASA Technical Reports Server (NTRS)

Biris, Alex S.; Trigwell, Steve; Sims, Robert A.; Mazumder, Malay K.

2005-01-01

Electrostatic powder deposition is widely used in a plethora of industrial-applications ranging from the pharmaceutical and food.industries, to farm equipment and automotive applications. The disadvantages of this technique are possible back corona (pin-like formations) onset and the Faraday penetration limitation (when the powder does not penetrate in some recessed areas). A possible solution to overcome these problems is to use tribochargers to electrostatically charge the powder. Tribocharging, or contact charging while two materials are in contact, is related to the work function difference between the contacting materials and generates bipolarly charged particles. The generation of an ion-free powder cloud by tribocharging with high bipolar charge and an overall charge density of almost zero, provides a better coverage of the recessed areas. In this study, acrylic and epoxy powders were fluidized and charged by passing through stainless steel, copper, aluminum, and polycarbonate static mixers, respectively. The particle velocity was varied to determine its effect on the net charge-to-mass ratio (QIM) acquired by the powders. In general, the Q/M increases rapidly when the velocity was increased from 1.5 to 2.5 m/s, remaining almost constant for higher velocities. Charge separation experiments showed bipolar charging for all chargers.

A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system

NASA Astrophysics Data System (ADS)

Lee, Hyun Geun; Choi, Jeong-Whan; Kim, Junseok

2012-02-01

We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component Cahn-Hilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The scheme allows us to convert the N-component Cahn-Hilliard system into a system of N-1 binary Cahn-Hilliard equations and significantly reduces the required computer memory and CPU time. We observe that our numerical solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed scheme with various numerical experiments.

Assessment of the reduction methods used to develop chemical schemes: building of a new chemical scheme for VOC oxidation suited to three-dimensional multiscale HOx-NOx-VOC chemistry simulations

NASA Astrophysics Data System (ADS)

Szopa, S.; Aumont, B.; Madronich, S.

2005-09-01

The objective of this work was to develop and assess an automatic procedure to generate reduced chemical schemes for the atmospheric photooxidation of volatile organic carbon (VOC) compounds. The procedure is based on (i) the development of a tool for writing the fully explicit schemes for VOC oxidation (see companion paper Aumont et al., 2005), (ii) the application of several commonly used reduction methods to the fully explicit scheme, and (iii) the assessment of resulting errors based on direct comparison between the reduced and full schemes.

The reference scheme included seventy emitted VOCs chosen to be representative of both anthropogenic and biogenic emissions, and their atmospheric degradation chemistry required more than two million reactions among 350000 species. Three methods were applied to reduce the size of the reference chemical scheme: (i) use of operators, based on the redundancy of the reaction sequences involved in the VOC oxidation, (ii) grouping of primary species having similar reactivities into surrogate species and (iii) grouping of some secondary products into surrogate species. The number of species in the final reduced scheme is 147, this being small enough for practical inclusion in current three-dimensional models. Comparisons between the fully explicit and reduced schemes, carried out with a box model for several typical tropospheric conditions, showed that the reduced chemical scheme accurately predicts ozone concentrations and some other aspects of oxidant chemistry for both polluted and clean tropospheric conditions.

Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng, Weixiong; Wang, Yaqi; DeHart, Mark D.

2016-09-01

In this report, we present a new upwinding scheme for the multiscale capability in Rattlesnake, the MOOSE based radiation transport application. Comparing with the initial implementation of multiscale utilizing Lagrange multipliers to impose strong continuity of angular flux on interface of in-between subdomains, this scheme does not require the particular domain partitioning. This upwinding scheme introduces discontinuity of angular flux and resembles the classic upwinding technique developed for solving first order transport equation using discontinuous finite element method (DFEM) on the subdomain interfaces. Because this scheme restores the causality of radiation streaming on the interfaces, significant accuracy improvement can bemore » observed with moderate increase of the degrees of freedom comparing with the continuous method over the entire solution domain. Hybrid SN-PN is implemented and tested with this upwinding scheme. Numerical results show that the angular smoothing required by Lagrange multiplier method is not necessary for the upwinding scheme.« less

Multi-criteria decision aid approach for the selection of the best compromise management scheme for ELVs: the case of Cyprus.

PubMed

Mergias, I; Moustakas, K; Papadopoulos, A; Loizidou, M

2007-08-25

Each alternative scheme for treating a vehicle at its end of life has its own consequences from a social, environmental, economic and technical point of view. Furthermore, the criteria used to determine these consequences are often contradictory and not equally important. In the presence of multiple conflicting criteria, an optimal alternative scheme never exists. A multiple-criteria decision aid (MCDA) method to aid the Decision Maker (DM) in selecting the best compromise scheme for the management of End-of-Life Vehicles (ELVs) is presented in this paper. The constitution of a set of alternatives schemes, the selection of a list of relevant criteria to evaluate these alternative schemes and the choice of an appropriate management system are also analyzed in this framework. The proposed procedure relies on the PROMETHEE method which belongs to the well-known family of multiple criteria outranking methods. For this purpose, level, linear and Gaussian functions are used as preference functions.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations. Part 1; Viscous Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Nielsen, Eric J.; Nishikawa, Hiroaki; White, Jeffery A.

2009-01-01

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and efficiency are studied for six nominally second-order accurate schemes: a node-centered scheme, cell-centered node-averaging schemes with and without clipping, and cell-centered schemes with unweighted, weighted, and approximately mapped least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Results from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The second class of tests are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes are less accurate, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to the complexity of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping of the surface anisotropy or modifying the scheme stencil to reflect the direction of strong coupling.

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

DOE PAGES

Su, Hongling; Li, Shengtai

2016-02-03

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Su, Hongling; Li, Shengtai

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

Multi-Hierarchical Gray Correlation Analysis Applied in the Selection of Green Building Design Scheme

NASA Astrophysics Data System (ADS)

Wang, Li; Li, Chuanghong

2018-02-01

As a sustainable form of ecological structure, green building is widespread concerned and advocated in society increasingly nowadays. In the survey and design phase of preliminary project construction, carrying out the evaluation and selection of green building design scheme, which is in accordance with the scientific and reasonable evaluation index system, can improve the ecological benefits of green building projects largely and effectively. Based on the new Green Building Evaluation Standard which came into effect on January 1, 2015, the evaluation index system of green building design scheme is constructed taking into account the evaluation contents related to the green building design scheme. We organized experts who are experienced in construction scheme optimization to mark and determine the weight of each evaluation index through the AHP method. The correlation degree was calculated between each evaluation scheme and ideal scheme by using multilevel gray relational analysis model and then the optimal scheme was determined. The feasibility and practicability of the evaluation method are verified by introducing examples.

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

NASA Astrophysics Data System (ADS)

Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

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

Gas-Kinetic Theory Based Flux Splitting Method for Ideal Magnetohydrodynamics

NASA Technical Reports Server (NTRS)

Xu, Kun

1998-01-01

A gas-kinetic solver is developed for the ideal magnetohydrodynamics (MHD) equations. The new scheme is based on the direct splitting of the flux function of the MHD equations with the inclusion of "particle" collisions in the transport process. Consequently, the artificial dissipation in the new scheme is much reduced in comparison with the MHD Flux Vector Splitting Scheme. At the same time, the new scheme is compared with the well-developed Roe-type MHD solver. It is concluded that the kinetic MHD scheme is more robust and efficient than the Roe- type method, and the accuracy is competitive. In this paper the general principle of splitting the macroscopic flux function based on the gas-kinetic theory is presented. The flux construction strategy may shed some light on the possible modification of AUSM- and CUSP-type schemes for the compressible Euler equations, as well as to the development of new schemes for a non-strictly hyperbolic system.

Verlet scheme non-conservativeness for simulation of spherical particles collisional dynamics and method of its compensation

NASA Astrophysics Data System (ADS)

Savin, Andrei V.; Smirnov, Petr G.

2018-05-01

Simulation of collisional dynamics of a large ensemble of monodisperse particles by the method of discrete elements is considered. Verle scheme is used for integration of the equations of motion. Non-conservativeness of the finite-difference scheme is discovered depending on the time step, which is equivalent to a pure-numerical energy source appearance in the process of collision. Compensation method for the source is proposed and tested.

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

Finite time step and spatial grid effects in δf simulation of warm plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sturdevant, Benjamin J., E-mail: benjamin.j.sturdevant@gmail.com; Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO 80309; Parker, Scott E.

2016-01-15

This paper introduces a technique for analyzing time integration methods used with the particle weight equations in δf method particle-in-cell (PIC) schemes. The analysis applies to the simulation of warm, uniform, periodic or infinite plasmas in the linear regime and considers the collective behavior similar to the analysis performed by Langdon for full-f PIC schemes [1,2]. We perform both a time integration analysis and spatial grid analysis for a kinetic ion, adiabatic electron model of ion acoustic waves. An implicit time integration scheme is studied in detail for δf simulations using our weight equation analysis and for full-f simulations usingmore » the method of Langdon. It is found that the δf method exhibits a CFL-like stability condition for low temperature ions, which is independent of the parameter characterizing the implicitness of the scheme. The accuracy of the real frequency and damping rate due to the discrete time and spatial schemes is also derived using a perturbative method. The theoretical analysis of numerical error presented here may be useful for the verification of simulations and for providing intuition for the design of new implicit time integration schemes for the δf method, as well as understanding differences between δf and full-f approaches to plasma simulation.« less

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2010-01-01

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

Analysis of 3D poroelastodynamics using BEM based on modified time-step scheme

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Petrov, A. N.; Vorobtsov, I. V.

2017-10-01

The development of 3d boundary elements modeling of dynamic partially saturated poroelastic media using a stepping scheme is presented in this paper. Boundary Element Method (BEM) in Laplace domain and the time-stepping scheme for numerical inversion of the Laplace transform are used to solve the boundary value problem. The modified stepping scheme with a varied integration step for quadrature coefficients calculation using the symmetry of the integrand function and integral formulas of Strongly Oscillating Functions was applied. The problem with force acting on a poroelastic prismatic console end was solved using the developed method. A comparison of the results obtained by the traditional stepping scheme with the solutions obtained by this modified scheme shows that the computational efficiency is better with usage of combined formulas.

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.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

Standardization, evaluation and early-phase method validation of an analytical scheme for batch-consistency N-glycosylation analysis of recombinant produced glycoproteins.

PubMed

Zietze, Stefan; Müller, Rainer H; Brecht, René

2008-03-01

In order to set up a batch-to-batch-consistency analytical scheme for N-glycosylation analysis, several sample preparation steps including enzyme digestions and fluorophore labelling and two HPLC-methods were established. The whole method scheme was standardized, evaluated and validated according to the requirements on analytical testing in early clinical drug development by usage of a recombinant produced reference glycoprotein (RGP). The standardization of the methods was performed by clearly defined standard operation procedures. During evaluation of the methods, the major interest was in the loss determination of oligosaccharides within the analytical scheme. Validation of the methods was performed with respect to specificity, linearity, repeatability, LOD and LOQ. Due to the fact that reference N-glycan standards were not available, a statistical approach was chosen to derive accuracy from the linearity data. After finishing the validation procedure, defined limits for method variability could be calculated and differences observed in consistency analysis could be separated into significant and incidental ones.

Field by field hybrid upwind splitting methods

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1993-01-01

A new and general approach to upwind splitting is presented. The design principle combines the robustness of flux vector splitting schemes in the capture of nonlinear waves and the accuracy of some flux difference splitting schemes in the resolution of linear waves. The new schemes are derived following a general hybridization technique performed directly at the basic level of the field by field decomposition involved in FDS methods. The scheme does not use a spatial switch to be tuned up according to the local smoothness of the approximate solution.

A constrained-gradient method to control divergence errors in numerical MHD

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2016-10-01

In numerical magnetohydrodynamics (MHD), a major challenge is maintaining nabla \\cdot {B}=0. Constrained transport (CT) schemes achieve this but have been restricted to specific methods. For more general (meshless, moving-mesh, ALE) methods, `divergence-cleaning' schemes reduce the nabla \\cdot {B} errors; however they can still be significant and can lead to systematic errors which converge away slowly. We propose a new constrained gradient (CG) scheme which augments these with a projection step, and can be applied to any numerical scheme with a reconstruction. This iteratively approximates the least-squares minimizing, globally divergence-free reconstruction of the fluid. Unlike `locally divergence free' methods, this actually minimizes the numerically unstable nabla \\cdot {B} terms, without affecting the convergence order of the method. We implement this in the mesh-free code GIZMO and compare various test problems. Compared to cleaning schemes, our CG method reduces the maximum nabla \\cdot {B} errors by ˜1-3 orders of magnitude (˜2-5 dex below typical errors if no nabla \\cdot {B} cleaning is used). By preventing large nabla \\cdot {B} at discontinuities, this eliminates systematic errors at jumps. Our CG results are comparable to CT methods; for practical purposes, the nabla \\cdot {B} errors are eliminated. The cost is modest, ˜30 per cent of the hydro algorithm, and the CG correction can be implemented in a range of numerical MHD methods. While for many problems, we find Dedner-type cleaning schemes are sufficient for good results, we identify a range of problems where using only Powell or `8-wave' cleaning can produce order-of-magnitude errors.

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 are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.

General relaxation schemes in multigrid algorithms for higher order singularity methods

NASA Technical Reports Server (NTRS)

Oskam, B.; Fray, J. M. J.

1981-01-01

Relaxation schemes based on approximate and incomplete factorization technique (AF) are described. The AF schemes allow construction of a fast multigrid method for solving integral equations of the second and first kind. The smoothing factors for integral equations of the first kind, and comparison with similar results from the second kind of equations are a novel item. Application of the MD algorithm shows convergence to the level of truncation error of a second order accurate panel method.

An explicit mixed numerical method for mesoscale model

NASA Technical Reports Server (NTRS)

Hsu, H.-M.

1981-01-01

A mixed numerical method has been developed for mesoscale models. The technique consists of a forward difference scheme for time tendency terms, an upstream scheme for advective terms, and a central scheme for the other terms in a physical system. It is shown that the mixed method is conditionally stable and highly accurate for approximating the system of either shallow-water equations in one dimension or primitive equations in three dimensions. Since the technique is explicit and two time level, it conserves computer and programming resources.

Power and spectrally efficient M-ARY QAM schemes for future mobile satellite communications

NASA Technical Reports Server (NTRS)

Sreenath, K.; Feher, K.

1990-01-01

An effective method to compensate nonlinear phase distortion caused by the mobile amplifier is proposed. As a first step towards the future use of spectrally efficient modulation schemes for mobile satellite applications, we have investigated effects of nonlinearities and the phase compensation method on 16-QAM. The new method provides about 2 dB savings in power for 16-QAM operation with cost effective amplifiers near saturation and thereby promising use of spectrally efficient linear modulation schemes for future mobile satellite applications.

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaofeng, E-mail: xfyang@math.sc.edu; Han, Daozhi, E-mail: djhan@iu.edu

2017-02-01

In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank–Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposedmore » schemes.« less

A Time-Accurate Upwind Unstructured Finite Volume Method for Compressible Flow with Cure of Pathological Behaviors

NASA Technical Reports Server (NTRS)

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

2007-01-01

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.

Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization

NASA Astrophysics Data System (ADS)

MacArt, Jonathan F.; Mueller, Michael E.

2016-12-01

Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza R.; Nishikawa, Hiroaki

2014-01-01

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

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 derivatives and a fourth-order Runge-Kutta method are denoted.

The method of space-time and conservation element and solution element: A new approach for solving the Navier-Stokes and Euler equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1995-01-01

A new numerical framework for solving conservation laws is being developed. This new framework differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to overcome several key limitations of the above traditional methods. A two-level scheme for solving the convection-diffusion equation is constructed and used to illuminate the major differences between the present method and those previously mentioned. This explicit scheme, referred to as the a-mu scheme, has two independent marching variables.

Von Neumann stability analysis of globally divergence-free RKDG schemes for the induction equation using multidimensional Riemann solvers

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Käppeli, Roger

2017-05-01

In this paper we focus on the numerical solution of the induction equation using Runge-Kutta Discontinuous Galerkin (RKDG)-like schemes that are globally divergence-free. The induction equation plays a role in numerical MHD and other systems like it. It ensures that the magnetic field evolves in a divergence-free fashion; and that same property is shared by the numerical schemes presented here. The algorithms presented here are based on a novel DG-like method as it applies to the magnetic field components in the faces of a mesh. (I.e., this is not a conventional DG algorithm for conservation laws.) The other two novel building blocks of the method include divergence-free reconstruction of the magnetic field and multidimensional Riemann solvers; both of which have been developed in recent years by the first author. Since the method is linear, a von Neumann stability analysis is carried out in two-dimensions to understand its stability properties. The von Neumann stability analysis that we develop in this paper relies on transcribing from a modal to a nodal DG formulation in order to develop discrete evolutionary equations for the nodal values. These are then coupled to a suitable Runge-Kutta timestepping strategy so that one can analyze the stability of the entire scheme which is suitably high order in space and time. We show that our scheme permits CFL numbers that are comparable to those of traditional RKDG schemes. We also analyze the wave propagation characteristics of the method and show that with increasing order of accuracy the wave propagation becomes more isotropic and free of dissipation for a larger range of long wavelength modes. This makes a strong case for investing in higher order methods. We also use the von Neumann stability analysis to show that the divergence-free reconstruction and multidimensional Riemann solvers are essential algorithmic ingredients of a globally divergence-free RKDG-like scheme. Numerical accuracy analyses of the RKDG-like schemes are presented and compared with the accuracy of PNPM schemes. It is found that PNPM retrieve much of the accuracy of the RKDG-like schemes while permitting a larger CFL number.

An Investigation of High-Order Shock-Capturing Methods for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Casper, Jay; Baysal, Oktay

1997-01-01

Topics covered include: Low-dispersion scheme for nonlinear acoustic waves in nonuniform flow; Computation of acoustic scattering by a low-dispersion scheme; Algorithmic extension of low-dispersion scheme and modeling effects for acoustic wave simulation; The accuracy of shock capturing in two spatial dimensions; Using high-order methods on lower-order geometries; and Computational considerations for the simulation of discontinuous flows.

Numerical Methods Using B-Splines

NASA Technical Reports Server (NTRS)

Shariff, Karim; Merriam, Marshal (Technical Monitor)

1997-01-01

The seminar will discuss (1) The current range of applications for which B-spline schemes may be appropriate (2) The property of high-resolution and the relationship between B-spline and compact schemes (3) Comparison between finite-element, Hermite finite element and B-spline schemes (4) Mesh embedding using B-splines (5) A method for the incompressible Navier-Stokes equations in curvilinear coordinates using divergence-free expansions.

Provider payment in community-based health insurance schemes in developing countries: a systematic review

PubMed Central

Robyn, Paul Jacob; Sauerborn, Rainer; Bärnighausen, Till

2013-01-01

Objectives Community-based health insurance (CBI) is a common mechanism to generate financial resources for health care in developing countries. We review for the first time provider payment methods used in CBI in developing countries and their impact on CBI performance. Methods We conducted a systematic review of the literature on provider payment methods used by CBI in developing countries published up to January 2010. Results Information on provider payment was available for a total of 32 CBI schemes in 34 reviewed publications: 17 schemes in South Asia, 10 in sub-Saharan Africa, 4 in East Asia and 1 in Latin America. Various types of provider payment were applied by the CBI schemes: 17 used fee-for-service, 12 used salaries, 9 applied a coverage ceiling, 7 used capitation and 6 applied a co-insurance. The evidence suggests that provider payment impacts CBI performance through provider participation and support for CBI, population enrolment and patient satisfaction with CBI, quantity and quality of services provided and provider and patient retention. Lack of provider participation in designing and choosing a CBI payment method can lead to reduced provider support for the scheme. Conclusion CBI schemes in developing countries have used a wide range of provider payment methods. The existing evidence suggests that payment methods are a key determinant of CBI performance and sustainability, but the strength of this evidence is limited since it is largely based on observational studies rather than on trials or on quasi-experimental research. According to the evidence, provider payment can affect provider participation, satisfaction and retention in CBI; the quantity and quality of services provided to CBI patients; patient demand of CBI services; and population enrollment, risk pooling and financial sustainability of CBI. CBI schemes should carefully consider how their current payment methods influence their performance, how changes in the methods could improve performance, and how such effects could be assessed with scientific rigour to increase the strength of evidence on this topic. PMID:22522770

Team interaction during surgery: a systematic review of communication coding schemes.

PubMed

Tiferes, Judith; Bisantz, Ann M; Guru, Khurshid A

2015-05-15

Communication problems have been systematically linked to human errors in surgery and a deep understanding of the underlying processes is essential. Although a number of tools exist to assess nontechnical skills, methods to study communication and other team-related processes are far from being standardized, making comparisons challenging. We conducted a systematic review to analyze methods used to study events in the operating room (OR) and to develop a synthesized coding scheme for OR team communication. Six electronic databases were accessed to search for articles that collected individual events during surgery and included detailed coding schemes. Additional articles were added based on cross-referencing. That collection was then classified based on type of events collected, environment type (real or simulated), number of procedures, type of surgical task, team characteristics, method of data collection, and coding scheme characteristics. All dimensions within each coding scheme were grouped based on emergent content similarity. Categories drawn from articles, which focused on communication events, were further analyzed and synthesized into one common coding scheme. A total of 34 of 949 articles met the inclusion criteria. The methodological characteristics and coding dimensions of the articles were summarized. A priori coding was used in nine studies. The synthesized coding scheme for OR communication included six dimensions as follows: information flow, period, statement type, topic, communication breakdown, and effects of communication breakdown. The coding scheme provides a standardized coding method for OR communication, which can be used to develop a priori codes for future studies especially in comparative effectiveness research. Copyright © 2015 Elsevier Inc. All rights reserved.

TU-EF-204-01: Accurate Prediction of CT Tube Current Modulation: Estimating Tube Current Modulation Schemes for Voxelized Patient Models Used in Monte Carlo Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

McMillan, K; Bostani, M; McNitt-Gray, M

2015-06-15

Purpose: Most patient models used in Monte Carlo-based estimates of CT dose, including computational phantoms, do not have tube current modulation (TCM) data associated with them. While not a problem for fixed tube current simulations, this is a limitation when modeling the effects of TCM. Therefore, the purpose of this work was to develop and validate methods to estimate TCM schemes for any voxelized patient model. Methods: For 10 patients who received clinically-indicated chest (n=5) and abdomen/pelvis (n=5) scans on a Siemens CT scanner, both CT localizer radiograph (“topogram”) and image data were collected. Methods were devised to estimate themore » complete x-y-z TCM scheme using patient attenuation data: (a) available in the Siemens CT localizer radiograph/topogram itself (“actual-topo”) and (b) from a simulated topogram (“sim-topo”) derived from a projection of the image data. For comparison, the actual TCM scheme was extracted from the projection data of each patient. For validation, Monte Carlo simulations were performed using each TCM scheme to estimate dose to the lungs (chest scans) and liver (abdomen/pelvis scans). Organ doses from simulations using the actual TCM were compared to those using each of the estimated TCM methods (“actual-topo” and “sim-topo”). Results: For chest scans, the average differences between doses estimated using actual TCM schemes and estimated TCM schemes (“actual-topo” and “sim-topo”) were 3.70% and 4.98%, respectively. For abdomen/pelvis scans, the average differences were 5.55% and 6.97%, respectively. Conclusion: Strong agreement between doses estimated using actual and estimated TCM schemes validates the methods for simulating Siemens topograms and converting attenuation data into TCM schemes. This indicates that the methods developed in this work can be used to accurately estimate TCM schemes for any patient model or computational phantom, whether a CT localizer radiograph is available or not. Funding Support: NIH Grant R01-EB017095; Disclosures - Michael McNitt-Gray: Institutional Research Agreement, Siemens AG; Research Support, Siemens AG; Consultant, Flaherty Sensabaugh Bonasso PLLC; Consultant, Fulbright and Jaworski; Disclosures - Cynthia McCollough: Research Grant, Siemens Healthcare.« less

A third-order gas-kinetic CPR method for the Euler and Navier-Stokes equations on triangular meshes

NASA Astrophysics Data System (ADS)

Zhang, Chao; Li, Qibing; Fu, Song; Wang, Z. J.

2018-06-01

A third-order accurate gas-kinetic scheme based on the correction procedure via reconstruction (CPR) framework is developed for the Euler and Navier-Stokes equations on triangular meshes. The scheme combines the accuracy and efficiency of the CPR formulation with the multidimensional characteristics and robustness of the gas-kinetic flux solver. Comparing with high-order finite volume gas-kinetic methods, the current scheme is more compact and efficient by avoiding wide stencils on unstructured meshes. Unlike the traditional CPR method where the inviscid and viscous terms are treated differently, the inviscid and viscous fluxes in the current scheme are coupled and computed uniformly through the kinetic evolution model. In addition, the present scheme adopts a fully coupled spatial and temporal gas distribution function for the flux evaluation, achieving high-order accuracy in both space and time within a single step. Numerical tests with a wide range of flow problems, from nearly incompressible to supersonic flows with strong shocks, for both inviscid and viscous problems, demonstrate the high accuracy and efficiency of the present scheme.

High-Order Space-Time Methods for Conservation Laws

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2013-01-01

Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown

A new Euler scheme based on harmonic-polygon approach for solving first order ordinary differential equation

NASA Astrophysics Data System (ADS)

Yusop, Nurhafizah Moziyana Mohd; Hasan, Mohammad Khatim; Wook, Muslihah; Amran, Mohd Fahmi Mohamad; Ahmad, Siti Rohaidah

2017-10-01

There are many benefits to improve Euler scheme for solving the Ordinary Differential Equation Problems. Among the benefits are simple implementation and low-cost computational. However, the problem of accuracy in Euler scheme persuade scholar to use complex method. Therefore, the main purpose of this research are show the construction a new modified Euler scheme that improve accuracy of Polygon scheme in various step size. The implementing of new scheme are used Polygon scheme and Harmonic mean concept that called as Harmonic-Polygon scheme. This Harmonic-Polygon can provide new advantages that Euler scheme could offer by solving Ordinary Differential Equation problem. Four set of problems are solved via Harmonic-Polygon. Findings show that new scheme or Harmonic-Polygon scheme can produce much better accuracy result.

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods - Part 1: Derivation and properties

NASA Astrophysics Data System (ADS)

Eldred, Christopher; Randall, David

2017-02-01

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restricted to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.

Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers

NASA Technical Reports Server (NTRS)

Kennedy, Christopher A.; Carpenter, Mark H.

1997-01-01

An investigation is conducted on several numerical schemes for use in the computation of two-dimensional, spatially evolving, laminar variable-density compressible shear layers. Schemes with various temporal accuracies and arbitrary spatial accuracy for both inviscid and viscous terms are presented and analyzed. All integration schemes use explicit or compact finite-difference derivative operators. Three classes of schemes are considered: an extension of MacCormack's original second-order temporally accurate method, a new third-order variant of the schemes proposed by Rusanov and by Kutier, Lomax, and Warming (RKLW), and third- and fourth-order Runge-Kutta schemes. In each scheme, stability and formal accuracy are considered for the interior operators on the convection-diffusion equation U(sub t) + aU(sub x) = alpha U(sub xx). Accuracy is also verified on the nonlinear problem, U(sub t) + F(sub x) = 0. Numerical treatments of various orders of accuracy are chosen and evaluated for asymptotic stability. Formally accurate boundary conditions are derived for several sixth- and eighth-order central-difference schemes. Damping of high wave-number data is accomplished with explicit filters of arbitrary order. Several schemes are used to compute variable-density compressible shear layers, where regions of large gradients exist.

Discrete maximal regularity of time-stepping schemes for fractional evolution equations.

PubMed

Jin, Bangti; Li, Buyang; Zhou, Zhi

2018-01-01

In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735-758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157-176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems.

Sparsity-Aware DOA Estimation Scheme for Noncircular Source in MIMO Radar.

PubMed

Wang, Xianpeng; Wang, Wei; Li, Xin; Liu, Qi; Liu, Jing

2016-04-14

In this paper, a novel sparsity-aware direction of arrival (DOA) estimation scheme for a noncircular source is proposed in multiple-input multiple-output (MIMO) radar. In the proposed method, the reduced-dimensional transformation technique is adopted to eliminate the redundant elements. Then, exploiting the noncircularity of signals, a joint sparsity-aware scheme based on the reweighted l1 norm penalty is formulated for DOA estimation, in which the diagonal elements of the weight matrix are the coefficients of the noncircular MUSIC-like (NC MUSIC-like) spectrum. Compared to the existing l1 norm penalty-based methods, the proposed scheme provides higher angular resolution and better DOA estimation performance. Results from numerical experiments are used to show the effectiveness of our proposed method.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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.

Satisfaction rates with the current Special Type Consultation (STC) reimbursement scheme among General Practitioners - A Mixed Methods Study.

PubMed

Kiely, A; O'Meara, S; Fitzgerald, N; Regan, A M; Durcan, P; McGuire, G; Kelly, M E

2017-03-10

The Special Type Consultation (STC) scheme is a fee-for-service reimbursement scheme for General Practitioners (GPs) in Ireland. Introduced in 1989, the scheme includes specified patient services involving the application of a learned skill, e.g. suturing. This study aims to establish the extent to which GPs believe this scheme is appropriate for current General Practice. This is an embedded mixed-methods study combining quantitative data on GPs working experience of and qualitative data on GPs attitudes towards the scheme. Data were collected by means of an anonymous postal questionnaire. The response rate was 60.4% (n=159.) Twenty-nine percent (n=46) disagreed and 65% (n=104) strongly disagreed that the current list of special items is satisfactory. Two overriding themes were identified: economics and advancement of the STC process. This study demonstrates an overwhelming consensus among GPs that the current STC scheme is outdated and in urgent need of revision to reflect modern General Practice.

Downlink Multihop Transmission Technique for Asymmetric Traffic Accommodation in DS-CDMA/FDD Cellular Communications

NASA Astrophysics Data System (ADS)

Mori, Kazuo; Naito, Katsuhiro; Kobayashi, Hideo

This paper proposes an asymmetric traffic accommodation scheme using a multihop transmission technique for CDMA/FDD cellular communication systems. The proposed scheme exploits the multihop transmission to downlink packet transmissions, which require the large transmission power at their single-hop transmissions, in order to increase the downlink capacity. In these multihop transmissions, vacant uplink band is used for the transmissions from relay stations to destination mobile stations, and this leads more capacity enhancement in the downlink communications. The relay route selection method and power control method for the multihop transmissions are also investigated in the proposed scheme. The proposed scheme is evaluated by computer simulation and the results show that the proposed scheme can achieve better system performance.

A Two Colorable Fourth Order Compact Difference Scheme and Parallel Iterative Solution of the 3D Convection Diffusion Equation

NASA Technical Reports Server (NTRS)

Zhang, Jun; Ge, Lixin; Kouatchou, Jules

2000-01-01

A new fourth order compact difference scheme for the three dimensional convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it Only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with the Gauss-Seidel type iterative method. This is compared with the known 19 point fourth order compact differenCe scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15 point and the 19 point fourth order compact schemes.

Decoy-state quantum key distribution with biased basis choice

PubMed Central

Wei, Zhengchao; Wang, Weilong; Zhang, Zhen; Gao, Ming; Ma, Zhi; Ma, Xiongfeng

2013-01-01

We propose a quantum key distribution scheme that combines a biased basis choice with the decoy-state method. In this scheme, Alice sends all signal states in the Z basis and decoy states in the X and Z basis with certain probabilities, and Bob measures received pulses with optimal basis choice. This scheme simplifies the system and reduces the random number consumption. From the simulation result taking into account of statistical fluctuations, we find that in a typical experimental setup, the proposed scheme can increase the key rate by at least 45% comparing to the standard decoy-state scheme. In the postprocessing, we also apply a rigorous method to upper bound the phase error rate of the single-photon components of signal states. PMID:23948999

Decoy-state quantum key distribution with biased basis choice.

PubMed

Wei, Zhengchao; Wang, Weilong; Zhang, Zhen; Gao, Ming; Ma, Zhi; Ma, Xiongfeng

2013-01-01

We propose a quantum key distribution scheme that combines a biased basis choice with the decoy-state method. In this scheme, Alice sends all signal states in the Z basis and decoy states in the X and Z basis with certain probabilities, and Bob measures received pulses with optimal basis choice. This scheme simplifies the system and reduces the random number consumption. From the simulation result taking into account of statistical fluctuations, we find that in a typical experimental setup, the proposed scheme can increase the key rate by at least 45% comparing to the standard decoy-state scheme. In the postprocessing, we also apply a rigorous method to upper bound the phase error rate of the single-photon components of signal states.

On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifth-order WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge-Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of the approximations.

A novel 2.5D finite difference scheme for simulations of resistivity logging in anisotropic media

NASA Astrophysics Data System (ADS)

Zeng, Shubin; Chen, Fangzhou; Li, Dawei; Chen, Ji; Chen, Jiefu

2018-03-01

The objective of this study is to develop a method to model 3D resistivity well logging problems in 2D formation with anisotropy, known as 2.5D modeling. The traditional 1D forward modeling extensively used in practice lacks the capability of modeling 2D formation. A 2.5D finite difference method (FDM) solving all the electric and magnetic field components simultaneously is proposed. Compared to other previous 2.5D FDM schemes, this method is more straightforward in modeling fully anisotropic media and easy to be implemented. Fourier transform is essential to this FDM scheme, and by employing Gauss-Legendre (GL) quadrature rule the computational time of this step can be greatly reduced. In the numerical examples, we first demonstrate the validity of the FDM scheme with GL rule by comparing with 1D forward modeling for layered anisotropic problems, and then we model a complicated 2D formation case and find that the proposed 2.5D FD scheme is much more efficient than 3D numerical methods.

Comparison of Implicit Schemes for the Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.

1995-01-01

For a computational flow simulation tool to be useful in a design environment, it must be very robust and efficient. To develop such a tool for incompressible flow applications, a number of different implicit schemes are compared for several two-dimensional flow problems in the current study. The schemes include Point-Jacobi relaxation, Gauss-Seidel line relaxation, incomplete lower-upper decomposition, and the generalized minimum residual method preconditioned with each of the three other schemes. The efficiency of the schemes is measured in terms of the computing time required to obtain a steady-state solution for the laminar flow over a backward-facing step, the flow over a NACA 4412 airfoil, and the flow over a three-element airfoil using overset grids. The flow solver used in the study is the INS2D code that solves the incompressible Navier-Stokes equations using the method of artificial compressibility and upwind differencing of the convective terms. The results show that the generalized minimum residual method preconditioned with the incomplete lower-upper factorization outperforms all other methods by at least a factor of 2.

Notes on two multiparty quantum secret sharing schemes

NASA Astrophysics Data System (ADS)

Gao, Gan

In the paper [H. Abulkasim et al., Int. J. Quantum Inform. 15 (2017) 1750023], Abulkasim et al. proposed a quantum secret sharing scheme based on Bell states. We study the security of the multiparty case in the proposed scheme and detect that it is not secure. In the paper [Y. Du and W. Bao, Opt. Commun. 308 (2013) 159], Du and Bao listed Gao’s scheme and gave a attack strategy on the listed scheme. We point out that their listing scheme is not the genuine Gao’s scheme and their research method is not advisable.

A joint precoding scheme for indoor downlink multi-user MIMO VLC systems

NASA Astrophysics Data System (ADS)

Zhao, Qiong; Fan, Yangyu; Kang, Bochao

2017-11-01

In this study, we aim to improve the system performance and reduce the implementation complexity of precoding scheme for visible light communication (VLC) systems. By incorporating the power-method algorithm and the block diagonalization (BD) algorithm, we propose a joint precoding scheme for indoor downlink multi-user multi-input-multi-output (MU-MIMO) VLC systems. In this scheme, we apply the BD algorithm to eliminate the co-channel interference (CCI) among users firstly. Secondly, the power-method algorithm is used to search the precoding weight for each user based on the optimal criterion of signal to interference plus noise ratio (SINR) maximization. Finally, the optical power restrictions of VLC systems are taken into account to constrain the precoding weight matrix. Comprehensive computer simulations in two scenarios indicate that the proposed scheme always has better bit error rate (BER) performance and lower computation complexity than that of the traditional scheme.

A space-time lower-upper symmetric Gauss-Seidel scheme for the time-spectral method

NASA Astrophysics Data System (ADS)

Zhan, Lei; Xiong, Juntao; Liu, Feng

2016-05-01

The time-spectral method (TSM) offers the advantage of increased order of accuracy compared to methods using finite-difference in time for periodic unsteady flow problems. Explicit Runge-Kutta pseudo-time marching and implicit schemes have been developed to solve iteratively the space-time coupled nonlinear equations resulting from TSM. Convergence of the explicit schemes is slow because of the stringent time-step limit. Many implicit methods have been developed for TSM. Their computational efficiency is, however, still limited in practice because of delayed implicit temporal coupling, multiple iterative loops, costly matrix operations, or lack of strong diagonal dominance of the implicit operator matrix. To overcome these shortcomings, an efficient space-time lower-upper symmetric Gauss-Seidel (ST-LU-SGS) implicit scheme with multigrid acceleration is presented. In this scheme, the implicit temporal coupling term is split as one additional dimension of space in the LU-SGS sweeps. To improve numerical stability for periodic flows with high frequency, a modification to the ST-LU-SGS scheme is proposed. Numerical results show that fast convergence is achieved using large or even infinite Courant-Friedrichs-Lewy (CFL) numbers for unsteady flow problems with moderately high frequency and with the use of moderately high numbers of time intervals. The ST-LU-SGS implicit scheme is also found to work well in calculating periodic flow problems where the frequency is not known a priori and needed to be determined by using a combined Fourier analysis and gradient-based search algorithm.

Revised Chapman-Enskog analysis for a class of forcing schemes in the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Li, Q.; Zhou, P.; Yan, H. J.

2016-10-01

In the lattice Boltzmann (LB) method, the forcing scheme, which is used to incorporate an external or internal force into the LB equation, plays an important role. It determines whether the force of the system is correctly implemented in an LB model and affects the numerical accuracy. In this paper we aim to clarify a critical issue about the Chapman-Enskog analysis for a class of forcing schemes in the LB method in which the velocity in the equilibrium density distribution function is given by u =∑αeαfα / ρ , while the actual fluid velocity is defined as u ̂=u +δtF / (2 ρ ) . It is shown that the usual Chapman-Enskog analysis for this class of forcing schemes should be revised so as to derive the actual macroscopic equations recovered from these forcing schemes. Three forcing schemes belonging to the above class are analyzed, among which Wagner's forcing scheme [A. J. Wagner, Phys. Rev. E 74, 056703 (2006), 10.1103/PhysRevE.74.056703] is shown to be capable of reproducing the correct macroscopic equations. The theoretical analyses are examined and demonstrated with two numerical tests, including the simulation of Womersley flow and the modeling of flat and circular interfaces by the pseudopotential multiphase LB model.

Provider payment in community-based health insurance schemes in developing countries: a systematic review.

PubMed

Robyn, Paul Jacob; Sauerborn, Rainer; Bärnighausen, Till

2013-03-01

Community-based health insurance (CBI) is a common mechanism to generate financial resources for health care in developing countries. We review for the first time provider payment methods used in CBI in developing countries and their impact on CBI performance. We conducted a systematic review of the literature on provider payment methods used by CBI in developing countries published up to January 2010. Information on provider payment was available for a total of 32 CBI schemes in 34 reviewed publications: 17 schemes in South Asia, 10 in sub-Saharan Africa, 4 in East Asia and 1 in Latin America. Various types of provider payment were applied by the CBI schemes: 17 used fee-for-service, 12 used salaries, 9 applied a coverage ceiling, 7 used capitation and 6 applied a co-insurance. The evidence suggests that provider payment impacts CBI performance through provider participation and support for CBI, population enrolment and patient satisfaction with CBI, quantity and quality of services provided and provider and patient retention. Lack of provider participation in designing and choosing a CBI payment method can lead to reduced provider support for the scheme. CBI schemes in developing countries have used a wide range of provider payment methods. The existing evidence suggests that payment methods are a key determinant of CBI performance and sustainability, but the strength of this evidence is limited since it is largely based on observational studies rather than on trials or on quasi-experimental research. According to the evidence, provider payment can affect provider participation, satisfaction and retention in CBI; the quantity and quality of services provided to CBI patients; patient demand of CBI services; and population enrollment, risk pooling and financial sustainability of CBI. CBI schemes should carefully consider how their current payment methods influence their performance, how changes in the methods could improve performance, and how such effects could be assessed with scientific rigour to increase the strength of evidence on this topic.

The Method of Space-time Conservation Element and Solution Element: Development of a New Implicit Solver

NASA Technical Reports Server (NTRS)

Chang, S. C.; Wang, X. Y.; Chow, C. Y.; Himansu, A.

1995-01-01

The method of space-time conservation element and solution element is a nontraditional numerical method designed from a physicist's perspective, i.e., its development is based more on physics than numerics. It uses only the simplest approximation techniques and yet is capable of generating nearly perfect solutions for a 2-D shock reflection problem used by Helen Yee and others. In addition to providing an overall view of the new method, we introduce a new concept in the design of implicit schemes, and use it to construct a highly accurate solver for a convection-diffusion equation. It is shown that, in the inviscid case, this new scheme becomes explicit and its amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, its principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

A family of high-order gas-kinetic schemes and its comparison with Riemann solver based high-order methods

NASA Astrophysics Data System (ADS)

Ji, Xing; Zhao, Fengxiang; Shyy, Wei; Xu, Kun

2018-03-01

Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The advantage of this kind of space-time separation approach is the easy implementation and stability enhancement by introducing more middle stages. However, the nth-order time accuracy needs no less than n stages for the RK method, which can be very time and memory consuming due to the reconstruction at each stage for a high order method. On the other hand, the multi-stage multi-derivative (MSMD) method can be used to achieve the same order of time accuracy using less middle stages with the use of the time derivatives of the flux function. For traditional Riemann solver based CFD methods, the lack of time derivatives in the flux function prevents its direct implementation of the MSMD method. However, the gas kinetic scheme (GKS) provides such a time accurate evolution model. By combining the second-order or third-order GKS flux functions with the MSMD technique, a family of high order gas kinetic methods can be constructed. As an extension of the previous 2-stage 4th-order GKS, the 5th-order schemes with 2 and 3 stages will be developed in this paper. Based on the same 5th-order WENO reconstruction, the performance of gas kinetic schemes from the 2nd- to the 5th-order time accurate methods will be evaluated. The results show that the 5th-order scheme can achieve the theoretical order of accuracy for the Euler equations, and present accurate Navier-Stokes solutions as well due to the coupling of inviscid and viscous terms in the GKS formulation. In comparison with Riemann solver based 5th-order RK method, the high order GKS has advantages in terms of efficiency, accuracy, and robustness, for all test cases. The 4th- and 5th-order GKS have the same robustness as the 2nd-order scheme for the capturing of discontinuous solutions. The current high order MSMD GKS is a multi-dimensional scheme with incorporation of both normal and tangential spatial derivatives of flow variables at a cell interface in the flux evaluation. The scheme can be extended straightforwardly to viscous flow computation in unstructured mesh. It provides a promising direction for the development of high-order CFD methods for the computation of complex flows, such as turbulence and acoustics with shock interactions.

Computational electrodynamics in material media with constraint-preservation, multidimensional Riemann solvers and sub-cell resolution - Part II, higher order FVTD schemes

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Garain, Sudip; Taflove, Allen; Montecinos, Gino

2018-02-01

The Finite Difference Time Domain (FDTD) scheme has served the computational electrodynamics community very well and part of its success stems from its ability to satisfy the constraints in Maxwell's equations. Even so, in the previous paper of this series we were able to present a second order accurate Godunov scheme for computational electrodynamics (CED) which satisfied all the same constraints and simultaneously retained all the traditional advantages of Godunov schemes. In this paper we extend the Finite Volume Time Domain (FVTD) schemes for CED in material media to better than second order of accuracy. From the FDTD method, we retain a somewhat modified staggering strategy of primal variables which enables a very beneficial constraint-preservation for the electric displacement and magnetic induction vector fields. This is accomplished with constraint-preserving reconstruction methods which are extended in this paper to third and fourth orders of accuracy. The idea of one-dimensional upwinding from Godunov schemes has to be significantly modified to use the multidimensionally upwinded Riemann solvers developed by the first author. In this paper, we show how they can be used within the context of a higher order scheme for CED. We also report on advances in timestepping. We show how Runge-Kutta IMEX schemes can be adapted to CED even in the presence of stiff source terms brought on by large conductivities as well as strong spatial variations in permittivity and permeability. We also formulate very efficient ADER timestepping strategies to endow our method with sub-cell resolving capabilities. As a result, our method can be stiffly-stable and resolve significant sub-cell variation in the material properties within a zone. Moreover, we present ADER schemes that are applicable to all hyperbolic PDEs with stiff source terms and at all orders of accuracy. Our new ADER formulation offers a treatment of stiff source terms that is much more efficient than previous ADER schemes. The computer algebra system scripts for generating ADER time update schemes for any general PDE with stiff source terms are also given in the electronic supplements to this paper. Second, third and fourth order accurate schemes for numerically solving Maxwell's equations in material media are presented in this paper. Several stringent tests are also presented to show that the method works and meets its design goals even when material permittivity and permeability vary by an order of magnitude over just a few zones. Furthermore, since the method is unconditionally stable and sub-cell-resolving in the presence of stiff source terms (i.e. for problems involving giant variations in conductivity over just a few zones), it can accurately handle such problems without any reduction in timestep. We also show that increasing the order of accuracy offers distinct advantages for resolving sub-cell variations in material properties. Most importantly, we show that when the accuracy requirements are stringent the higher order schemes offer the shortest time to solution. This makes a compelling case for the use of higher order, sub-cell resolving schemes in CED.

Modelling spoilage of fresh turbot and evaluation of a time-temperature integrator (TTI) label under fluctuating temperature.

PubMed

Nuin, Maider; Alfaro, Begoña; Cruz, Ziortza; Argarate, Nerea; George, Susie; Le Marc, Yvan; Olley, June; Pin, Carmen

2008-10-31

Kinetic models were developed to predict the microbial spoilage and the sensory quality of fresh fish and to evaluate the efficiency of a commercial time-temperature integrator (TTI) label, Fresh Check(R), to monitor shelf life. Farmed turbot (Psetta maxima) samples were packaged in PVC film and stored at 0, 5, 10 and 15 degrees C. Microbial growth and sensory attributes were monitored at regular time intervals. The response of the Fresh Check device was measured at the same temperatures during the storage period. The sensory perception was quantified according to a global sensory indicator obtained by principal component analysis as well as to the Quality Index Method, QIM, as described by Rahman and Olley [Rahman, H.A., Olley, J., 1984. Assessment of sensory techniques for quality assessment of Australian fish. CSIRO Tasmanian Regional Laboratory. Occasional paper n. 8. Available from the Australian Maritime College library. Newnham. Tasmania]. Both methods were found equally valid to monitor the loss of sensory quality. The maximum specific growth rate of spoilage bacteria, the rate of change of the sensory indicators and the rate of change of the colour measurements of the TTI label were modelled as a function of temperature. The temperature had a similar effect on the bacteria, sensory and Fresh Check kinetics. At the time of sensory rejection, the bacterial load was ca. 10(5)-10(6) cfu/g. The end of shelf life indicated by the Fresh Check label was close to the sensory rejection time. The performance of the models was validated under fluctuating temperature conditions by comparing the predicted and measured values for all microbial, sensory and TTI responses. The models have been implemented in a Visual Basic add-in for Excel called "Fish Shelf Life Prediction (FSLP)". This program predicts sensory acceptability and growth of spoilage bacteria in fish and the response of the TTI at constant and fluctuating temperature conditions. The program is freely available at http://www.azti.es/muestracontenido.asp?idcontenido=980&content=15&nodo1=30&nodo2=0.

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

PubMed Central

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

PubMed

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

Numerical methods for the simulation of complex multi-body flows with applications for the integrated Space Shuttle vehicle

NASA Technical Reports Server (NTRS)

Chan, William M.

1992-01-01

The following papers are presented: (1) numerical methods for the simulation of complex multi-body flows with applications for the Integrated Space Shuttle vehicle; (2) a generalized scheme for 3-D hyperbolic grid generation; (3) collar grids for intersecting geometric components within the Chimera overlapped grid scheme; and (4) application of the Chimera overlapped grid scheme to simulation of Space Shuttle ascent flows.

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

DTIC Science & Technology

2015-06-22

Galerkin methodology formulated in the framework of the residual-distribution method. For both second- and third- 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...construct these schemes based on the Low-Diffusion-A and the Streamwise-Upwind-Petrov-Galerkin methodology formulated in the framework of the residual...methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

NASA Technical Reports Server (NTRS)

Sandham, N. D.; Yee, H. C.; Kwak, Dochan (Technical Monitor)

2000-01-01

A stable high order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy splitting approach splits the inviscid flux derivatives into conservative and non-conservative portions. The spatial difference operators satisfy a summation by parts condition leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier-Stokes equations is used to ensure that any tendency to odd-even decoupling associated with central schemes can be countered by the fluid viscosity. A special formulation of the continuity equation is used, based on similar arguments. The resulting methods are able to minimize spurious high frequency oscillation producing nonlinear instability associated with pure central schemes, especially for long time integration simulation such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at a friction Mach number of 0.1 where a very accurate turbulence data base exists. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with incompressible channel data, as expected at this Mach number. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

Developing a new case based computer-aided detection scheme and an adaptive cueing method to improve performance in detecting mammographic lesions

PubMed Central

Tan, Maxine; Aghaei, Faranak; Wang, Yunzhi; Zheng, Bin

2017-01-01

The purpose of this study is to evaluate a new method to improve performance of computer-aided detection (CAD) schemes of screening mammograms with two approaches. In the first approach, we developed a new case based CAD scheme using a set of optimally selected global mammographic density, texture, spiculation, and structural similarity features computed from all four full-field digital mammography (FFDM) images of the craniocaudal (CC) and mediolateral oblique (MLO) views by using a modified fast and accurate sequential floating forward selection feature selection algorithm. Selected features were then applied to a “scoring fusion” artificial neural network (ANN) classification scheme to produce a final case based risk score. In the second approach, we combined the case based risk score with the conventional lesion based scores of a conventional lesion based CAD scheme using a new adaptive cueing method that is integrated with the case based risk scores. We evaluated our methods using a ten-fold cross-validation scheme on 924 cases (476 cancer and 448 recalled or negative), whereby each case had all four images from the CC and MLO views. The area under the receiver operating characteristic curve was AUC = 0.793±0.015 and the odds ratio monotonically increased from 1 to 37.21 as CAD-generated case based detection scores increased. Using the new adaptive cueing method, the region based and case based sensitivities of the conventional CAD scheme at a false positive rate of 0.71 per image increased by 2.4% and 0.8%, respectively. The study demonstrated that supplementary information can be derived by computing global mammographic density image features to improve CAD-cueing performance on the suspicious mammographic lesions. PMID:27997380

Tag-KEM from Set Partial Domain One-Way Permutations

NASA Astrophysics Data System (ADS)

Abe, Masayuki; Cui, Yang; Imai, Hideki; Kurosawa, Kaoru

Recently a framework called Tag-KEM/DEM was introduced to construct efficient hybrid encryption schemes. Although it is known that generic encode-then-encrypt construction of chosen ciphertext secure public-key encryption also applies to secure Tag-KEM construction and some known encoding method like OAEP can be used for this purpose, it is worth pursuing more efficient encoding method dedicated for Tag-KEM construction. This paper proposes an encoding method that yields efficient Tag-KEM schemes when combined with set partial one-way permutations such as RSA and Rabin's encryption scheme. To our knowledge, this leads to the most practical hybrid encryption scheme of this type. We also present an efficient Tag-KEM which is CCA-secure under general factoring assumption rather than Blum factoring assumption.

Sparsity-Aware DOA Estimation Scheme for Noncircular Source in MIMO Radar

PubMed Central

Wang, Xianpeng; Wang, Wei; Li, Xin; Liu, Qi; Liu, Jing

2016-01-01

In this paper, a novel sparsity-aware direction of arrival (DOA) estimation scheme for a noncircular source is proposed in multiple-input multiple-output (MIMO) radar. In the proposed method, the reduced-dimensional transformation technique is adopted to eliminate the redundant elements. Then, exploiting the noncircularity of signals, a joint sparsity-aware scheme based on the reweighted l1 norm penalty is formulated for DOA estimation, in which the diagonal elements of the weight matrix are the coefficients of the noncircular MUSIC-like (NC MUSIC-like) spectrum. Compared to the existing l1 norm penalty-based methods, the proposed scheme provides higher angular resolution and better DOA estimation performance. Results from numerical experiments are used to show the effectiveness of our proposed method. PMID:27089345

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1992-01-01

The development of efficient iterative solution methods for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations is discussed. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. In this work, another approach based on the classical conjugate gradient method, known as the Generalized Minimum Residual (GMRES) algorithm is investigated. The GMRES algorithm has been used in the past by a number of researchers for solving steady viscous and inviscid flow problems. Here, we investigate the suitability of this algorithm for solving the system of non-linear equations that arise in unsteady Navier-Stokes solvers at each time step.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods

NASA Astrophysics Data System (ADS)

Syrakos, Alexandros; Varchanis, Stylianos; Dimakopoulos, Yannis; Goulas, Apostolos; Tsamopoulos, John

2017-12-01

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM.

Final Report for''Numerical Methods and Studies of High-Speed Reactive and Non-Reactive Flows''

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schwendeman, D W

2002-11-20

The work carried out under this subcontract involved the development and use of an adaptive numerical method for the accurate calculation of high-speed reactive flows on overlapping grids. The flow is modeled by the reactive Euler equations with an assumed equation of state and with various reaction rate models. A numerical method has been developed to solve the nonlinear hyperbolic partial differential equations in the model. The method uses an unsplit, shock-capturing scheme, and uses a Godunov-type scheme to compute fluxes and a Runge-Kutta error control scheme to compute the source term modeling the chemical reactions. An adaptive mesh refinementmore » (AMR) scheme has been implemented in order to locally increase grid resolution. The numerical method uses composite overlapping grids to handle complex flow geometries. The code is part of the ''Overture-OverBlown'' framework of object-oriented codes [1, 2], and the development has occurred in close collaboration with Bill Henshaw and David Brown, and other members of the Overture team within CASC. During the period of this subcontract, a number of tasks were accomplished, including: (1) an extension of the numerical method to handle ''ignition and grow'' reaction models and a JWL equations of state; (2) an improvement in the efficiency of the AMR scheme and the error estimator; (3) an addition of a scheme of numerical dissipation designed to suppress numerical oscillations/instabilities near expanding detonations and along grid overlaps; and (4) an exploration of the evolution to detonation in an annulus and of detonation failure in an expanding channel.« less

A Hybrid Key Management Scheme for WSNs Based on PPBR and a Tree-Based Path Key Establishment Method

PubMed Central

Zhang, Ying; Liang, Jixing; Zheng, Bingxin; Chen, Wei

2016-01-01

With the development of wireless sensor networks (WSNs), in most application scenarios traditional WSNs with static sink nodes will be gradually replaced by Mobile Sinks (MSs), and the corresponding application requires a secure communication environment. Current key management researches pay less attention to the security of sensor networks with MS. This paper proposes a hybrid key management schemes based on a Polynomial Pool-based key pre-distribution and Basic Random key pre-distribution (PPBR) to be used in WSNs with MS. The scheme takes full advantages of these two kinds of methods to improve the cracking difficulty of the key system. The storage effectiveness and the network resilience can be significantly enhanced as well. The tree-based path key establishment method is introduced to effectively solve the problem of communication link connectivity. Simulation clearly shows that the proposed scheme performs better in terms of network resilience, connectivity and storage effectiveness compared to other widely used schemes. PMID:27070624

Multigrid calculation of three-dimensional turbomachinery flows

NASA Technical Reports Server (NTRS)

Caughey, David A.

1989-01-01

Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.

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.

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods $-$ Part 1: Derivation and properties

DOE PAGES

Eldred, Christopher; Randall, David

2017-02-17

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restrictedmore » to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Lastly, detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.« less

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

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.

Achieving bifunctional cloak via combination of passive and active schemes

NASA Astrophysics Data System (ADS)

Lan, Chuwen; Bi, Ke; Gao, Zehua; Li, Bo; Zhou, Ji

2016-11-01

In this study, a simple and delicate approach to realizing manipulation of multi-physics field simultaneously through combination of passive and active schemes is proposed. In the design, one physical field is manipulated with passive scheme while the other with active scheme. As a proof of this concept, a bifunctional device is designed and fabricated to behave as electric and thermal invisibility cloak simultaneously. It is found that the experimental results are consistent with the simulated ones well, confirming the feasibility of our method. Furthermore, the proposed method could also be extended to other multi-physics fields, which might lead to potential applications in thermal, electric, and acoustic areas.

A Novel Passive Tracking Scheme Exploiting Geometric and Intercept Theorems

PubMed Central

Zhou, Biao; Sun, Chao; Ahn, Deockhyeon; Kim, Youngok

2018-01-01

Passive tracking aims to track targets without assistant devices, that is, device-free targets. Passive tracking based on Radio Frequency (RF) Tomography in wireless sensor networks has recently been addressed as an emerging field. The passive tracking scheme using geometric theorems (GTs) is one of the most popular RF Tomography schemes, because the GT-based method can effectively mitigate the demand for a high density of wireless nodes. In the GT-based tracking scheme, the tracking scenario is considered as a two-dimensional geometric topology and then geometric theorems are applied to estimate crossing points (CPs) of the device-free target on line-of-sight links (LOSLs), which reveal the target’s trajectory information in a discrete form. In this paper, we review existing GT-based tracking schemes, and then propose a novel passive tracking scheme by exploiting the Intercept Theorem (IT). To create an IT-based CP estimation scheme available in the noisy non-parallel LOSL situation, we develop the equal-ratio traverse (ERT) method. Finally, we analyze properties of three GT-based tracking algorithms and the performance of these schemes is evaluated experimentally under various trajectories, node densities, and noisy topologies. Analysis of experimental results shows that tracking schemes exploiting geometric theorems can achieve remarkable positioning accuracy even under rather a low density of wireless nodes. Moreover, the proposed IT scheme can provide generally finer tracking accuracy under even lower node density and noisier topologies, in comparison to other schemes. PMID:29562621

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.

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Xia, E-mail: cui_xia@iapcm.ac.cn; Yuan, Guang-wei; Shen, Zhi-jun

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-ordermore » accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.« less

Image processing via level set curvature flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Malladi, R.; Sethian, J.A.

We present a controlled image smoothing and enhancement method based on a curvature flow interpretation of the geometric heat equation. Compared to existing techniques, the model has several distinct advantages. (i) It contains just one enhancement parameter. (ii) The scheme naturally inherits a stopping criterion from the image; continued application of the scheme produces no further change. (iii) The method is one of the fastest possible schemes based on a curvature-controlled approach. 15 ref., 6 figs.

Using exact solutions to develop an implicit scheme for the baroclinic primitive equations

NASA Technical Reports Server (NTRS)

Marchesin, D.

1984-01-01

The exact solutions presently obtained by means of a novel method for nonlinear initial value problems are used in the development of numerical schemes for the computer solution of these problems. The method is applied to a new, fully implicit scheme on a vertical slice of the isentropic baroclinic equations. It was not possible to find a global scale phenomenon that could be simulated by the baroclinic primitive equations on a vertical slice.

Performance of Improved High-Order Filter Schemes for Turbulent Flows with Shocks

NASA Technical Reports Server (NTRS)

Kotov, Dmitry Vladimirovich; Yee, Helen M C.

2013-01-01

The performance of the filter scheme with improved dissipation control ? has been demonstrated for different flow types. The scheme with local ? is shown to obtain more accurate results than its counterparts with global or constant ?. At the same time no additional tuning is needed to achieve high accuracy of the method when using the local ? technique. However, further improvement of the method might be needed for even more complex and/or extreme flows.

Finite Volume Methods: Foundation and Analysis

NASA Technical Reports Server (NTRS)

Barth, Timothy; Ohlberger, Mario

2003-01-01

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Protostellar hydrodynamics: Constructing and testing a spacially and temporally second-order accurate method. 2: Cartesian coordinates

NASA Technical Reports Server (NTRS)

Myhill, Elizabeth A.; Boss, Alan P.

1993-01-01

In Boss & Myhill (1992) we described the derivation and testing of a spherical coordinate-based scheme for solving the hydrodynamic equations governing the gravitational collapse of nonisothermal, nonmagnetic, inviscid, radiative, three-dimensional protostellar clouds. Here we discuss a Cartesian coordinate-based scheme based on the same set of hydrodynamic equations. As with the spherical coorrdinate-based code, the Cartesian coordinate-based scheme employs explicit Eulerian methods which are both spatially and temporally second-order accurate. We begin by describing the hydrodynamic equations in Cartesian coordinates and the numerical methods used in this particular code. Following Finn & Hawley (1989), we pay special attention to the proper implementations of high-order accuracy, finite difference methods. We evaluate the ability of the Cartesian scheme to handle shock propagation problems, and through convergence testing, we show that the code is indeed second-order accurate. To compare the Cartesian scheme discussed here with the spherical coordinate-based scheme discussed in Boss & Myhill (1992), the two codes are used to calculate the standard isothermal collapse test case described by Bodenheimer & Boss (1981). We find that with the improved codes, the intermediate bar-configuration found previously disappears, and the cloud fragments directly into a binary protostellar system. Finally, we present the results from both codes of a new test for nonisothermal protostellar collapse.

A genetic fuzzy analytical hierarchy process based projection pursuit method for selecting schemes of water transportation projects

NASA Astrophysics Data System (ADS)

Jin, Juliang; Li, Lei; Wang, Wensheng; Zhang, Ming

2006-10-01

The optimal selection of schemes of water transportation projects is a process of choosing a relatively optimal scheme from a number of schemes of water transportation programming and management projects, which is of importance in both theory and practice in water resource systems engineering. In order to achieve consistency and eliminate the dimensions of fuzzy qualitative and fuzzy quantitative evaluation indexes, to determine the weights of the indexes objectively, and to increase the differences among the comprehensive evaluation index values of water transportation project schemes, a projection pursuit method, named FPRM-PP for short, was developed in this work for selecting the optimal water transportation project scheme based on the fuzzy preference relation matrix. The research results show that FPRM-PP is intuitive and practical, the correction range of the fuzzy preference relation matrix A it produces is relatively small, and the result obtained is both stable and accurate; therefore FPRM-PP can be widely used in the optimal selection of different multi-factor decision-making schemes.

Which missing value imputation method to use in expression profiles: a comparative study and two selection schemes.

PubMed

Brock, Guy N; Shaffer, John R; Blakesley, Richard E; Lotz, Meredith J; Tseng, George C

2008-01-10

Gene expression data frequently contain missing values, however, most down-stream analyses for microarray experiments require complete data. In the literature many methods have been proposed to estimate missing values via information of the correlation patterns within the gene expression matrix. Each method has its own advantages, but the specific conditions for which each method is preferred remains largely unclear. In this report we describe an extensive evaluation of eight current imputation methods on multiple types of microarray experiments, including time series, multiple exposures, and multiple exposures x time series data. We then introduce two complementary selection schemes for determining the most appropriate imputation method for any given data set. We found that the optimal imputation algorithms (LSA, LLS, and BPCA) are all highly competitive with each other, and that no method is uniformly superior in all the data sets we examined. The success of each method can also depend on the underlying "complexity" of the expression data, where we take complexity to indicate the difficulty in mapping the gene expression matrix to a lower-dimensional subspace. We developed an entropy measure to quantify the complexity of expression matrixes and found that, by incorporating this information, the entropy-based selection (EBS) scheme is useful for selecting an appropriate imputation algorithm. We further propose a simulation-based self-training selection (STS) scheme. This technique has been used previously for microarray data imputation, but for different purposes. The scheme selects the optimal or near-optimal method with high accuracy but at an increased computational cost. Our findings provide insight into the problem of which imputation method is optimal for a given data set. Three top-performing methods (LSA, LLS and BPCA) are competitive with each other. Global-based imputation methods (PLS, SVD, BPCA) performed better on mcroarray data with lower complexity, while neighbour-based methods (KNN, OLS, LSA, LLS) performed better in data with higher complexity. We also found that the EBS and STS schemes serve as complementary and effective tools for selecting the optimal imputation algorithm.

Sensor-less pseudo-sinusoidal drive for a permanent-magnet brushless ac motor

NASA Astrophysics Data System (ADS)

Liu, Li-Hsiang; Chern, Tzuen-Lih; Pan, Ping-Lung; Huang, Tsung-Mou; Tsay, Der-Min; Kuang, Jao-Hwa

2012-04-01

The precise rotor-position information is required for a permanent-magnet brushless ac motor (BLACM) drive. In the conventional sinusoidal drive method, either an encoder or a resolver is usually employed. For position sensor-less vector control schemes, the rotor flux estimation and torque components are obtained by complicated coordinate transformations. These computational intensive methods are susceptible to current distortions and parameter variations. To simplify the method complexity, this work presents a sensor-less pseudo-sinusoidal drive scheme with speed control for a three-phase BLACM. Based on the sinusoidal drive scheme, a floating period of each phase current is inserted for back electromotive force detection. The zero-crossing point is determined directly by the proposed scheme, and the rotor magnetic position and rotor speed can be estimated simultaneously. Several experiments for various active angle periods are undertaken. Furthermore, a current feedback control is included to minimize and compensate the torque fluctuation. The experimental results show that the proposed method has a competitive performance compared with the conventional drive manners for BLACM. The proposed scheme is straightforward, bringing the benefits of sensor-less drive and negating the need for coordinate transformations in the operating process.

Application of viscous-inviscid interaction methods to transonic turbulent flows

NASA Technical Reports Server (NTRS)

Lee, D.; Pletcher, R. H.

1986-01-01

Two different viscous-inviscid interaction schemes were developed for the analysis of steady, turbulent, transonic, separated flows over axisymmetric bodies. The viscous and inviscid solutions are coupled through the displacement concept using a transpiration velocity approach. In the semi-inverse interaction scheme, the viscous and inviscid equations are solved in an explicitly separate manner and the displacement thickness distribution is iteratively updated by a simple coupling algorithm. In the simultaneous interaction method, local solutions of viscous and inviscid equations are treated simultaneously, and the displacement thickness is treated as an unknown and is obtained as a part of the solution through a global iteration procedure. The inviscid flow region is described by a direct finite-difference solution of a velocity potential equation in conservative form. The potential equation is solved on a numerically generated mesh by an approximate factorization (AF2) scheme in the semi-inverse interaction method and by a successive line overrelaxation (SLOR) scheme in the simultaneous interaction method. The boundary-layer equations are used for the viscous flow region. The continuity and momentum equations are solved inversely in a coupled manner using a fully implicit finite-difference scheme.

Variance reduction for Fokker–Planck based particle Monte Carlo schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorji, M. Hossein, E-mail: gorjih@ifd.mavt.ethz.ch; Andric, Nemanja; Jenny, Patrick

Recently, Fokker–Planck based particle Monte Carlo schemes have been proposed and evaluated for simulations of rarefied gas flows [1–3]. In this paper, the variance reduction for particle Monte Carlo simulations based on the Fokker–Planck model is considered. First, deviational based schemes were derived and reviewed, and it is shown that these deviational methods are not appropriate for practical Fokker–Planck based rarefied gas flow simulations. This is due to the fact that the deviational schemes considered in this study lead either to instabilities in the case of two-weight methods or to large statistical errors if the direct sampling method is applied.more » Motivated by this conclusion, we developed a novel scheme based on correlated stochastic processes. The main idea here is to synthesize an additional stochastic process with a known solution, which is simultaneously solved together with the main one. By correlating the two processes, the statistical errors can dramatically be reduced; especially for low Mach numbers. To assess the methods, homogeneous relaxation, planar Couette and lid-driven cavity flows were considered. For these test cases, it could be demonstrated that variance reduction based on parallel processes is very robust and effective.« less

Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed

NASA Astrophysics Data System (ADS)

Canestrelli, Alberto; Dumbser, Michael; Siviglia, Annunziato; Toro, Eleuterio F.

2010-03-01

In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space-time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data.

A comparative study of Rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xiaodong; Xia, Yidong; Luo, Hong

A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flowsmore » to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.« less

A comparative study of Rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations

DOE PAGES

Liu, Xiaodong; Xia, Yidong; Luo, Hong; ...

2016-10-05

A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flowsmore » to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.« less

I = 2 ππ scattering phase shift from the HAL QCD method with the LapH smearing

NASA Astrophysics Data System (ADS)

Kawai, Daisuke; Aoki, Sinya; Doi, Takumi; Ikeda, Yoichi; Inoue, Takashi; Iritani, Takumi; Ishii, Noriyoshi; Miyamoto, Takaya; Nemura, Hidekatsu; Sasaki, Kenji

2018-04-01

Physical observables, such as the scattering phase shifts and binding energy, calculated from the non-local HAL QCD potential do not depend on the sink operators used to define the potential. In practical applications, the derivative expansion of the non-local potential is employed, so that physical observables may receive some scheme dependence at a given order of the expansion. In this paper, we compare the I=2ππ scattering phase shifts obtained in the point-sink scheme (the standard scheme in the HAL QCD method) and the smeared-sink scheme (the LapH smearing newly introduced in the HAL QCD method). Although potentials in different schemes have different forms as expected, we find that, for reasonably small smearing size, the resultant scattering phase shifts agree with each other if the next-to-leading-order (NLO) term is taken into account. We also find that the HAL QCD potential in the point-sink scheme has a negligible NLO term for a wide range of energies, which implies good convergence of the derivative expansion, while the potential in the smeared-sink scheme has a non-negligible NLO contribution. The implications of this observation for future studies of resonance channels (such as the I=0 and 1ππ scatterings) with smeared all-to-all propagators are briefly discussed.

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Stable and low diffusive hybrid upwind splitting methods

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1992-01-01

We introduce in this paper a new concept for upwinding: the Hybrid Upwind Splitting (HUS). This original strategy for upwinding is achieved by combining the two previous existing approaches, the Flux Vector (FVS) and Flux Difference Splittings (FDS), while retaining their own interesting features. Indeed, our approach yields upwind methods that share the robustness of FVS schemes in the capture of nonlinear waves and the accuracy of some FDS schemes in the capture of linear waves. We describe here some examples of such HUS methods obtained by hybridizing the Osher approach with FVS schemes. Numerical illustrations are displayed and will prove in particular the relevance of the HUS methods we propose for viscous calculations.

The Battlefield Environment Division Modeling Framework (BMF). Part 1: Optimizing the Atmospheric Boundary Layer Environment Model for Cluster Computing

DTIC Science & Technology

2014-02-01

idle waiting for the wavefront to reach it. To overcome this, Reeve et al. (2001) 3 developed a scheme in analogy to the red-black Gauss - Seidel iterative ...understandable procedure calls. Parallelization of the SIMPLE iterative scheme with SIP used a red-black scheme similar to the red-black Gauss - Seidel ...scheme, the SIMPLE method, for pressure-velocity coupling. The result is a slowing convergence of the outer iterations . The red-black scheme excites a 2

Shelf life extension of whole Norway lobster Nephrops norvegicus using modified atmosphere packaging.

PubMed

Gornik, Sebastian G; Albalat, Amaya; Theethakaew, Chonchanok; Neil, Douglas M

2013-11-01

Once a nuisance by-catch, today the Norway lobster (Nephrops norvegicus) is a valuable UK fisheries commodity. Unfortunately, the species is very susceptible to quality deterioration post harvest as it quickly develops black spots and also spoils rapidly due to bacterial growth. Treatment with chemicals can stop the blackening and carefully monitored cold storage can result in a sensory shelf life of up to 6.5 days. The high susceptibility to spoilage greatly restricts the extent to which N. norvegicus can be distributed to retailers and displayed for sale. The application of modified atmosphere (MA) could be extremely beneficial, allowing the chilled product to stay fresh for a long period of time, thus ensuring higher sales. In the present study, we identified a gas mix for the MA packaging (MAP) of whole N. norvegicus lobster into 200 g retail packs. Our results show that a shelf life extension to 13 days can be achieved when retail packs are stored in MAP at 1 °C. Effectiveness of the MAP was evaluated by using a newly developed QIM for MA-packaged whole N. norvegicus and also by analyzing bacterial plate counts. Changes in the microflora and effects of different storage temperatures on the quality of the MA packs are also presented. The main specific spoilage organism (SSO) of modified atmosphere packaged Norway lobster is Photobacterium phosphoreum. © 2013.

Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2

NASA Technical Reports Server (NTRS)

Engquist, B. E. (Editor); Osher, S. (Editor); Somerville, R. C. J. (Editor)

1985-01-01

Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.

Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

NASA Astrophysics Data System (ADS)

Ge, Yongbin; Cao, Fujun

2011-05-01

In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection-diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33-53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.

Graphical Evaluation of Hierarchical Clustering Schemes. Technical Report No. 1.

ERIC Educational Resources Information Center

Halff, Henry M.

Graphical methods for evaluating the fit of Johnson's hierarchical clustering schemes are presented together with an example. These evaluation methods examine the extent to which the clustering algorithm can minimize the overlap of the distributions of intracluster and intercluster distances. (Author)

A new local-global approach for classification.

PubMed

Peres, R T; Pedreira, C E

2010-09-01

In this paper, we propose a new local-global pattern classification scheme that combines supervised and unsupervised approaches, taking advantage of both, local and global environments. We understand as global methods the ones concerned with the aim of constructing a model for the whole problem space using the totality of the available observations. Local methods focus into sub regions of the space, possibly using an appropriately selected subset of the sample. In the proposed method, the sample is first divided in local cells by using a Vector Quantization unsupervised algorithm, the LBG (Linde-Buzo-Gray). In a second stage, the generated assemblage of much easier problems is locally solved with a scheme inspired by Bayes' rule. Four classification methods were implemented for comparison purposes with the proposed scheme: Learning Vector Quantization (LVQ); Feedforward Neural Networks; Support Vector Machine (SVM) and k-Nearest Neighbors. These four methods and the proposed scheme were implemented in eleven datasets, two controlled experiments, plus nine public available datasets from the UCI repository. The proposed method has shown a quite competitive performance when compared to these classical and largely used classifiers. Our method is simple concerning understanding and implementation and is based on very intuitive concepts. Copyright 2010 Elsevier Ltd. All rights reserved.

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, Helen C.; Mansour, Nagi (Technical Monitor)

2002-01-01

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

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.

On the solution of evolution equations based on multigrid and explicit iterative methods

NASA Astrophysics Data System (ADS)

Zhukov, V. T.; Novikova, N. D.; Feodoritova, O. B.

2015-08-01

Two schemes for solving initial-boundary value problems for three-dimensional parabolic equations are studied. One is implicit and is solved using the multigrid method, while the other is explicit iterative and is based on optimal properties of the Chebyshev polynomials. In the explicit iterative scheme, the number of iteration steps and the iteration parameters are chosen as based on the approximation and stability conditions, rather than on the optimization of iteration convergence to the solution of the implicit scheme. The features of the multigrid scheme include the implementation of the intergrid transfer operators for the case of discontinuous coefficients in the equation and the adaptation of the smoothing procedure to the spectrum of the difference operators. The results produced by these schemes as applied to model problems with anisotropic discontinuous coefficients are compared.

A FRACTAL-BASED STOCHASTIC INTERPOLATION SCHEME IN SUBSURFACE HYDROLOGY

EPA Science Inventory

The need for a realistic and rational method for interpolating sparse data sets is widespread. Real porosity and hydraulic conductivity data do not vary smoothly over space, so an interpolation scheme that preserves irregularity is desirable. Such a scheme based on the properties...

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Yang, H. Q.

1989-01-01

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

Error Reduction Program. [combustor performance evaluation codes

NASA Technical Reports Server (NTRS)

Syed, S. A.; Chiappetta, L. M.; Gosman, A. D.

1985-01-01

The details of a study to select, incorporate and evaluate the best available finite difference scheme to reduce numerical error in combustor performance evaluation codes are described. The combustor performance computer programs chosen were the two dimensional and three dimensional versions of Pratt & Whitney's TEACH code. The criteria used to select schemes required that the difference equations mirror the properties of the governing differential equation, be more accurate than the current hybrid difference scheme, be stable and economical, be compatible with TEACH codes, use only modest amounts of additional storage, and be relatively simple. The methods of assessment used in the selection process consisted of examination of the difference equation, evaluation of the properties of the coefficient matrix, Taylor series analysis, and performance on model problems. Five schemes from the literature and three schemes developed during the course of the study were evaluated. This effort resulted in the incorporation of a scheme in 3D-TEACH which is usuallly more accurate than the hybrid differencing method and never less accurate.

Weighted analysis methods for mapped plot forest inventory data: Tables, regressions, maps and graphs

Treesearch

Paul C. Van Deusen; Linda S. Heath

2010-01-01

Weighted estimation methods for analysis of mapped plot forest inventory data are discussed. The appropriate weighting scheme can vary depending on the type of analysis and graphical display. Both statistical issues and user expectations need to be considered in these methods. A weighting scheme is proposed that balances statistical considerations and the logical...

Asymptotic-induced numerical methods for conservation laws

NASA Technical Reports Server (NTRS)

Garbey, Marc; Scroggs, Jeffrey S.

1990-01-01

Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.

High-Order Methods for Computational Fluid Dynamics: A Brief Review of Compact Differential Formulations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Huynh, H. T.; Wang, Z. J.; Vincent, P. E.

2013-01-01

Popular high-order schemes with compact stencils for Computational Fluid Dynamics (CFD) include Discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV) methods. The recently proposed Flux Reconstruction (FR) approach or Correction Procedure using Reconstruction (CPR) is based on a differential formulation and provides a unifying framework for these high-order schemes. Here we present a brief review of recent developments for the FR/CPR schemes as well as some pacing items.

Numerical solution of modified differential equations based on symmetry preservation.

PubMed

Ozbenli, Ersin; Vedula, Prakash

2017-12-01

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

Consistent forcing scheme in the cascaded lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Fei, Linlin; Luo, Kai Hong

2017-11-01

In this paper, we give an alternative derivation for the cascaded lattice Boltzmann method (CLBM) within a general multiple-relaxation-time (MRT) framework by introducing a shift matrix. When the shift matrix is a unit matrix, the CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is developed for the CLBM. The consistency of the nonslip rule, the second-order convergence rate in space, and the property of isotropy for the consistent forcing scheme is demonstrated through numerical simulations of several canonical problems. Several existing forcing schemes previously used in the CLBM are also examined. The study clarifies the relation between MRT LBM and CLBM under a general framework.

Differential Privacy Preserving in Big Data Analytics for Connected Health.

PubMed

Lin, Chi; Song, Zihao; Song, Houbing; Zhou, Yanhong; Wang, Yi; Wu, Guowei

2016-04-01

In Body Area Networks (BANs), big data collected by wearable sensors usually contain sensitive information, which is compulsory to be appropriately protected. Previous methods neglected privacy protection issue, leading to privacy exposure. In this paper, a differential privacy protection scheme for big data in body sensor network is developed. Compared with previous methods, this scheme will provide privacy protection with higher availability and reliability. We introduce the concept of dynamic noise thresholds, which makes our scheme more suitable to process big data. Experimental results demonstrate that, even when the attacker has full background knowledge, the proposed scheme can still provide enough interference to big sensitive data so as to preserve the privacy.

A semi-implicit level set method for multiphase flows and fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Cottet, Georges-Henri; Maitre, Emmanuel

2016-06-01

In this paper we present a novel semi-implicit time-discretization of the level set method introduced in [8] for fluid-structure interaction problems. The idea stems from a linear stability analysis derived on a simplified one-dimensional problem. The semi-implicit scheme relies on a simple filter operating as a pre-processing on the level set function. It applies to multiphase flows driven by surface tension as well as to fluid-structure interaction problems. The semi-implicit scheme avoids the stability constraints that explicit scheme need to satisfy and reduces significantly the computational cost. It is validated through comparisons with the original explicit scheme and refinement studies on two-dimensional benchmarks.

Galilean invariant resummation schemes of cosmological perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peloso, Marco; Pietroni, Massimo, E-mail: peloso@physics.umn.edu, E-mail: massimo.pietroni@unipr.it

2017-01-01

Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them inmore » the so called Time-Flow, or TRG, equations.« less

Computational aspects of helicopter trim analysis and damping levels from Floquet theory

NASA Technical Reports Server (NTRS)

Gaonkar, Gopal H.; Achar, N. S.

1992-01-01

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Maximum-likelihood curve-fitting scheme for experiments with pulsed lasers subject to intensity fluctuations.

PubMed

Metz, Thomas; Walewski, Joachim; Kaminski, Clemens F

2003-03-20

Evaluation schemes, e.g., least-squares fitting, are not generally applicable to any types of experiments. If the evaluation schemes were not derived from a measurement model that properly described the experiment to be evaluated, poorer precision or accuracy than attainable from the measured data could result. We outline ways in which statistical data evaluation schemes should be derived for all types of experiment, and we demonstrate them for laser-spectroscopic experiments, in which pulse-to-pulse fluctuations of the laser power cause correlated variations of laser intensity and generated signal intensity. The method of maximum likelihood is demonstrated in the derivation of an appropriate fitting scheme for this type of experiment. Statistical data evaluation contains the following steps. First, one has to provide a measurement model that considers statistical variation of all enclosed variables. Second, an evaluation scheme applicable to this particular model has to be derived or provided. Third, the scheme has to be characterized in terms of accuracy and precision. A criterion for accepting an evaluation scheme is that it have accuracy and precision as close as possible to the theoretical limit. The fitting scheme derived for experiments with pulsed lasers is compared to well-established schemes in terms of fitting power and rational functions. The precision is found to be as much as three timesbetter than for simple least-squares fitting. Our scheme also suppresses the bias on the estimated model parameters that other methods may exhibit if they are applied in an uncritical fashion. We focus on experiments in nonlinear spectroscopy, but the fitting scheme derived is applicable in many scientific disciplines.

Simple adaptive sparse representation based classification schemes for EEG based brain-computer interface applications.

PubMed

Shin, Younghak; Lee, Seungchan; Ahn, Minkyu; Cho, Hohyun; Jun, Sung Chan; Lee, Heung-No

2015-11-01

One of the main problems related to electroencephalogram (EEG) based brain-computer interface (BCI) systems is the non-stationarity of the underlying EEG signals. This results in the deterioration of the classification performance during experimental sessions. Therefore, adaptive classification techniques are required for EEG based BCI applications. In this paper, we propose simple adaptive sparse representation based classification (SRC) schemes. Supervised and unsupervised dictionary update techniques for new test data and a dictionary modification method by using the incoherence measure of the training data are investigated. The proposed methods are very simple and additional computation for the re-training of the classifier is not needed. The proposed adaptive SRC schemes are evaluated using two BCI experimental datasets. The proposed methods are assessed by comparing classification results with the conventional SRC and other adaptive classification methods. On the basis of the results, we find that the proposed adaptive schemes show relatively improved classification accuracy as compared to conventional methods without requiring additional computation. Copyright © 2015 Elsevier Ltd. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shadid, John Nicolas; Fish, Jacob; Waisman, Haim

Two heuristic strategies intended to enhance the performance of the generalized global basis (GGB) method [H. Waisman, J. Fish, R.S. Tuminaro, J. Shadid, The Generalized Global Basis (GGB) method, International Journal for Numerical Methods in Engineering 61(8), 1243-1269] applied to nonlinear systems are presented. The standard GGB accelerates a multigrid scheme by an additional coarse grid correction that filters out slowly converging modes. This correction requires a potentially costly eigen calculation. This paper considers reusing previously computed eigenspace information. The GGB? scheme enriches the prolongation operator with new eigenvectors while the modified method (MGGB) selectively reuses the same prolongation. Bothmore » methods use the criteria of principal angles between subspaces spanned between the previous and current prolongation operators. Numerical examples clearly indicate significant time savings in particular for the MGGB scheme.« less

Linear response coupled cluster theory with the polarizable continuum model within the singles approximation for the solvent response.

PubMed

Caricato, Marco

2018-04-07

We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.

Linear response coupled cluster theory with the polarizable continuum model within the singles approximation for the solvent response

NASA Astrophysics Data System (ADS)

Caricato, Marco

2018-04-01

We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.

Genome-wide association analysis of secondary imaging phenotypes from the Alzheimer's disease neuroimaging initiative study.

PubMed

Zhu, Wensheng; Yuan, Ying; Zhang, Jingwen; Zhou, Fan; Knickmeyer, Rebecca C; Zhu, Hongtu

2017-02-01

The aim of this paper is to systematically evaluate a biased sampling issue associated with genome-wide association analysis (GWAS) of imaging phenotypes for most imaging genetic studies, including the Alzheimer's Disease Neuroimaging Initiative (ADNI). Specifically, the original sampling scheme of these imaging genetic studies is primarily the retrospective case-control design, whereas most existing statistical analyses of these studies ignore such sampling scheme by directly correlating imaging phenotypes (called the secondary traits) with genotype. Although it has been well documented in genetic epidemiology that ignoring the case-control sampling scheme can produce highly biased estimates, and subsequently lead to misleading results and suspicious associations, such findings are not well documented in imaging genetics. We use extensive simulations and a large-scale imaging genetic data analysis of the Alzheimer's Disease Neuroimaging Initiative (ADNI) data to evaluate the effects of the case-control sampling scheme on GWAS results based on some standard statistical methods, such as linear regression methods, while comparing it with several advanced statistical methods that appropriately adjust for the case-control sampling scheme. Copyright © 2016 Elsevier Inc. All rights reserved.

Compressed Semi-Discrete Central-Upwind Schemes for Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Kurganov, Alexander; Levy, Doron; Petrova, Guergana

2003-01-01

We introduce a new family of Godunov-type semi-discrete central schemes for multidimensional Hamilton-Jacobi equations. These schemes are a less dissipative generalization of the central-upwind schemes that have been recently proposed in series of works. We provide the details of the new family of methods in one, two, and three space dimensions, and then verify their expected low-dissipative property in a variety of examples.

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.

Two Dimensional Finite Element Based Magnetotelluric Inversion using Singular Value Decomposition Method on Transverse Electric Mode

NASA Astrophysics Data System (ADS)

Tjong, Tiffany; Yihaa’ Roodhiyah, Lisa; Nurhasan; Sutarno, Doddy

2018-04-01

In this work, an inversion scheme was performed using a vector finite element (VFE) based 2-D magnetotelluric (MT) forward modelling. We use an inversion scheme with Singular value decomposition (SVD) method toimprove the accuracy of MT inversion.The inversion scheme was applied to transverse electric (TE) mode of MT. SVD method was used in this inversion to decompose the Jacobian matrices. Singular values which obtained from the decomposition process were analyzed. This enabled us to determine the importance of data and therefore to define a threshold for truncation process. The truncation of singular value in inversion processcould improve the resulted model.

Efficient high-order structure-preserving methods for the generalized Rosenau-type equation with power law nonlinearity

NASA Astrophysics Data System (ADS)

Cai, Jiaxiang; Liang, Hua; Zhang, Chun

2018-06-01

Based on the multi-symplectic Hamiltonian formula of the generalized Rosenau-type equation, a multi-symplectic scheme and an energy-preserving scheme are proposed. To improve the accuracy of the solution, we apply the composition technique to the obtained schemes to develop high-order schemes which are also multi-symplectic and energy-preserving respectively. Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes. Numerical results verify that all the proposed schemes have satisfactory performance in providing accurate solution and preserving the discrete mass and energy invariants. Numerical results also show that although each basic time step is divided into several composition steps, the computational efficiency of the composition schemes is much higher than that of the non-composite schemes.

Effective Fragment Potential Method for H-Bonding: How To Obtain Parameters for Nonrigid Fragments.

PubMed

Dubinets, Nikita; Slipchenko, Lyudmila V

2017-07-20

Accuracy of the effective fragment potential (EFP) method was explored for describing intermolecular interaction energies in three dimers with strong H-bonded interactions, formic acid, formamide, and formamidine dimers, which are a part of HBC6 database of noncovalent interactions. Monomer geometries in these dimers change significantly as a function of intermonomer separation. Several EFP schemes were considered, in which fragment parameters were prepared for a fragment in its gas-phase geometry or recomputed for each unique fragment geometry. Additionally, a scheme in which gas-phase fragment parameters are shifted according to relaxed fragment geometries is introduced and tested. EFP data are compared against the coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) method in a complete basis set (CBS) and the symmetry adapted perturbation theory (SAPT). All considered EFP schemes provide a good agreement with CCSD(T)/CBS for binding energies at equilibrium separations, with discrepancies not exceeding 2 kcal/mol. However, only the schemes that utilize relaxed fragment geometries remain qualitatively correct at shorter than equilibrium intermolecular distances. The EFP scheme with shifted parameters behaves quantitatively similar to the scheme in which parameters are recomputed for each monomer geometry and thus is recommended as a computationally efficient approach for large-scale EFP simulations of flexible systems.

Wavelet-based Encoding Scheme for Controlling Size of Compressed ECG Segments in Telecardiology Systems.

PubMed

Al-Busaidi, Asiya M; Khriji, Lazhar; Touati, Farid; Rasid, Mohd Fadlee; Mnaouer, Adel Ben

2017-09-12

One of the major issues in time-critical medical applications using wireless technology is the size of the payload packet, which is generally designed to be very small to improve the transmission process. Using small packets to transmit continuous ECG data is still costly. Thus, data compression is commonly used to reduce the huge amount of ECG data transmitted through telecardiology devices. In this paper, a new ECG compression scheme is introduced to ensure that the compressed ECG segments fit into the available limited payload packets, while maintaining a fixed CR to preserve the diagnostic information. The scheme automatically divides the ECG block into segments, while maintaining other compression parameters fixed. This scheme adopts discrete wavelet transform (DWT) method to decompose the ECG data, bit-field preserving (BFP) method to preserve the quality of the DWT coefficients, and a modified running-length encoding (RLE) scheme to encode the coefficients. The proposed dynamic compression scheme showed promising results with a percentage packet reduction (PR) of about 85.39% at low percentage root-mean square difference (PRD) values, less than 1%. ECG records from MIT-BIH Arrhythmia Database were used to test the proposed method. The simulation results showed promising performance that satisfies the needs of portable telecardiology systems, like the limited payload size and low power consumption.

Comparison of PDF and Moment Closure Methods in the Modeling of Turbulent Reacting Flows

NASA Technical Reports Server (NTRS)

Norris, Andrew T.; Hsu, Andrew T.

1994-01-01

In modeling turbulent reactive flows, Probability Density Function (PDF) methods have an advantage over the more traditional moment closure schemes in that the PDF formulation treats the chemical reaction source terms exactly, while moment closure methods are required to model the mean reaction rate. The common model used is the laminar chemistry approximation, where the effects of turbulence on the reaction are assumed negligible. For flows with low turbulence levels and fast chemistry, the difference between the two methods can be expected to be small. However for flows with finite rate chemistry and high turbulence levels, significant errors can be expected in the moment closure method. In this paper, the ability of the PDF method and the moment closure scheme to accurately model a turbulent reacting flow is tested. To accomplish this, both schemes were used to model a CO/H2/N2- air piloted diffusion flame near extinction. Identical thermochemistry, turbulence models, initial conditions and boundary conditions are employed to ensure a consistent comparison can be made. The results of the two methods are compared to experimental data as well as to each other. The comparison reveals that the PDF method provides good agreement with the experimental data, while the moment closure scheme incorrectly shows a broad, laminar-like flame structure.

East Asian winter monsoon forecasting schemes based on the NCEP's climate forecast system

NASA Astrophysics Data System (ADS)

Tian, Baoqiang; Fan, Ke; Yang, Hongqing

2017-12-01

The East Asian winter monsoon (EAWM) is the major climate system in the Northern Hemisphere during boreal winter. In this study, we developed two schemes to improve the forecasting skill of the interannual variability of the EAWM index (EAWMI) using the interannual increment prediction method, also known as the DY method. First, we found that version 2 of the NCEP's Climate Forecast System (CFSv2) showed higher skill in predicting the EAWMI in DY form than not. So, based on the advantage of the DY method, Scheme-I was obtained by adding the EAWMI DY predicted by CFSv2 to the observed EAWMI in the previous year. This scheme showed higher forecasting skill than CFSv2. Specifically, during 1983-2016, the temporal correlation coefficient between the Scheme-I-predicted and observed EAWMI was 0.47, exceeding the 99% significance level, with the root-mean-square error (RMSE) decreased by 12%. The autumn Arctic sea ice and North Pacific sea surface temperature (SST) are two important external forcing factors for the interannual variability of the EAWM. Therefore, a second (hybrid) prediction scheme, Scheme-II, was also developed. This scheme not only involved the EAWMI DY of CFSv2, but also the sea-ice concentration (SIC) observed the previous autumn in the Laptev and East Siberian seas and the temporal coefficients of the third mode of the North Pacific SST in DY form. We found that a negative SIC anomaly in the preceding autumn over the Laptev and the East Siberian seas could lead to a significant enhancement of the Aleutian low and East Asian westerly jet in the following winter. However, the intensity of the winter Siberian high was mainly affected by the third mode of the North Pacific autumn SST. Scheme-I and Scheme-II also showed higher predictive ability for the EAWMI in negative anomaly years compared to CFSv2. More importantly, the improvement in the prediction skill of the EAWMI by the new schemes, especially for Scheme-II, could enhance the forecasting skill of the winter 2-m air temperature (T-2m) in most parts of China, as well as the intensity of the Aleutian low and Siberian high in winter. The new schemes provide a theoretical basis for improving the prediction of winter climate in China.

Application of the implicit MacCormack scheme to the PNS equations

NASA Technical Reports Server (NTRS)

Lawrence, S. L.; Tannehill, J. C.; Chaussee, D. S.

1983-01-01

The two-dimensional parabolized Navier-Stokes equations are solved using MacCormack's (1981) implicit finite-difference scheme. It is shown that this method for solving the parabolized Navier-Stokes equations does not require the inversion of block tridiagonal systems of algebraic equations and allows the original explicit scheme to be employed in those regions where implicit treatment is not needed. The finite-difference algorithm is discussed and the computational results for two laminar test cases are presented. Results obtained using this method for the case of a flat plate boundary layer are compared with those obtained using the conventional Beam-Warming scheme, as well as those obtained from a boundary layer code. The computed results for a more severe test of the method, the hypersonic flow past a 15 deg compression corner, are found to compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

A Noise-Filtered Under-Sampling Scheme for Imbalanced Classification.

PubMed

Kang, Qi; Chen, XiaoShuang; Li, SiSi; Zhou, MengChu

2017-12-01

Under-sampling is a popular data preprocessing method in dealing with class imbalance problems, with the purposes of balancing datasets to achieve a high classification rate and avoiding the bias toward majority class examples. It always uses full minority data in a training dataset. However, some noisy minority examples may reduce the performance of classifiers. In this paper, a new under-sampling scheme is proposed by incorporating a noise filter before executing resampling. In order to verify the efficiency, this scheme is implemented based on four popular under-sampling methods, i.e., Undersampling + Adaboost, RUSBoost, UnderBagging, and EasyEnsemble through benchmarks and significance analysis. Furthermore, this paper also summarizes the relationship between algorithm performance and imbalanced ratio. Experimental results indicate that the proposed scheme can improve the original undersampling-based methods with significance in terms of three popular metrics for imbalanced classification, i.e., the area under the curve, -measure, and -mean.

Optimised Iteration in Coupled Monte Carlo - Thermal-Hydraulics Calculations

NASA Astrophysics Data System (ADS)

Hoogenboom, J. Eduard; Dufek, Jan

2014-06-01

This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration method are also tested and it is concluded that the presented iteration method is near optimal.

Cryptanalysis and Improvement of "A Secure Password Authentication Mechanism for Seamless Handover in Proxy Mobile IPv6 Networks".

PubMed

Alizadeh, Mojtaba; Zamani, Mazdak; Baharun, Sabariah; Abdul Manaf, Azizah; Sakurai, Kouichi; Anada, Hiroaki; Anada, Hiroki; Keshavarz, Hassan; Ashraf Chaudhry, Shehzad; Khurram Khan, Muhammad

2015-01-01

Proxy Mobile IPv6 is a network-based localized mobility management protocol that supports mobility without mobile nodes' participation in mobility signaling. The details of user authentication procedure are not specified in this standard, hence, many authentication schemes have been proposed for this standard. In 2013, Chuang et al., proposed an authentication method for PMIPv6, called SPAM. However, Chuang et al.'s Scheme protects the network against some security attacks, but it is still vulnerable to impersonation and password guessing attacks. In addition, we discuss other security drawbacks such as lack of revocation procedure in case of loss or stolen device, and anonymity issues of the Chuang et al.'s scheme. We further propose an enhanced authentication method to mitigate the security issues of SPAM method and evaluate our scheme using BAN logic.

Cryptanalysis and Improvement of "A Secure Password Authentication Mechanism for Seamless Handover in Proxy Mobile IPv6 Networks"

PubMed Central

Alizadeh, Mojtaba; Zamani, Mazdak; Baharun, Sabariah; Abdul Manaf, Azizah; Sakurai, Kouichi; Anada, Hiroki; Keshavarz, Hassan; Ashraf Chaudhry, Shehzad; Khurram Khan, Muhammad

2015-01-01

Proxy Mobile IPv6 is a network-based localized mobility management protocol that supports mobility without mobile nodes’ participation in mobility signaling. The details of user authentication procedure are not specified in this standard, hence, many authentication schemes have been proposed for this standard. In 2013, Chuang et al., proposed an authentication method for PMIPv6, called SPAM. However, Chuang et al.’s Scheme protects the network against some security attacks, but it is still vulnerable to impersonation and password guessing attacks. In addition, we discuss other security drawbacks such as lack of revocation procedure in case of loss or stolen device, and anonymity issues of the Chuang et al.’s scheme. We further propose an enhanced authentication method to mitigate the security issues of SPAM method and evaluate our scheme using BAN logic. PMID:26580963

All-Particle Multiscale Computation of Hypersonic Rarefied Flow

NASA Astrophysics Data System (ADS)

Jun, E.; Burt, J. M.; Boyd, I. D.

2011-05-01

This study examines a new hybrid particle scheme used as an alternative means of multiscale flow simulation. The hybrid particle scheme employs the direct simulation Monte Carlo (DSMC) method in rarefied flow regions and the low diffusion (LD) particle method in continuum flow regions. The numerical procedures of the low diffusion particle method are implemented within an existing DSMC algorithm. The performance of the LD-DSMC approach is assessed by studying Mach 10 nitrogen flow over a sphere with a global Knudsen number of 0.002. The hybrid scheme results show good overall agreement with results from standard DSMC and CFD computation. Subcell procedures are utilized to improve computational efficiency and reduce sensitivity to DSMC cell size in the hybrid scheme. This makes it possible to perform the LD-DSMC simulation on a much coarser mesh that leads to a significant reduction in computation time.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

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

Efficient implementation of arbitrary quantum state engineering in four-state system by counterdiabatic driving

NASA Astrophysics Data System (ADS)

Wang, Song-Bai; Chen, Ye-Hong; Wu, Qi-Cheng; Shi, Zhi-Cheng; Huang, Bi-Hua; Song, Jie; Xia, Yan

2018-07-01

A scheme is proposed to implement quantum state engineering (QSE) in a four-state system via counterdiabatic driving. In the scheme, single- and multi-mode driving methods are used respectively to drive the system to a target state at a predefined time. It is found that a fast QSE can be realized by utilizing simply designed pulses. In addition, a beneficial discussion on the energy consumption between the single- and multi-mode driving protocols shows that the multi-mode driving method seems to have a wider range of applications than the single-mode driving method with respect to different parameters. Finally, the scheme is also helpful for implementing the generalization QSE in high-dimensional systems via the concept of a dressed state. Therefore, the scheme can be implemented with the present experimental technology, which is useful in quantum information processing.

Large Eddy simulation of compressible flows with a low-numerical dissipation patch-based adaptive mesh refinement method

NASA Astrophysics Data System (ADS)

Pantano, Carlos

2005-11-01

We describe a hybrid finite difference method for large-eddy simulation (LES) of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). Numerical experiments and validation calculations are presented including a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability. The approach is a conservative flux-based SAMR formulation and as such, it utilizes refinement to computational advantage. The numerical method for the resolved scale terms encompasses the cases of scheme alternation and internal mesh interfaces resulting from SAMR. An explicit centered scheme that is consistent with a skew-symmetric finite difference formulation is used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. The subgrid stresses and transports are calculated by means of the streched-vortex model, Misra & Pullin (1997)

A Summary of the Space-Time Conservation Element and Solution Element (CESE) Method

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen J.

2015-01-01

The space-time Conservation Element and Solution Element (CESE) method for solving conservation laws is examined for its development motivation and design requirements. The characteristics of the resulting scheme are discussed. The discretization of the Euler equations is presented to show readers how to construct a scheme based on the CESE method. The differences and similarities between the CESE method and other traditional methods are discussed. The strengths and weaknesses of the method are also addressed.

Thin-thick quadrature frequency conversion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eimerl, D.

1985-02-07

The quadrature conversion scheme is a method of generating the second harmonic. The scheme, which uses two crystals in series, has several advantages over single-crystal or other two crystal schemes. The most important is that it is capable of high conversion efficiency over a large dynamic range of drive intensity and detuning angle.

Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping

NASA Astrophysics Data System (ADS)

Smith, Timothy; Pantano, Carlos

2017-11-01

We present a new method to enforce field bounds in high-order Legendre-WENO finite volume schemes. The strategy consists of reconstructing each field through an intermediate mapping, which by design satisfies realizability constraints. Determination of the coefficients of the polynomial reconstruction involves nonlinear equations that are solved using Newton's method. The selection between the original or mapped reconstruction is implemented dynamically to minimize computational cost. The method has also been generalized to fields that exhibit interdependencies, requiring multi-dimensional mappings. Further, the method does not depend on the existence of a numerical flux function. We will discuss details of the proposed scheme and show results for systems in conservation and non-conservation form. This work was funded by the NSF under Grant DMS 1318161.

A conjugate gradient method for solving the non-LTE line radiation transfer problem

NASA Astrophysics Data System (ADS)

Paletou, F.; Anterrieu, E.

2009-12-01

This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently proposed Gauss-Seidel and successive over-relaxation (GS/SOR) schemes. Our study is indeed based on applying a preconditioned bi-conjugate gradient method (BiCG-P). Standard tests, in 1D plane parallel geometry and in the frame of the two-level atom model with monochromatic scattering are discussed. Rates of convergence between the previously mentioned iterative schemes are compared, as are their respective timing properties. The smoothing capability of the BiCG-P method is also demonstrated.

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

NASA Astrophysics Data System (ADS)

Kolkovska, N.

2013-10-01

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

Multilevel Green's function interpolation method for scattering from composite metallic and dielectric objects.

PubMed

Shi, Yan; Wang, Hao Gang; Li, Long; Chan, Chi Hou

2008-10-01

A multilevel Green's function interpolation method based on two kinds of multilevel partitioning schemes--the quasi-2D and the hybrid partitioning scheme--is proposed for analyzing electromagnetic scattering from objects comprising both conducting and dielectric parts. The problem is formulated using the surface integral equation for homogeneous dielectric and conducting bodies. A quasi-2D multilevel partitioning scheme is devised to improve the efficiency of the Green's function interpolation. In contrast to previous multilevel partitioning schemes, noncubic groups are introduced to discretize the whole EM structure in this quasi-2D multilevel partitioning scheme. Based on the detailed analysis of the dimension of the group in this partitioning scheme, a hybrid quasi-2D/3D multilevel partitioning scheme is proposed to effectively handle objects with fine local structures. Selection criteria for some key parameters relating to the interpolation technique are given. The proposed algorithm is ideal for the solution of problems involving objects such as missiles, microstrip antenna arrays, photonic bandgap structures, etc. Numerical examples are presented to show that CPU time is between O(N) and O(N log N) while the computer memory requirement is O(N).

Optimal updating magnitude in adaptive flat-distribution sampling

NASA Astrophysics Data System (ADS)

Zhang, Cheng; Drake, Justin A.; Ma, Jianpeng; Pettitt, B. Montgomery

2017-11-01

We present a study on the optimization of the updating magnitude for a class of free energy methods based on flat-distribution sampling, including the Wang-Landau (WL) algorithm and metadynamics. These methods rely on adaptive construction of a bias potential that offsets the potential of mean force by histogram-based updates. The convergence of the bias potential can be improved by decreasing the updating magnitude with an optimal schedule. We show that while the asymptotically optimal schedule for the single-bin updating scheme (commonly used in the WL algorithm) is given by the known inverse-time formula, that for the Gaussian updating scheme (commonly used in metadynamics) is often more complex. We further show that the single-bin updating scheme is optimal for very long simulations, and it can be generalized to a class of bandpass updating schemes that are similarly optimal. These bandpass updating schemes target only a few long-range distribution modes and their optimal schedule is also given by the inverse-time formula. Constructed from orthogonal polynomials, the bandpass updating schemes generalize the WL and Langfeld-Lucini-Rago algorithms as an automatic parameter tuning scheme for umbrella sampling.

A fast numerical scheme for causal relativistic hydrodynamics with dissipation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takamoto, Makoto, E-mail: takamoto@tap.scphys.kyoto-u.ac.jp; Inutsuka, Shu-ichiro

2011-08-01

Highlights: {yields} We have developed a new multi-dimensional numerical scheme for causal relativistic hydrodynamics with dissipation. {yields} Our new scheme can calculate the evolution of dissipative relativistic hydrodynamics faster and more effectively than existing schemes. {yields} Since we use the Riemann solver for solving the advection steps, our method can capture shocks very accurately. - Abstract: In this paper, we develop a stable and fast numerical scheme for relativistic dissipative hydrodynamics based on Israel-Stewart theory. Israel-Stewart theory is a stable and causal description of dissipation in relativistic hydrodynamics although it includes relaxation process with the timescale for collision of constituentmore » particles, which introduces stiff equations and makes practical numerical calculation difficult. In our new scheme, we use Strang's splitting method, and use the piecewise exact solutions for solving the extremely short timescale problem. In addition, since we split the calculations into inviscid step and dissipative step, Riemann solver can be used for obtaining numerical flux for the inviscid step. The use of Riemann solver enables us to capture shocks very accurately. Simple numerical examples are shown. The present scheme can be applied to various high energy phenomena of astrophysics and nuclear physics.« less

Optimal updating magnitude in adaptive flat-distribution sampling.

PubMed

Zhang, Cheng; Drake, Justin A; Ma, Jianpeng; Pettitt, B Montgomery

2017-11-07

We present a study on the optimization of the updating magnitude for a class of free energy methods based on flat-distribution sampling, including the Wang-Landau (WL) algorithm and metadynamics. These methods rely on adaptive construction of a bias potential that offsets the potential of mean force by histogram-based updates. The convergence of the bias potential can be improved by decreasing the updating magnitude with an optimal schedule. We show that while the asymptotically optimal schedule for the single-bin updating scheme (commonly used in the WL algorithm) is given by the known inverse-time formula, that for the Gaussian updating scheme (commonly used in metadynamics) is often more complex. We further show that the single-bin updating scheme is optimal for very long simulations, and it can be generalized to a class of bandpass updating schemes that are similarly optimal. These bandpass updating schemes target only a few long-range distribution modes and their optimal schedule is also given by the inverse-time formula. Constructed from orthogonal polynomials, the bandpass updating schemes generalize the WL and Langfeld-Lucini-Rago algorithms as an automatic parameter tuning scheme for umbrella sampling.

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

NASA Astrophysics Data System (ADS)

Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

2018-06-01

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

One-dimensional high-order compact method for solving Euler's equations

NASA Astrophysics Data System (ADS)

Mohamad, M. A. H.; Basri, S.; Basuno, B.

2012-06-01

In the field of computational fluid dynamics, many numerical algorithms have been developed to simulate inviscid, compressible flows problems. Among those most famous and relevant are based on flux vector splitting and Godunov-type schemes. Previously, this system was developed through computational studies by Mawlood [1]. However the new test cases for compressible flows, the shock tube problems namely the receding flow and shock waves were not investigated before by Mawlood [1]. Thus, the objective of this study is to develop a high-order compact (HOC) finite difference solver for onedimensional Euler equation. Before developing the solver, a detailed investigation was conducted to assess the performance of the basic third-order compact central discretization schemes. Spatial discretization of the Euler equation is based on flux-vector splitting. From this observation, discretization of the convective flux terms of the Euler equation is based on a hybrid flux-vector splitting, known as the advection upstream splitting method (AUSM) scheme which combines the accuracy of flux-difference splitting and the robustness of flux-vector splitting. The AUSM scheme is based on the third-order compact scheme to the approximate finite difference equation was completely analyzed consequently. In one-dimensional problem for the first order schemes, an explicit method is adopted by using time integration method. In addition to that, development and modification of source code for the one-dimensional flow is validated with four test cases namely, unsteady shock tube, quasi-one-dimensional supersonic-subsonic nozzle flow, receding flow and shock waves in shock tubes. From these results, it was also carried out to ensure that the definition of Riemann problem can be identified. Further analysis had also been done in comparing the characteristic of AUSM scheme against experimental results, obtained from previous works and also comparative analysis with computational results generated by van Leer, KFVS and AUSMPW schemes. Furthermore, there is a remarkable improvement with the extension of the AUSM scheme from first-order to third-order accuracy in terms of shocks, contact discontinuities and rarefaction waves.

The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

1995-01-01

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

Blind compressive sensing dynamic MRI

PubMed Central

Lingala, Sajan Goud; Jacob, Mathews

2013-01-01

We propose a novel blind compressive sensing (BCS) frame work to recover dynamic magnetic resonance images from undersampled measurements. This scheme models the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. In contrast to classical compressed sensing, the BCS scheme simultaneously estimates the dictionary and the sparse coefficients from the undersampled measurements. Apart from the sparsity of the coefficients, the key difference of the BCS scheme with current low rank methods is the non-orthogonal nature of the dictionary basis functions. Since the number of degrees of freedom of the BCS model is smaller than that of the low-rank methods, it provides improved reconstructions at high acceleration rates. We formulate the reconstruction as a constrained optimization problem; the objective function is the linear combination of a data consistency term and sparsity promoting ℓ1 prior of the coefficients. The Frobenius norm dictionary constraint is used to avoid scale ambiguity. We introduce a simple and efficient majorize-minimize algorithm, which decouples the original criterion into three simpler sub problems. An alternating minimization strategy is used, where we cycle through the minimization of three simpler problems. This algorithm is seen to be considerably faster than approaches that alternates between sparse coding and dictionary estimation, as well as the extension of K-SVD dictionary learning scheme. The use of the ℓ1 penalty and Frobenius norm dictionary constraint enables the attenuation of insignificant basis functions compared to the ℓ0 norm and column norm constraint assumed in most dictionary learning algorithms; this is especially important since the number of basis functions that can be reliably estimated is restricted by the available measurements. We also observe that the proposed scheme is more robust to local minima compared to K-SVD method, which relies on greedy sparse coding. Our phase transition experiments demonstrate that the BCS scheme provides much better recovery rates than classical Fourier-based CS schemes, while being only marginally worse than the dictionary aware setting. Since the overhead in additionally estimating the dictionary is low, this method can be very useful in dynamic MRI applications, where the signal is not sparse in known dictionaries. We demonstrate the utility of the BCS scheme in accelerating contrast enhanced dynamic data. We observe superior reconstruction performance with the BCS scheme in comparison to existing low rank and compressed sensing schemes. PMID:23542951

High-order Discontinuous Element-based Schemes for the Inviscid Shallow Water Equations: Spectral Multidomain Penalty and Discontinuous Galerkin Methods

DTIC Science & Technology

2011-07-19

multidomain methods, Discontinuous Galerkin methods, interfacial treatment ∗ Jorge A. Escobar-Vargas, School of Civil and Environmental Engineering, Cornell...Click here to view linked References 1. Introduction Geophysical flows exhibit a complex structure and dynamics over a broad range of scales that...hyperbolic problems, where the interfacial patching was implemented with an upwind scheme based on a modified method of characteristics. This approach

Efficient adaptive pseudo-symplectic numerical integration techniques for Landau-Lifshitz dynamics

NASA Astrophysics Data System (ADS)

d'Aquino, M.; Capuano, F.; Coppola, G.; Serpico, C.; Mayergoyz, I. D.

2018-05-01

Numerical time integration schemes for Landau-Lifshitz magnetization dynamics are considered. Such dynamics preserves the magnetization amplitude and, in the absence of dissipation, also implies the conservation of the free energy. This property is generally lost when time discretization is performed for the numerical solution. In this work, explicit numerical schemes based on Runge-Kutta methods are introduced. The schemes are termed pseudo-symplectic in that they are accurate to order p, but preserve magnetization amplitude and free energy to order q > p. An effective strategy for adaptive time-stepping control is discussed for schemes of this class. Numerical tests against analytical solutions for the simulation of fast precessional dynamics are performed in order to point out the effectiveness of the proposed methods.

Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms

NASA Astrophysics Data System (ADS)

Huang, Juntao; Shu, Chi-Wang

2018-05-01

In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source terms by extending the idea in Zhang and Shu [43]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical solutions. It is also straightforward to extend the method to two dimensions on rectangular and triangular meshes. Even though we only discuss the bound-preserving limiter for DG schemes, it can also be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well.

A Legendre tau-spectral method for solving time-fractional heat equation with nonlocal conditions.

PubMed

Bhrawy, A H; Alghamdi, M A

2014-01-01

We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials are used as the base function. The main advantage in using the presented scheme is that it converts the T-FHE with nonlocal condition to a system of algebraic equations that simplifies the problem. For demonstrating the validity and applicability of the developed spectral scheme, two numerical examples are presented. The logarithmic graphs of the maximum absolute errors is presented to achieve the exponential convergence of the proposed method. Comparing between our spectral method and other methods ensures that our method is more accurate than those solved similar problem.

A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions

PubMed Central

Bhrawy, A. H.; Alghamdi, M. A.

2014-01-01

We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials are used as the base function. The main advantage in using the presented scheme is that it converts the T-FHE with nonlocal condition to a system of algebraic equations that simplifies the problem. For demonstrating the validity and applicability of the developed spectral scheme, two numerical examples are presented. The logarithmic graphs of the maximum absolute errors is presented to achieve the exponential convergence of the proposed method. Comparing between our spectral method and other methods ensures that our method is more accurate than those solved similar problem. PMID:25057507

Fourth-order numerical solutions of diffusion equation by using SOR method with Crank-Nicolson approach

NASA Astrophysics Data System (ADS)

Muhiddin, F. A.; Sulaiman, J.

2017-09-01

The aim of this paper is to investigate the effectiveness of the Successive Over-Relaxation (SOR) iterative method by using the fourth-order Crank-Nicolson (CN) discretization scheme to derive a five-point Crank-Nicolson approximation equation in order to solve diffusion equation. From this approximation equation, clearly, it can be shown that corresponding system of five-point approximation equations can be generated and then solved iteratively. In order to access the performance results of the proposed iterative method with the fourth-order CN scheme, another point iterative method which is Gauss-Seidel (GS), also presented as a reference method. Finally the numerical results obtained from the use of the fourth-order CN discretization scheme, it can be pointed out that the SOR iterative method is superior in terms of number of iterations, execution time, and maximum absolute error.

On epicardial potential reconstruction using regularization schemes with the L1-norm data term.

PubMed

Shou, Guofa; Xia, Ling; Liu, Feng; Jiang, Mingfeng; Crozier, Stuart

2011-01-07

The electrocardiographic (ECG) inverse problem is ill-posed and usually solved by regularization schemes. These regularization methods, such as the Tikhonov method, are often based on the L2-norm data and constraint terms. However, L2-norm-based methods inherently provide smoothed inverse solutions that are sensitive to measurement errors, and also lack the capability of localizing and distinguishing multiple proximal cardiac electrical sources. This paper presents alternative regularization schemes employing the L1-norm data term for the reconstruction of epicardial potentials (EPs) from measured body surface potentials (BSPs). During numerical implementation, the iteratively reweighted norm algorithm was applied to solve the L1-norm-related schemes, and measurement noises were considered in the BSP data. The proposed L1-norm data term-based regularization schemes (with L1 and L2 penalty terms of the normal derivative constraint (labelled as L1TV and L1L2)) were compared with the L2-norm data terms (Tikhonov with zero-order and normal derivative constraints, labelled as ZOT and FOT, and the total variation method labelled as L2TV). The studies demonstrated that, with averaged measurement noise, the inverse solutions provided by the L1L2 and FOT algorithms have less relative error values. However, when larger noise occurred in some electrodes (for example, signal lost during measurement), the L1TV and L1L2 methods can obtain more accurate EPs in a robust manner. Therefore the L1-norm data term-based solutions are generally less perturbed by measurement noises, suggesting that the new regularization scheme is promising for providing practical ECG inverse solutions.

New Developments in the Method of Space-Time Conservation Element and Solution Element-Applications to Two-Dimensional Time-Marching Problems

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Wang, Xiao-Yen; Chow, Chuen-Yen

1994-01-01

A new numerical discretization method for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is motivated by several important physical/numerical considerations and designed to avoid several key limitations of the above traditional methods. As a result of the above considerations, a set of key principles for the design of numerical schemes was put forth in a previous report. These principles were used to construct several numerical schemes that model a 1-D time-dependent convection-diffusion equation. These schemes were then extended to solve the time-dependent Euler and Navier-Stokes equations of a perfect gas. It was shown that the above schemes compared favorably with the traditional schemes in simplicity, generality, and accuracy. In this report, the 2-D versions of the above schemes, except the Navier-Stokes solver, are constructed using the same set of design principles. Their constructions are simplified greatly by the use of a nontraditional space-time mesh. Its use results in the simplest stencil possible, i.e., a tetrahedron in a 3-D space-time with a vertex at the upper time level and other three at the lower time level. Because of the similarity in their design, each of the present 2-D solvers virtually shares with its 1-D counterpart the same fundamental characteristics. Moreover, it is shown that the present Euler solver is capable of generating highly accurate solutions for a famous 2-D shock reflection problem. Specifically, both the incident and the reflected shocks can be resolved by a single data point without the presence of numerical oscillations near the discontinuity.

A PDE Sensitivity Equation Method for Optimal Aerodynamic Design

NASA Technical Reports Server (NTRS)

Borggaard, Jeff; Burns, John

1996-01-01

The use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design. A typical procedure uses a simulation scheme to evaluate the objective function (from the approximate states) and its gradient, then passes this information to an optimization algorithm. Once the simulation scheme (CFD flow solver) has been selected and used to provide approximate function evaluations, there are several possible approaches to the problem of computing gradients. One popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients. Although this black-box approach has many advantages in shape optimization problems, one must compute mesh sensitivities in order to compute the design sensitivity. In this paper, we present an alternative approach using the PDE sensitivity equation to develop algorithms for computing gradients. This approach has the advantage that mesh sensitivities need not be computed. Moreover, when it is possible to use the CFD scheme for both the forward problem and the sensitivity equation, then there are computational advantages. An apparent disadvantage of this approach is that it does not always produce consistent derivatives. However, for a proper combination of discretization schemes, one can show asymptotic consistency under mesh refinement, which is often sufficient to guarantee convergence of the optimal design algorithm. In particular, we show that when asymptotically consistent schemes are combined with a trust-region optimization algorithm, the resulting optimal design method converges. We denote this approach as the sensitivity equation method. The sensitivity equation method is presented, convergence results are given and the approach is illustrated on two optimal design problems involving shocks.

An asymptotic preserving multidimensional ALE method for a system of two compressible flows coupled with friction

NASA Astrophysics Data System (ADS)

Del Pino, S.; Labourasse, E.; Morel, G.

2018-06-01

We present a multidimensional asymptotic preserving scheme for the approximation of a mixture of compressible flows. Fluids are modelled by two Euler systems of equations coupled with a friction term. The asymptotic preserving property is mandatory for this kind of model, to derive a scheme that behaves well in all regimes (i.e. whatever the friction parameter value is). The method we propose is defined in ALE coordinates, using a Lagrange plus remap approach. This imposes a multidimensional definition and analysis of the scheme.

Computation of turbulent pipe and duct flow using third order upwind scheme

NASA Technical Reports Server (NTRS)

Kawamura, T.

1986-01-01

The fully developed turbulence in a circular pipe and in a square duct is simulated directly without using turbulence models in the Navier-Stokes equations. The utilized method employs a third-order upwind scheme for the approximation to the nonlinear term and the second-order Adams-Bashforth method for the time derivative in the Navier-Stokes equation. The computational results appear to capture the large-scale turbulent structures at least qualitatively. The significance of the artificial viscosity inherent in the present scheme is discussed.

Intra-generational Redistribution under Public Pension Planning Based on Generation-based Funding Scheme

NASA Astrophysics Data System (ADS)

Banjo, Daisuke; Tamura, Hiroyuki; Murata, Tadahiko

In this paper, we propose a method of determining the pension in the generation-based funding scheme. In this proposal, we include two types of pensions in the scheme. One is the payment-amount related pension and the other is the payment-frequency related pension. We set the ratio of the total amount of payment-amount related pension to the total amount of both pensions, and simulate income gaps and the relationship between contributions and benefits for each individual when the proposed method is applied.

A new scheme for grading the quality of scientific reports that evaluate imaging modalities for cerebrovascular diseases.

PubMed

Qureshi, Adnan I

2007-10-01

Imaging of head and neck vasculature continues to improve with the application of new technology. To judge the value of new technologies reported in the literature, it is imperative to develop objective standards optimized against bias and favoring statistical power and clinical relevance. A review of the existing literature identified the following items as lending scientific value to a report on imaging technology: prospective design, comparison with an accepted modality, unbiased patient selection, standardized image acquisition, blinded interpretation, and measurement of reliability. These were incorporated into a new grading scheme. Two physicians tested the new scheme and an established scheme to grade reports published in the medical literature. Inter-observer reliability for both methods was calculated using the kappa coefficient. A total of 22 reports evaluating imaging modalities for cervical internal carotid artery stenosis were identified from a literature search and graded by both schemes. Agreement between the two physicians in grading the level of scientific evidence using the new scheme was excellent (kappa coefficient: 0.93, p<0.0001). Agreement using the established scheme was less rigorous (kappa coefficient: 0.39, p<0.0001). The weighted kappa coefficients were 0.95 and 0.38 for the new and established schemes, respectively. Overall agreement was higher for the newer scheme (95% versus 64%). The new grading scheme can be used reliably to categorize the strength of scientific knowledge provided by individual studies of vascular imaging. The new method could assist clinicians and researchers in determining appropriate clinical applications of newly reported technical advances.

A spectral radius scaling semi-implicit iterative time stepping method for reactive flow simulations with detailed chemistry

NASA Astrophysics Data System (ADS)

Xie, Qing; Xiao, Zhixiang; Ren, Zhuyin

2018-09-01

A spectral radius scaling semi-implicit time stepping scheme has been developed for simulating unsteady compressible reactive flows with detailed chemistry, in which the spectral radius in the LUSGS scheme has been augmented to account for viscous/diffusive and reactive terms and a scalar matrix is proposed to approximate the chemical Jacobian using the minimum species destruction timescale. The performance of the semi-implicit scheme, together with a third-order explicit Runge-Kutta scheme and a Strang splitting scheme, have been investigated in auto-ignition and laminar premixed and nonpremixed flames of three representative fuels, e.g., hydrogen, methane, and n-heptane. Results show that the minimum species destruction time scale can well represent the smallest chemical time scale in reactive flows and the proposed scheme can significantly increase the allowable time steps in simulations. The scheme is stable when the time step is as large as 10 μs, which is about three to five orders of magnitude larger than the smallest time scales in various tests considered. For the test flames considered, the semi-implicit scheme achieves second order of accuracy in time. Moreover, the errors in quantities of interest are smaller than those from the Strang splitting scheme indicating the accuracy gain when the reaction and transport terms are solved coupled. Results also show that the relative efficiency of different schemes depends on fuel mechanisms and test flames. When the minimum time scale in reactive flows is governed by transport processes instead of chemical reactions, the proposed semi-implicit scheme is more efficient than the splitting scheme. Otherwise, the relative efficiency depends on the cost in sub-iterations for convergence within each time step and in the integration for chemistry substep. Then, the capability of the compressible reacting flow solver and the proposed semi-implicit scheme is demonstrated for capturing the hydrogen detonation waves. Finally, the performance of the proposed method is demonstrated in a two-dimensional hydrogen/air diffusion flame.

On the Quality of Velocity Interpolation Schemes for Marker-in-Cell Method and Staggered Grids

NASA Astrophysics Data System (ADS)

Pusok, Adina E.; Kaus, Boris J. P.; Popov, Anton A.

2017-03-01

The marker-in-cell method is generally considered a flexible and robust method to model the advection of heterogenous non-diffusive properties (i.e., rock type or composition) in geodynamic problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without considering the divergence of the velocity field at the interpolated locations (i.e., non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Journal of Computational Physics 166:218-252, 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. To remedy this at low computational costs, Jenny et al. (Journal of Computational Physics 166:218-252, 2001) and Meyer and Jenny (Proceedings in Applied Mathematics and Mechanics 4:466-467, 2004) proposed a simple, conservative velocity interpolation scheme for 2-D staggered grid, while Wang et al. (Geochemistry, Geophysics, Geosystems 16(6):2015-2023, 2015) extended the formulation to 3-D finite element methods. Here, we adapt this formulation for 3-D staggered grids (correction interpolation) and we report on the quality of various velocity interpolation methods for 2-D and 3-D staggered grids. We test the interpolation schemes in combination with different advection schemes on incompressible Stokes problems with strong velocity gradients, which are discretized using a finite difference method. Our results suggest that a conservative formulation reduces the dispersion and clustering of markers, minimizing the need of unphysical marker control in geodynamic models.

Development of a Single Locus Sequence Typing (SLST) Scheme for Typing Bacterial Species Directly from Complex Communities.

PubMed

Scholz, Christian F P; Jensen, Anders

2017-01-01

The protocol describes a computational method to develop a Single Locus Sequence Typing (SLST) scheme for typing bacterial species. The resulting scheme can be used to type bacterial isolates as well as bacterial species directly from complex communities using next-generation sequencing technologies.

Numerical methods for incompressible viscous flows with engineering applications

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Alternating direction implicit methods for parabolic equations with a mixed derivative

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1980-01-01

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A(0)-stable linear two-step methods in conjunction with the method of approximate factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A(0)-stable method. The parameter space for which the resulting ADI schemes are second-order accurate and unconditionally stable is determined. Some numerical examples are given.

Alternating direction implicit methods for parabolic equations with a mixed derivative

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1979-01-01

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given.

Newton-like methods for Navier-Stokes solution

NASA Astrophysics Data System (ADS)

Qin, N.; Xu, X.; Richards, B. E.

1992-12-01

The paper reports on Newton-like methods called SFDN-alpha-GMRES and SQN-alpha-GMRES methods that have been devised and proven as powerful schemes for large nonlinear problems typical of viscous compressible Navier-Stokes solutions. They can be applied using a partially converged solution from a conventional explicit or approximate implicit method. Developments have included the efficient parallelization of the schemes on a distributed memory parallel computer. The methods are illustrated using a RISC workstation and a transputer parallel system respectively to solve a hypersonic vortical flow.

Efficient method for computing the electronic transport properties of a multiterminal system

NASA Astrophysics Data System (ADS)

Lima, Leandro R. F.; Dusko, Amintor; Lewenkopf, Caio

2018-04-01

We present a multiprobe recursive Green's function method to compute the transport properties of mesoscopic systems using the Landauer-Büttiker approach. By introducing an adaptive partition scheme, we map the multiprobe problem into the standard two-probe recursive Green's function method. We apply the method to compute the longitudinal and Hall resistances of a disordered graphene sample, a system of current interest. We show that the performance and accuracy of our method compares very well with other state-of-the-art schemes.

A Novel Iterative Scheme for the Very Fast and Accurate Solution of Non-LTE Radiative Transfer Problems

NASA Astrophysics Data System (ADS)

Trujillo Bueno, J.; Fabiani Bendicho, P.

1995-12-01

Iterative schemes based on Gauss-Seidel (G-S) and optimal successive over-relaxation (SOR) iteration are shown to provide a dramatic increase in the speed with which non-LTE radiation transfer (RT) problems can be solved. The convergence rates of these new RT methods are identical to those of upper triangular nonlocal approximate operator splitting techniques, but the computing time per iteration and the memory requirements are similar to those of a local operator splitting method. In addition to these properties, both methods are particularly suitable for multidimensional geometry, since they neither require the actual construction of nonlocal approximate operators nor the application of any matrix inversion procedure. Compared with the currently used Jacobi technique, which is based on the optimal local approximate operator (see Olson, Auer, & Buchler 1986), the G-S method presented here is faster by a factor 2. It gives excellent smoothing of the high-frequency error components, which makes it the iterative scheme of choice for multigrid radiative transfer. This G-S method can also be suitably combined with standard acceleration techniques to achieve even higher performance. Although the convergence rate of the optimal SOR scheme developed here for solving non-LTE RT problems is much higher than G-S, the computing time per iteration is also minimal, i.e., virtually identical to that of a local operator splitting method. While the conventional optimal local operator scheme provides the converged solution after a total CPU time (measured in arbitrary units) approximately equal to the number n of points per decade of optical depth, the time needed by this new method based on the optimal SOR iterations is only √n/2√2. This method is competitive with those that result from combining the above-mentioned Jacobi and G-S schemes with the best acceleration techniques. Contrary to what happens with the local operator splitting strategy currently in use, these novel methods remain effective even under extreme non-LTE conditions in very fine grids.

Method for digital measurement of phase-frequency characteristics for a fixed-length ultrasonic spectrometer

NASA Astrophysics Data System (ADS)

Astashev, M. E.; Belosludtsev, K. N.; Kharakoz, D. P.

2014-05-01

One of the most accurate methods for measuring the compressibility of liquids is resonance measurement of sound velocity in a fixed-length interferometer. This method combines high sensitivity, accuracy, and small sample volume of the test liquid. The measuring principle is to study the resonance properties of a composite resonator that contains a test liquid sample. Ealier, the phase-locked loop (PLL) scheme was used for this. In this paper, we propose an alternative measurement scheme based on digital analysis of harmonic signals, describe the implementation of this scheme using commercially available data acquisition modules, and give examples of test measurements with accuracy evaluations of the results.

Local unitary transformation method for large-scale two-component relativistic calculations: case for a one-electron Dirac Hamiltonian.

PubMed

Seino, Junji; Nakai, Hiromi

2012-06-28

An accurate and efficient scheme for two-component relativistic calculations at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level is presented. The present scheme, termed local unitary transformation (LUT), is based on the locality of the relativistic effect. Numerical assessments of the LUT scheme were performed in diatomic molecules such as HX and X(2) (X = F, Cl, Br, I, and At) and hydrogen halide clusters, (HX)(n) (X = F, Cl, Br, and I). Total energies obtained by the LUT method agree well with conventional IODKH results. The computational costs of the LUT method are drastically lower than those of conventional methods since in the former there is linear-scaling with respect to the system size and a small prefactor.

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

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.

Differences exist across insurance schemes in China post-consolidation

PubMed Central

Yi, Danhui; Wang, Xiaojun; Jiang, Yan; Wang, Yu; Liu, Xinchun

2017-01-01

Background In China, the basic insurance system consists of three schemes: the UEBMI (Urban Employee Basic Medical Insurance), URBMI (Urban Resident Basic Medical Insurance), and NCMS (New Cooperative Medical Scheme), across which significant differences have been observed. Since 2009, the central government has been experimenting with consolidating these schemes in selected areas. This study examines whether differences still exist across schemes after the consolidation. Methods A survey was conducted in the city of Suzhou, collecting data on subjects 45 years old and above with at least one inpatient or outpatient treatment during a period of twelve months. Analysis on 583 subjects was performed comparing subjects’ characteristics across insurance schemes. A resampling-based method was applied to compute the predicted gross medical cost, OOP (out-of-pocket) cost, and insurance reimbursement rate. Results Subjects under different insurance schemes differ in multiple aspects. For inpatient treatments, subjects under the URBMI have the highest observed and predicted gross and OOP costs, while those under the UEBMI have the lowest. For outpatient treatments, subjects under the UEBMI and URBMI have comparable costs, while those under the NCMS have much lower costs. Subjects under the NCMS also have a much lower reimbursement rate. Conclusions Differences still exist across schemes in medical costs and insurance reimbursement rate post-consolidation. Further investigations are needed to identify the causes, and interventions are needed to eliminate such differences. PMID:29125837

A New Scrambling Evaluation Scheme Based on Spatial Distribution Entropy and Centroid Difference of Bit-Plane

NASA Astrophysics Data System (ADS)

Zhao, Liang; Adhikari, Avishek; Sakurai, Kouichi

Watermarking is one of the most effective techniques for copyright protection and information hiding. It can be applied in many fields of our society. Nowadays, some image scrambling schemes are used as one part of the watermarking algorithm to enhance the security. Therefore, how to select an image scrambling scheme and what kind of the image scrambling scheme may be used for watermarking are the key problems. Evaluation method of the image scrambling schemes can be seen as a useful test tool for showing the property or flaw of the image scrambling method. In this paper, a new scrambling evaluation system based on spatial distribution entropy and centroid difference of bit-plane is presented to obtain the scrambling degree of image scrambling schemes. Our scheme is illustrated and justified through computer simulations. The experimental results show (in Figs. 6 and 7) that for the general gray-scale image, the evaluation degree of the corresponding cipher image for the first 4 significant bit-planes selection is nearly the same as that for the 8 bit-planes selection. That is why, instead of taking 8 bit-planes of a gray-scale image, it is sufficient to take only the first 4 significant bit-planes for the experiment to find the scrambling degree. This 50% reduction in the computational cost makes our scheme efficient.

Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

NASA Technical Reports Server (NTRS)

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

1988-01-01

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.

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.

ID-based encryption scheme with revocation

NASA Astrophysics Data System (ADS)

Othman, Hafizul Azrie; Ismail, Eddie Shahril

2017-04-01

In 2015, Meshram proposed an efficient ID-based cryptographic encryption based on the difficulty of solving discrete logarithm and integer-factoring problems. The scheme was pairing free and claimed to be secure against adaptive chosen plaintext attacks (CPA). Later, Tan et al. proved that the scheme was insecure by presenting a method to recover the secret master key and to obtain prime factorization of modulo n. In this paper, we propose a new pairing-free ID-based encryption scheme with revocation based on Meshram's ID-based encryption scheme, which is also secure against Tan et al.'s attacks.

An efficient numerical scheme for the study of equal width equation

NASA Astrophysics Data System (ADS)

Ghafoor, Abdul; Haq, Sirajul

2018-06-01

In this work a new numerical scheme is proposed in which Haar wavelet method is coupled with finite difference scheme for the solution of a nonlinear partial differential equation. The scheme transforms the partial differential equation to a system of algebraic equations which can be solved easily. The technique is applied to equal width equation in order to study the behaviour of one, two, three solitary waves, undular bore and soliton collision. For efficiency and accuracy of the scheme, L2 and L∞ norms and invariants are computed. The results obtained are compared with already existing results in literature.

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.

Dynamic neural network-based methods for compensation of nonlinear effects in multimode communication lines

NASA Astrophysics Data System (ADS)

Sidelnikov, O. S.; Redyuk, A. A.; Sygletos, S.

2017-12-01

We consider neural network-based schemes of digital signal processing. It is shown that the use of a dynamic neural network-based scheme of signal processing ensures an increase in the optical signal transmission quality in comparison with that provided by other methods for nonlinear distortion compensation.

A stable and high-order accurate discontinuous Galerkin based splitting method for the incompressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Piatkowski, Marian; Müthing, Steffen; Bastian, Peter

2018-03-01

In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order rotational incremental pressure correction scheme. The major focus of the paper is threefold: i) We propose a modified upwind scheme based on the Vijayasundaram numerical flux that has favourable properties in the context of DG. ii) We present a novel postprocessing technique in the Helmholtz projection step based on H (div) reconstruction of the pressure correction that is computed locally, is a projection in the discrete setting and ensures that the projected velocity satisfies the discrete continuity equation exactly. As a consequence it also provides local mass conservation of the projected velocity. iii) Numerical results demonstrate the properties of the scheme for different polynomial degrees applied to two-dimensional problems with known solution as well as large-scale three-dimensional problems. In particular we address second-order convergence in time of the splitting scheme as well as its long-time stability.

Local unitary transformation method for large-scale two-component relativistic calculations. II. Extension to two-electron Coulomb interaction.

PubMed

Seino, Junji; Nakai, Hiromi

2012-10-14

The local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys. 136, 244102 (2012)], which is based on the locality of relativistic effects, has been extended to a four-component Dirac-Coulomb Hamiltonian. In the previous study, the LUT scheme was applied only to a one-particle IODKH Hamiltonian with non-relativistic two-electron Coulomb interaction, termed IODKH/C. The current study extends the LUT scheme to a two-particle IODKH Hamiltonian as well as one-particle one, termed IODKH/IODKH, which has been a real bottleneck in numerical calculation. The LUT scheme with the IODKH/IODKH Hamiltonian was numerically assessed in the diatomic molecules HX and X(2) and hydrogen halide molecules, (HX)(n) (X = F, Cl, Br, and I). The total Hartree-Fock energies calculated by the LUT method agree well with conventional IODKH/IODKH results. The computational cost of the LUT method is reduced drastically compared with that of the conventional method. In addition, the LUT method achieves linear-scaling with respect to the system size and a small prefactor.

An efficient blocking M2L translation for low-frequency fast multipole method in three dimensions

NASA Astrophysics Data System (ADS)

Takahashi, Toru; Shimba, Yuta; Isakari, Hiroshi; Matsumoto, Toshiro

2016-05-01

We propose an efficient scheme to perform the multipole-to-local (M2L) translation in the three-dimensional low-frequency fast multipole method (LFFMM). Our strategy is to combine a group of matrix-vector products associated with M2L translation into a matrix-matrix product in order to diminish the memory traffic. For this purpose, we first developed a grouping method (termed as internal blocking) based on the congruent transformations (rotational and reflectional symmetries) of M2L-translators for each target box in the FMM hierarchy (adaptive octree). Next, we considered another method of grouping (termed as external blocking) that was able to handle M2L translations for multiple target boxes collectively by using the translational invariance of the M2L translation. By combining these internal and external blockings, the M2L translation can be performed efficiently whilst preservingthe numerical accuracy exactly. We assessed the proposed blocking scheme numerically and applied it to the boundary integral equation method to solve electromagnetic scattering problems for perfectly electrical conductor. From the numerical results, it was found that the proposed M2L scheme achieved a few times speedup compared to the non-blocking scheme.

The finite element method scheme for a solution of an evolution variational inequality with a nonlocal space operator

NASA Astrophysics Data System (ADS)

Glazyrina, O. V.; Pavlova, M. F.

2016-11-01

We consider the parabolic inequality with monotone with respect to a gradient space operator, which is depended on integral with respect to space variables solution characteristic. We construct a two-layer differential scheme for this problem with use of penalty method, semidiscretization with respect to time variable method and the finite element method (FEM) with respect to space variables. We proved a convergence of constructed mothod.

Advanced Computational Aeroacoustics Methods for Fan Noise Prediction

NASA Technical Reports Server (NTRS)

Envia, Edmane (Technical Monitor); Tam, Christopher

2003-01-01

Direct computation of fan noise is presently not possible. One of the major difficulties is the geometrical complexity of the problem. In the case of fan noise, the blade geometry is critical to the loading on the blade and hence the intensity of the radiated noise. The precise geometry must be incorporated into the computation. In computational fluid dynamics (CFD), there are two general ways to handle problems with complex geometry. One way is to use unstructured grids. The other is to use body fitted overset grids. In the overset grid method, accurate data transfer is of utmost importance. For acoustic computation, it is not clear that the currently used data transfer methods are sufficiently accurate as not to contaminate the very small amplitude acoustic disturbances. In CFD, low order schemes are, invariably, used in conjunction with unstructured grids. However, low order schemes are known to be numerically dispersive and dissipative. dissipative errors are extremely undesirable for acoustic wave problems. The objective of this project is to develop a high order unstructured grid Dispersion-Relation-Preserving (DRP) scheme. would minimize numerical dispersion and dissipation errors. contains the results of the funded portion of the project. scheme on an unstructured grid has been developed. constructed in the wave number space. The characteristics of the scheme can be improved by the inclusion of additional constraints. Stability of the scheme has been investigated. Stability can be improved by adopting the upwinding strategy.

Perfect Detection of Spikes in the Linear Sub-threshold Dynamics of Point Neurons

PubMed Central

Krishnan, Jeyashree; Porta Mana, PierGianLuca; Helias, Moritz; Diesmann, Markus; Di Napoli, Edoardo

2018-01-01

Spiking neuronal networks are usually simulated with one of three main schemes: the classical time-driven and event-driven schemes, and the more recent hybrid scheme. All three schemes evolve the state of a neuron through a series of checkpoints: equally spaced in the first scheme and determined neuron-wise by spike events in the latter two. The time-driven and the hybrid scheme determine whether the membrane potential of a neuron crosses a threshold at the end of the time interval between consecutive checkpoints. Threshold crossing can, however, occur within the interval even if this test is negative. Spikes can therefore be missed. The present work offers an alternative geometric point of view on neuronal dynamics, and derives, implements, and benchmarks a method for perfect retrospective spike detection. This method can be applied to neuron models with affine or linear subthreshold dynamics. The idea behind the method is to propagate the threshold with a time-inverted dynamics, testing whether the threshold crosses the neuron state to be evolved, rather than vice versa. Algebraically this translates into a set of inequalities necessary and sufficient for threshold crossing. This test is slower than the imperfect one, but can be optimized in several ways. Comparison confirms earlier results that the imperfect tests rarely miss spikes (less than a fraction 1/108 of missed spikes) in biologically relevant settings. PMID:29379430

Improved Secret Image Sharing Scheme in Embedding Capacity without Underflow and Overflow.

PubMed

Pang, Liaojun; Miao, Deyu; Li, Huixian; Wang, Qiong

2015-01-01

Computational secret image sharing (CSIS) is an effective way to protect a secret image during its transmission and storage, and thus it has attracted lots of attentions since its appearance. Nowadays, it has become a hot topic for researchers to improve the embedding capacity and eliminate the underflow and overflow situations, which is embarrassing and difficult to deal with. The scheme, which has the highest embedding capacity among the existing schemes, has the underflow and overflow problems. Although the underflow and overflow situations have been well dealt with by different methods, the embedding capacities of these methods are reduced more or less. Motivated by these concerns, we propose a novel scheme, in which we take the differential coding, Huffman coding, and data converting to compress the secret image before embedding it to further improve the embedding capacity, and the pixel mapping matrix embedding method with a newly designed matrix is used to embed secret image data into the cover image to avoid the underflow and overflow situations. Experiment results show that our scheme can improve the embedding capacity further and eliminate the underflow and overflow situations at the same time.

A method of LED free-form tilted lens rapid modeling based on scheme language

NASA Astrophysics Data System (ADS)

Dai, Yidan

2017-10-01

According to nonimaging optical principle and traditional LED free-form surface lens, a new kind of LED free-form tilted lens was designed. And a method of rapid modeling based on Scheme language was proposed. The mesh division method was applied to obtain the corresponding surface configuration according to the character of the light source and the desired energy distribution on the illumination plane. Then 3D modeling software and the Scheme language programming are used to generate lens model respectively. With the help of optical simulation software, a light source with the size of 1mm*1mm*1mm in volume is used in experiment, and the lateral migration distance of illumination area is 0.5m, in which total one million rays are computed. We could acquire the simulated results of both models. The simulated output result shows that the Scheme language can prevent the model deformation problems caused by the process of the model transfer, and the degree of illumination uniformity is reached to 82%, and the offset angle is 26°. Also, the efficiency of modeling process is greatly increased by using Scheme language.

Improved Secret Image Sharing Scheme in Embedding Capacity without Underflow and Overflow

PubMed Central

Pang, Liaojun; Miao, Deyu; Li, Huixian; Wang, Qiong

2015-01-01

Computational secret image sharing (CSIS) is an effective way to protect a secret image during its transmission and storage, and thus it has attracted lots of attentions since its appearance. Nowadays, it has become a hot topic for researchers to improve the embedding capacity and eliminate the underflow and overflow situations, which is embarrassing and difficult to deal with. The scheme, which has the highest embedding capacity among the existing schemes, has the underflow and overflow problems. Although the underflow and overflow situations have been well dealt with by different methods, the embedding capacities of these methods are reduced more or less. Motivated by these concerns, we propose a novel scheme, in which we take the differential coding, Huffman coding, and data converting to compress the secret image before embedding it to further improve the embedding capacity, and the pixel mapping matrix embedding method with a newly designed matrix is used to embed secret image data into the cover image to avoid the underflow and overflow situations. Experiment results show that our scheme can improve the embedding capacity further and eliminate the underflow and overflow situations at the same time. PMID:26351657

On Multi-Dimensional Unstructured Mesh Adaption

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1999-01-01

Anisotropic unstructured mesh adaption is developed for a truly multi-dimensional upwind fluctuation splitting scheme, as applied to scalar advection-diffusion. The adaption is performed locally using edge swapping, point insertion/deletion, and nodal displacements. Comparisons are made versus the current state of the art for aggressive anisotropic unstructured adaption, which is based on a posteriori error estimates. Demonstration of both schemes to model problems, with features representative of compressible gas dynamics, show the present method to be superior to the a posteriori adaption for linear advection. The performance of the two methods is more similar when applied to nonlinear advection, with a difference in the treatment of shocks. The a posteriori adaption can excessively cluster points to a shock, while the present multi-dimensional scheme tends to merely align with a shock, using fewer nodes. As a consequence of this alignment tendency, an implementation of eigenvalue limiting for the suppression of expansion shocks is developed for the multi-dimensional distribution scheme. The differences in the treatment of shocks by the adaption schemes, along with the inherently low levels of artificial dissipation in the fluctuation splitting solver, suggest the present method is a strong candidate for applications to compressible gas dynamics.

On the validation of cloud parametrization schemes in numerical atmospheric models with satellite data from ISCCP

NASA Astrophysics Data System (ADS)

Meinke, I.

2003-04-01

A new method is presented to validate cloud parametrization schemes in numerical atmospheric models with satellite data of scanning radiometers. This method is applied to the regional atmospheric model HRM (High Resolution Regional Model) using satellite data from ISCCP (International Satellite Cloud Climatology Project). Due to the limited reliability of former validations there has been a need for developing a new validation method: Up to now differences between simulated and measured cloud properties are mostly declared as deficiencies of the cloud parametrization scheme without further investigation. Other uncertainties connected with the model or with the measurements have not been taken into account. Therefore changes in the cloud parametrization scheme based on such kind of validations might not be realistic. The new method estimates uncertainties of the model and the measurements. Criteria for comparisons of simulated and measured data are derived to localize deficiencies in the model. For a better specification of these deficiencies simulated clouds are classified regarding their parametrization. With this classification the localized model deficiencies are allocated to a certain parametrization scheme. Applying this method to the regional model HRM the quality of forecasting cloud properties is estimated in detail. The overestimation of simulated clouds in low emissivity heights especially during the night is localized as model deficiency. This is caused by subscale cloudiness. As the simulation of subscale clouds in the regional model HRM is described by a relative humidity parametrization these deficiencies are connected with this parameterization.

A unified inversion scheme to process multifrequency measurements of various dispersive electromagnetic properties

NASA Astrophysics Data System (ADS)

Han, Y.; Misra, S.

2018-04-01

Multi-frequency measurement of a dispersive electromagnetic (EM) property, such as electrical conductivity, dielectric permittivity, or magnetic permeability, is commonly analyzed for purposes of material characterization. Such an analysis requires inversion of the multi-frequency measurement based on a specific relaxation model, such as Cole-Cole model or Pelton's model. We develop a unified inversion scheme that can be coupled to various type of relaxation models to independently process multi-frequency measurement of varied EM properties for purposes of improved EM-based geomaterial characterization. The proposed inversion scheme is firstly tested in few synthetic cases in which different relaxation models are coupled into the inversion scheme and then applied to multi-frequency complex conductivity, complex resistivity, complex permittivity, and complex impedance measurements. The method estimates up to seven relaxation-model parameters exhibiting convergence and accuracy for random initializations of the relaxation-model parameters within up to 3-orders of magnitude variation around the true parameter values. The proposed inversion method implements a bounded Levenberg algorithm with tuning initial values of damping parameter and its iterative adjustment factor, which are fixed in all the cases shown in this paper and irrespective of the type of measured EM property and the type of relaxation model. Notably, jump-out step and jump-back-in step are implemented as automated methods in the inversion scheme to prevent the inversion from getting trapped around local minima and to honor physical bounds of model parameters. The proposed inversion scheme can be easily used to process various types of EM measurements without major changes to the inversion scheme.

A third-order moving mesh cell-centered scheme for one-dimensional elastic-plastic flows

NASA Astrophysics Data System (ADS)

Cheng, Jun-Bo; Huang, Weizhang; Jiang, Song; Tian, Baolin

2017-11-01

A third-order moving mesh cell-centered scheme without the remapping of physical variables is developed for the numerical solution of one-dimensional elastic-plastic flows with the Mie-Grüneisen equation of state, the Wilkins constitutive model, and the von Mises yielding criterion. The scheme combines the Lagrangian method with the MMPDE moving mesh method and adaptively moves the mesh to better resolve shock and other types of waves while preventing the mesh from crossing and tangling. It can be viewed as a direct arbitrarily Lagrangian-Eulerian method but can also be degenerated to a purely Lagrangian scheme. It treats the relative velocity of the fluid with respect to the mesh as constant in time between time steps, which allows high-order approximation of free boundaries. A time dependent scaling is used in the monitor function to avoid possible sudden movement of the mesh points due to the creation or diminishing of shock and rarefaction waves or the steepening of those waves. A two-rarefaction Riemann solver with elastic waves is employed to compute the Godunov values of the density, pressure, velocity, and deviatoric stress at cell interfaces. Numerical results are presented for three examples. The third-order convergence of the scheme and its ability to concentrate mesh points around shock and elastic rarefaction waves are demonstrated. The obtained numerical results are in good agreement with those in literature. The new scheme is also shown to be more accurate in resolving shock and rarefaction waves than an existing third-order cell-centered Lagrangian scheme.

An efficient and provable secure revocable identity-based encryption scheme.

PubMed

Wang, Changji; Li, Yuan; Xia, Xiaonan; Zheng, Kangjia

2014-01-01

Revocation functionality is necessary and crucial to identity-based cryptosystems. Revocable identity-based encryption (RIBE) has attracted a lot of attention in recent years, many RIBE schemes have been proposed in the literature but shown to be either insecure or inefficient. In this paper, we propose a new scalable RIBE scheme with decryption key exposure resilience by combining Lewko and Waters' identity-based encryption scheme and complete subtree method, and prove our RIBE scheme to be semantically secure using dual system encryption methodology. Compared to existing scalable and semantically secure RIBE schemes, our proposed RIBE scheme is more efficient in term of ciphertext size, public parameters size and decryption cost at price of a little looser security reduction. To the best of our knowledge, this is the first construction of scalable and semantically secure RIBE scheme with constant size public system parameters.

Toward the Reliability of Fault Representation Methods in Finite Difference Schemes for Simulation of Shear Rupture Propagation

NASA Astrophysics Data System (ADS)

Dalguer, L. A.; Day, S. M.

2006-12-01

Accuracy in finite difference (FD) solutions to spontaneous rupture problems is controlled principally by the scheme used to represent the fault discontinuity, and not by the grid geometry used to represent the continuum. We have numerically tested three fault representation methods, the Thick Fault (TF) proposed by Madariaga et al (1998), the Stress Glut (SG) described by Andrews (1999), and the Staggered-Grid Split-Node (SGSN) methods proposed by Dalguer and Day (2006), each implemented in a the fourth-order velocity-stress staggered-grid (VSSG) FD scheme. The TF and the SG methods approximate the discontinuity through inelastic increments to stress components ("inelastic-zone" schemes) at a set of stress grid points taken to lie on the fault plane. With this type of scheme, the fault surface is indistinguishable from an inelastic zone with a thickness given by a spatial step dx for the SG, and 2dx for the TF model. The SGSN method uses the traction-at-split-node (TSN) approach adapted to the VSSG FD. This method represents the fault discontinuity by explicitly incorporating discontinuity terms at velocity nodes in the grid, with interactions between the "split nodes" occurring exclusively through the tractions (frictional resistance) acting between them. These tractions in turn are controlled by the jump conditions and a friction law. Our 3D tests problem solutions show that the inelastic-zone TF and SG methods show much poorer performance than does the SGSN formulation. The SG inelastic-zone method achieved solutions that are qualitatively meaningful and quantitatively reliable to within a few percent. The TF inelastic-zone method did not achieve qualitatively agreement with the reference solutions to the 3D test problem, and proved to be sufficiently computationally inefficient that it was not feasible to explore convergence quantitatively. The SGSN method gives very accurate solutions, and is also very efficient. Reliable solution of the rupture time is reached with a median resolution of the cohesive zone of only ~2 grid points, and efficiency is competitive with the Boundary Integral (BI) method. The results presented here demonstrate that appropriate fault representation in a numerical scheme is crucial to reduce uncertainties in numerical simulations of earthquake source dynamics and ground motion, and therefore important to improving our understanding of earthquake physics in general.

On Formulations of Discontinuous Galerkin and Related Methods for Conservation Laws

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2014-01-01

A formulation for the discontinuous Galerkin (DG) method that leads to solutions using the differential form of the equation (as opposed to the standard integral form) is presented. The formulation includes (a) a derivative calculation that involves only data within each cell with no data interaction among cells, and (b) for each cell, corrections to this derivative that deal with the jumps in fluxes at the cell boundaries and allow data across cells to interact. The derivative with no interaction is obtained by a projection, but for nodal-type methods, evaluating this derivative by interpolation at the nodal points is more economical. The corrections are derived using the approximate (Dirac) delta functions. The formulation results in a family of schemes: different approximate delta functions give rise to different methods. It is shown that the current formulation is essentially equivalent to the flux reconstruction (FR) formulation. Due to the use of approximate delta functions, an energy stability proof simpler than that of Vincent, Castonguay, and Jameson (2011) for a family of schemes is derived. Accuracy and stability of resulting schemes are discussed via Fourier analyses. Similar to FR, the current formulation provides a unifying framework for high-order methods by recovering the DG, spectral difference (SD), and spectral volume (SV) schemes. It also yields stable, accurate, and economical methods.

Evaluation of an Optimal Epidemiological Typing Scheme for Legionella pneumophila with Whole-Genome Sequence Data Using Validation Guidelines

PubMed Central

Mentasti, Massimo; Tewolde, Rediat; Aslett, Martin; Harris, Simon R.; Afshar, Baharak; Underwood, Anthony; Harrison, Timothy G.

2016-01-01

Sequence-based typing (SBT), analogous to multilocus sequence typing (MLST), is the current “gold standard” typing method for investigation of legionellosis outbreaks caused by Legionella pneumophila. However, as common sequence types (STs) cause many infections, some investigations remain unresolved. In this study, various whole-genome sequencing (WGS)-based methods were evaluated according to published guidelines, including (i) a single nucleotide polymorphism (SNP)-based method, (ii) extended MLST using different numbers of genes, (iii) determination of gene presence or absence, and (iv) a kmer-based method. L. pneumophila serogroup 1 isolates (n = 106) from the standard “typing panel,” previously used by the European Society for Clinical Microbiology Study Group on Legionella Infections (ESGLI), were tested together with another 229 isolates. Over 98% of isolates were considered typeable using the SNP- and kmer-based methods. Percentages of isolates with complete extended MLST profiles ranged from 99.1% (50 genes) to 86.8% (1,455 genes), while only 41.5% produced a full profile with the gene presence/absence scheme. Replicates demonstrated that all methods offer 100% reproducibility. Indices of discrimination range from 0.972 (ribosomal MLST) to 0.999 (SNP based), and all values were higher than that achieved with SBT (0.940). Epidemiological concordance is generally inversely related to discriminatory power. We propose that an extended MLST scheme with ∼50 genes provides optimal epidemiological concordance while substantially improving the discrimination offered by SBT and can be used as part of a hierarchical typing scheme that should maintain backwards compatibility and increase discrimination where necessary. This analysis will be useful for the ESGLI to design a scheme that has the potential to become the new gold standard typing method for L. pneumophila. PMID:27280420

Evaluation of an Optimal Epidemiological Typing Scheme for Legionella pneumophila with Whole-Genome Sequence Data Using Validation Guidelines.

PubMed

David, Sophia; Mentasti, Massimo; Tewolde, Rediat; Aslett, Martin; Harris, Simon R; Afshar, Baharak; Underwood, Anthony; Fry, Norman K; Parkhill, Julian; Harrison, Timothy G

2016-08-01

Sequence-based typing (SBT), analogous to multilocus sequence typing (MLST), is the current "gold standard" typing method for investigation of legionellosis outbreaks caused by Legionella pneumophila However, as common sequence types (STs) cause many infections, some investigations remain unresolved. In this study, various whole-genome sequencing (WGS)-based methods were evaluated according to published guidelines, including (i) a single nucleotide polymorphism (SNP)-based method, (ii) extended MLST using different numbers of genes, (iii) determination of gene presence or absence, and (iv) a kmer-based method. L. pneumophila serogroup 1 isolates (n = 106) from the standard "typing panel," previously used by the European Society for Clinical Microbiology Study Group on Legionella Infections (ESGLI), were tested together with another 229 isolates. Over 98% of isolates were considered typeable using the SNP- and kmer-based methods. Percentages of isolates with complete extended MLST profiles ranged from 99.1% (50 genes) to 86.8% (1,455 genes), while only 41.5% produced a full profile with the gene presence/absence scheme. Replicates demonstrated that all methods offer 100% reproducibility. Indices of discrimination range from 0.972 (ribosomal MLST) to 0.999 (SNP based), and all values were higher than that achieved with SBT (0.940). Epidemiological concordance is generally inversely related to discriminatory power. We propose that an extended MLST scheme with ∼50 genes provides optimal epidemiological concordance while substantially improving the discrimination offered by SBT and can be used as part of a hierarchical typing scheme that should maintain backwards compatibility and increase discrimination where necessary. This analysis will be useful for the ESGLI to design a scheme that has the potential to become the new gold standard typing method for L. pneumophila. Copyright © 2016 David et al.

A parameterized logarithmic image processing method with Laplacian of Gaussian filtering for lung nodule enhancement in chest radiographs.

PubMed

Chen, Sheng; Yao, Liping; Chen, Bao

2016-11-01

The enhancement of lung nodules in chest radiographs (CXRs) plays an important role in the manual as well as computer-aided detection (CADe) lung cancer. In this paper, we proposed a parameterized logarithmic image processing (PLIP) method combined with the Laplacian of a Gaussian (LoG) filter to enhance lung nodules in CXRs. We first applied several LoG filters with varying parameters to an original CXR to enhance the nodule-like structures as well as the edges in the image. We then applied the PLIP model, which can enhance lung nodule images with high contrast and was beneficial in extracting effective features for nodule detection in the CADe scheme. Our method combined the advantages of both the PLIP algorithm and the LoG algorithm, which can enhance lung nodules in chest radiographs with high contrast. To test our nodule enhancement method, we tested a CADe scheme, with a relatively high performance in nodule detection, using a publically available database containing 140 nodules in 140 CXRs enhanced through our nodule enhancement method. The CADe scheme attained a sensitivity of 81 and 70 % with an average of 5.0 frame rate (FP) and 2.0 FP, respectively, in a leave-one-out cross-validation test. By contrast, the CADe scheme based on the original image recorded a sensitivity of 77 and 63 % at 5.0 FP and 2.0 FP, respectively. We introduced the measurement of enhancement by entropy evaluation to objectively assess our method. Experimental results show that the proposed method obtains an effective enhancement of lung nodules in CXRs for both radiologists and CADe schemes.

Large scale Brownian dynamics of confined suspensions of rigid particles

NASA Astrophysics Data System (ADS)

Sprinkle, Brennan; Balboa Usabiaga, Florencio; Patankar, Neelesh A.; Donev, Aleksandar

2017-12-01

We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217-296 (2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can efficiently generate deterministic and random displacements for many particles using preconditioned Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and its "square" root are available for the given boundary conditions. These kernel operations can be computed with near linear scaling for periodic domains using the positively split Ewald method. Here we study particles partially confined by gravity above a no-slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector product, combined with a preconditioned Lanczos iteration for generating Brownian displacements. We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint scheme, our methods utilize random finite differences and do not require the solution of resistance problems or the computation of the action of the inverse square root of the RPY mobility matrix. We construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to be solved per time step while capturing the required stochastic drift terms. We validate and compare these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense suspensions of confined microrollers, whose height above the wall is set by a combination of thermal noise and active flows. We find the existence of two populations of active particles, slower ones closer to the bottom and faster ones above them, and demonstrate that our method provides quantitative accuracy even with relatively coarse resolutions of the particle geometry.

The Selection of Computed Tomography Scanning Schemes for Lengthy Symmetric Objects

NASA Astrophysics Data System (ADS)

Trinh, V. B.; Zhong, Y.; Osipov, S. P.

2017-04-01

. The article describes the basic computed tomography scan schemes for lengthy symmetric objects: continuous (discrete) rotation with a discrete linear movement; continuous (discrete) rotation with discrete linear movement to acquire 2D projection; continuous (discrete) linear movement with discrete rotation to acquire one-dimensional projection and continuous (discrete) rotation to acquire of 2D projection. The general method to calculate the scanning time is discussed in detail. It should be extracted the comparison principle to select a scanning scheme. This is because data are the same for all scanning schemes: the maximum energy of the X-ray radiation; the power of X-ray radiation source; the angle of the X-ray cone beam; the transverse dimension of a single detector; specified resolution and the maximum time, which is need to form one point of the original image and complies the number of registered photons). It demonstrates the possibilities of the above proposed method to compare the scanning schemes. Scanning object was a cylindrical object with the mass thickness is 4 g/cm2, the effective atomic number is 15 and length is 1300 mm. It analyzes data of scanning time and concludes about the efficiency of scanning schemes. It examines the productivity of all schemes and selects the effective one.

Comparison of Grouping Schemes for Exposure to Total Dust in Cement Factories in Korea.

PubMed

Koh, Dong-Hee; Kim, Tae-Woo; Jang, Seung Hee; Ryu, Hyang-Woo; Park, Donguk

2015-08-01

The purpose of this study was to evaluate grouping schemes for exposure to total dust in cement industry workers using non-repeated measurement data. In total, 2370 total dust measurements taken from nine Portland cement factories in 1995-2009 were analyzed. Various grouping schemes were generated based on work process, job, factory, or average exposure. To characterize variance components of each grouping scheme, we developed mixed-effects models with a B-spline time trend incorporated as fixed effects and a grouping variable incorporated as a random effect. Using the estimated variance components, elasticity was calculated. To compare the prediction performances of different grouping schemes, 10-fold cross-validation tests were conducted, and root mean squared errors and pooled correlation coefficients were calculated for each grouping scheme. The five exposure groups created a posteriori by ranking job and factory combinations according to average dust exposure showed the best prediction performance and highest elasticity among various grouping schemes. Our findings suggest a grouping method based on ranking of job, and factory combinations would be the optimal choice in this population. Our grouping method may aid exposure assessment efforts in similar occupational settings, minimizing the misclassification of exposures. © The Author 2015. Published by Oxford University Press on behalf of the British Occupational Hygiene Society.

Progress in multi-dimensional upwind differencing

NASA Technical Reports Server (NTRS)

Vanleer, Bram

1992-01-01

Multi-dimensional upwind-differencing schemes for the Euler equations are reviewed. On the basis of the first-order upwind scheme for a one-dimensional convection equation, the two approaches to upwind differencing are discussed: the fluctuation approach and the finite-volume approach. The usual extension of the finite-volume method to the multi-dimensional Euler equations is not entirely satisfactory, because the direction of wave propagation is always assumed to be normal to the cell faces. This leads to smearing of shock and shear waves when these are not grid-aligned. Multi-directional methods, in which upwind-biased fluxes are computed in a frame aligned with a dominant wave, overcome this problem, but at the expense of robustness. The same is true for the schemes incorporating a multi-dimensional wave model not based on multi-dimensional data but on an 'educated guess' of what they could be. The fluctuation approach offers the best possibilities for the development of genuinely multi-dimensional upwind schemes. Three building blocks are needed for such schemes: a wave model, a way to achieve conservation, and a compact convection scheme. Recent advances in each of these components are discussed; putting them all together is the present focus of a worldwide research effort. Some numerical results are presented, illustrating the potential of the new multi-dimensional schemes.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients.

PubMed

Saleem, M Rehan; Ashraf, Waqas; Zia, Saqib; Ali, Ishtiaq; Qamar, Shamsul

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

PubMed Central

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme. PMID:29851978

Development of upwind schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1987-01-01

Described are many algorithmic and computational aspects of upwind schemes and their second-order accurate formulations based on Total-Variation-Diminishing (TVD) approaches. An operational unification of the underlying first-order scheme is first presented encompassing Godunov's, Roe's, Osher's, and Split-Flux methods. For higher order versions, the preprocessing and postprocessing approaches to constructing TVD discretizations are considered. TVD formulations can be used to construct relaxation methods for unfactored implicit upwind schemes, which in turn can be exploited to construct space-marching procedures for even the unsteady Euler equations. A major part of the report describes time- and space-marching procedures for solving the Euler equations in 2-D, 3-D, Cartesian, and curvilinear coordinates. Along with many illustrative examples, several results of efficient computations on 3-D supersonic flows with subsonic pockets are presented.

Advanced lattice Boltzmann scheme for high-Reynolds-number magneto-hydrodynamic flows

NASA Astrophysics Data System (ADS)

De Rosis, Alessandro; Lévêque, Emmanuel; Chahine, Robert

2018-06-01

Is the lattice Boltzmann method suitable to investigate numerically high-Reynolds-number magneto-hydrodynamic (MHD) flows? It is shown that a standard approach based on the Bhatnagar-Gross-Krook (BGK) collision operator rapidly yields unstable simulations as the Reynolds number increases. In order to circumvent this limitation, it is here suggested to address the collision procedure in the space of central moments for the fluid dynamics. Therefore, an hybrid lattice Boltzmann scheme is introduced, which couples a central-moment scheme for the velocity with a BGK scheme for the space-and-time evolution of the magnetic field. This method outperforms the standard approach in terms of stability, allowing us to simulate high-Reynolds-number MHD flows with non-unitary Prandtl number while maintaining accuracy and physical consistency.

High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bran R. (Technical Monitor)

2002-01-01

We present high-order semi-discrete central-upwind numerical schemes for approximating solutions of multi-dimensional Hamilton-Jacobi (HJ) equations. This scheme is based on the use of fifth-order central interpolants like those developed in [1], in fluxes presented in [3]. These interpolants use the weighted essentially nonoscillatory (WENO) approach to avoid spurious oscillations near singularities, and become "central-upwind" in the semi-discrete limit. This scheme provides numerical approximations whose error is as much as an order of magnitude smaller than those in previous WENO-based fifth-order methods [2, 1]. Thee results are discussed via examples in one, two and three dimensions. We also pregnant explicit N-dimensional formulas for the fluxes, discuss their monotonicity and tl!e connection between this method and that in [2].

Unfolding energy spectra of double-periodicity two-dimensional systems: Twisted bilayer graphene and MoS2 on graphene

NASA Astrophysics Data System (ADS)

Matsushita, Yu-ichiro; Nishi, Hirofumi; Iwata, Jun-ichi; Kosugi, Taichi; Oshiyama, Atsushi

2018-01-01

We propose an unfolding scheme to analyze energy spectra of complex large-scale systems which are inherently of double periodicity on the basis of the density-functional theory. Applying our method to a twisted bilayer graphene (tBLG) and a stack of monolayer MoS2 on graphene (MoS2/graphene) as examples, we first show that the conventional unfolding scheme in the past using a single primitive-cell representation causes serious problems in analyses of the energy spectra. We then introduce our multispace representation scheme in the unfolding method and clarify its validity. Velocity renormalization of Dirac electrons in tBLG and mini gaps of Dirac cones in MoS2/graphene are elucidated in the present unfolding scheme.

A projection hybrid high order finite volume/finite element method for incompressible turbulent flows

NASA Astrophysics Data System (ADS)

Busto, S.; Ferrín, J. L.; Toro, E. F.; Vázquez-Cendón, M. E.

2018-01-01

In this paper the projection hybrid FV/FE method presented in [1] is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the k-ε model. Regarding the transport diffusion stage new schemes of high order of accuracy are developed. The CVC Kolgan-type scheme and ADER methodology are extended to 3D. The latter is modified in order to profit from the dual mesh employed by the projection algorithm and the derivatives involved in the diffusion term are discretized using a Galerkin approach. The accuracy and stability analysis of the new method are carried out for the advection-diffusion-reaction equation. Within the projection stage the pressure correction is computed by a piecewise linear finite element method. Numerical results are presented, aimed at verifying the formal order of accuracy of the scheme and to assess the performance of the method on several realistic test problems.

A shock-capturing SPH scheme based on adaptive kernel estimation

NASA Astrophysics Data System (ADS)

Sigalotti, Leonardo Di G.; López, Hender; Donoso, Arnaldo; Sira, Eloy; Klapp, Jaime

2006-02-01

Here we report a method that converts standard smoothed particle hydrodynamics (SPH) into a working shock-capturing scheme without relying on solutions to the Riemann problem. Unlike existing adaptive SPH simulations, the present scheme is based on an adaptive kernel estimation of the density, which combines intrinsic features of both the kernel and nearest neighbor approaches in a way that the amount of smoothing required in low-density regions is effectively controlled. Symmetrized SPH representations of the gas dynamic equations along with the usual kernel summation for the density are used to guarantee variational consistency. Implementation of the adaptive kernel estimation involves a very simple procedure and allows for a unique scheme that handles strong shocks and rarefactions the same way. Since it represents a general improvement of the integral interpolation on scattered data, it is also applicable to other fluid-dynamic models. When the method is applied to supersonic compressible flows with sharp discontinuities, as in the classical one-dimensional shock-tube problem and its variants, the accuracy of the results is comparable, and in most cases superior, to that obtained from high quality Godunov-type methods and SPH formulations based on Riemann solutions. The extension of the method to two- and three-space dimensions is straightforward. In particular, for the two-dimensional cylindrical Noh's shock implosion and Sedov point explosion problems the present scheme produces much better results than those obtained with conventional SPH codes.

Exact density functional and wave function embedding schemes based on orbital localization

NASA Astrophysics Data System (ADS)

Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály

2016-08-01

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roehm, Dominic; Pavel, Robert S.; Barros, Kipton

We present an adaptive sampling method supplemented by a distributed database and a prediction method for multiscale simulations using the Heterogeneous Multiscale Method. A finite-volume scheme integrates the macro-scale conservation laws for elastodynamics, which are closed by momentum and energy fluxes evaluated at the micro-scale. In the original approach, molecular dynamics (MD) simulations are launched for every macro-scale volume element. Our adaptive sampling scheme replaces a large fraction of costly micro-scale MD simulations with fast table lookup and prediction. The cloud database Redis provides the plain table lookup, and with locality aware hashing we gather input data for our predictionmore » scheme. For the latter we use kriging, which estimates an unknown value and its uncertainty (error) at a specific location in parameter space by using weighted averages of the neighboring points. We find that our adaptive scheme significantly improves simulation performance by a factor of 2.5 to 25, while retaining high accuracy for various choices of the algorithm parameters.« less

A strong shock tube problem calculated by different numerical schemes

NASA Astrophysics Data System (ADS)

Lee, Wen Ho; Clancy, Sean P.

1996-05-01

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

Operator splitting method for simulation of dynamic flows in natural gas pipeline networks

DOE PAGES

Dyachenko, Sergey A.; Zlotnik, Anatoly; Korotkevich, Alexander O.; ...

2017-09-19

Here, we develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme ismore » unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.« less

An atomistic simulation scheme for modeling crystal formation from solution.

PubMed

Kawska, Agnieszka; Brickmann, Jürgen; Kniep, Rüdiger; Hochrein, Oliver; Zahn, Dirk

2006-01-14

We present an atomistic simulation scheme for investigating crystal growth from solution. Molecular-dynamics simulation studies of such processes typically suffer from considerable limitations concerning both system size and simulation times. In our method this time-length scale problem is circumvented by an iterative scheme which combines a Monte Carlo-type approach for the identification of ion adsorption sites and, after each growth step, structural optimization of the ion cluster and the solvent by means of molecular-dynamics simulation runs. An important approximation of our method is based on assuming full structural relaxation of the aggregates between each of the growth steps. This concept only holds for compounds of low solubility. To illustrate our method we studied CaF2 aggregate growth from aqueous solution, which may be taken as prototypes for compounds of very low solubility. The limitations of our simulation scheme are illustrated by the example of NaCl aggregation from aqueous solution, which corresponds to a solute/solvent combination of very high salt solubility.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

New methods of multimode fiber interferometer signal processing

NASA Astrophysics Data System (ADS)

Vitrik, Oleg B.; Kulchin, Yuri N.; Maxaev, Oleg G.; Kirichenko, Oleg V.; Kamenev, Oleg T.; Petrov, Yuri S.

1995-06-01

New methods of multimode fiber interferometers signal processing are suggested. For scheme of single fiber multimode interferometers with two excited modes, the method based on using of special fiber unit is developed. This unit provides the modes interaction and further sum optical field filtering. As a result the amplitude of output signal is modulated by external influence on interferometer. The stabilization of interferometer sensitivity is achieved by using additional special modulation of output signal. For scheme of single fiber multimode interferometers with excitation of wide mode spectrum, the signal of intermode interference is registered by photodiode matrix and then special electronic unit performs correlation processing. For elimination of temperature destabilization, the registered signal is adopted to multimode interferometers optical signal temperature changes. The achieved parameters for double mode scheme: temporary stability--0.6% per hour, sensitivity to interferometer length deviations--3,2 nm; for multimode scheme: temperature stability--(0.5%)/(K), temporary nonstability--0.2% per hour, sensitivity to interferometer length deviations--20 nm, dynamic range--35 dB.

Generation and coherent detection of QPSK signal using a novel method of digital signal processing

NASA Astrophysics Data System (ADS)

Zhao, Yuan; Hu, Bingliang; He, Zhen-An; Xie, Wenjia; Gao, Xiaohui

2018-02-01

We demonstrate an optical quadrature phase-shift keying (QPSK) signal transmitter and an optical receiver for demodulating optical QPSK signal with homodyne detection and digital signal processing (DSP). DSP on the homodyne detection scheme is employed without locking the phase of the local oscillator (LO). In this paper, we present an extracting one-dimensional array of down-sampling method for reducing unwanted samples of constellation diagram measurement. Such a novel scheme embodies the following major advantages over the other conventional optical QPSK signal detection methods. First, this homodyne detection scheme does not need strict requirement on LO in comparison with linear optical sampling, such as having a flat spectral density and phase over the spectral support of the source under test. Second, the LabVIEW software is directly used for recovering the QPSK signal constellation without employing complex DSP circuit. Third, this scheme is applicable to multilevel modulation formats such as M-ary PSK and quadrature amplitude modulation (QAM) or higher speed signals by making minor changes.

Distributed database kriging for adaptive sampling (D²KAS)

DOE PAGES

Roehm, Dominic; Pavel, Robert S.; Barros, Kipton; ...

2015-03-18

We present an adaptive sampling method supplemented by a distributed database and a prediction method for multiscale simulations using the Heterogeneous Multiscale Method. A finite-volume scheme integrates the macro-scale conservation laws for elastodynamics, which are closed by momentum and energy fluxes evaluated at the micro-scale. In the original approach, molecular dynamics (MD) simulations are launched for every macro-scale volume element. Our adaptive sampling scheme replaces a large fraction of costly micro-scale MD simulations with fast table lookup and prediction. The cloud database Redis provides the plain table lookup, and with locality aware hashing we gather input data for our predictionmore » scheme. For the latter we use kriging, which estimates an unknown value and its uncertainty (error) at a specific location in parameter space by using weighted averages of the neighboring points. We find that our adaptive scheme significantly improves simulation performance by a factor of 2.5 to 25, while retaining high accuracy for various choices of the algorithm parameters.« less

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

NASA Astrophysics Data System (ADS)

Hâkansson, P.; Mella, M.; Bressanini, Dario; Morosi, Gabriele; Patrone, Marta

2006-11-01

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with Itô calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Itô calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.

Optical colour image watermarking based on phase-truncated linear canonical transform and image decomposition

NASA Astrophysics Data System (ADS)

Su, Yonggang; Tang, Chen; Li, Biyuan; Lei, Zhenkun

2018-05-01

This paper presents a novel optical colour image watermarking scheme based on phase-truncated linear canonical transform (PT-LCT) and image decomposition (ID). In this proposed scheme, a PT-LCT-based asymmetric cryptography is designed to encode the colour watermark into a noise-like pattern, and an ID-based multilevel embedding method is constructed to embed the encoded colour watermark into a colour host image. The PT-LCT-based asymmetric cryptography, which can be optically implemented by double random phase encoding with a quadratic phase system, can provide a higher security to resist various common cryptographic attacks. And the ID-based multilevel embedding method, which can be digitally implemented by a computer, can make the information of the colour watermark disperse better in the colour host image. The proposed colour image watermarking scheme possesses high security and can achieve a higher robustness while preserving the watermark’s invisibility. The good performance of the proposed scheme has been demonstrated by extensive experiments and comparison with other relevant schemes.

Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.

PubMed

Ran, Qiwen; Zhang, Haiying; Zhang, Jin; Tan, Liying; Ma, Jing

2009-06-01

Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process. (c) 2009 Optical Society of America.

A three dimensional multigrid multiblock multistage time stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa; Cannizzaro, Frank; Melson, N. D.

1991-01-01

A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.

Computing Evans functions numerically via boundary-value problems

NASA Astrophysics Data System (ADS)

Barker, Blake; Nguyen, Rose; Sandstede, Björn; Ventura, Nathaniel; Wahl, Colin

2018-03-01

The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been developed. In this paper, an alternative scheme for the numerical computation of Evans functions is presented that relies on an appropriate boundary-value problem formulation. Convergence of the algorithm is proved, and several examples, including the computation of eigenvalues for a multi-dimensional problem, are given. The main advantage of the scheme proposed here compared with earlier methods is that the scheme is linear and scalable to large problems.

Batch mode grid generation: An endangered species

NASA Technical Reports Server (NTRS)

Schuster, David M.

1992-01-01

Non-interactive grid generation schemes should thrive as emphasis shifts from development of numerical analysis and design methods to application of these tools to real engineering problems. A strong case is presented for the continued development and application of non-interactive geometry modeling methods. Guidelines, strategies, and techniques for developing and implementing these tools are presented using current non-interactive grid generation methods as examples. These schemes play an important role in the development of multidisciplinary analysis methods and some of these applications are also discussed.

A study of pressure-based methodology for resonant flows in non-linear combustion instabilities

NASA Technical Reports Server (NTRS)

Yang, H. Q.; Pindera, M. Z.; Przekwas, A. J.; Tucker, K.

1992-01-01

This paper presents a systematic assessment of a large variety of spatial and temporal differencing schemes on nonstaggered grids by the pressure-based methods for the problems of fast transient flows. The observation from the present study is that for steady state flow problems, pressure-based methods can be very competitive with the density-based methods. For transient flow problems, pressure-based methods utilizing the same differencing scheme are less accurate, even though the wave speeds are correctly predicted.

Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids

NASA Astrophysics Data System (ADS)

Lee, Euntaek; Ahn, Hyung Taek; Luo, Hong

2018-02-01

We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

What's in a Name? A Comparison of Methods for Classifying Predominant Type of Maltreatment

ERIC Educational Resources Information Center

Lau, A.S.; Leeb, R.T.; English, D.; Graham, J.C.; Briggs, E.C.; Brody, K.E.; Marshall, J.M.

2005-01-01

Objective:: The primary aim of the study was to identify a classification scheme, for determining the predominant type of maltreatment in a child's history that best predicts differences in developmental outcomes. Method:: Three different predominant type classification schemes were examined in a sample of 519 children with a history of alleged…

Development of Implicit Methods in CFD NASA Ames Research Center 1970's - 1980's

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.

2010-01-01

The focus here is on the early development (mid 1970's-1980's) at NASA Ames Research Center of implicit methods in Computational Fluid Dynamics (CFD). A class of implicit finite difference schemes of the Beam and Warming approximate factorization type will be addressed. The emphasis will be on the Euler equations. A review of material pertinent to the solution of the Euler equations within the framework of implicit methods will be presented. The eigensystem of the equations will be used extensively in developing a framework for various methods applied to the Euler equations. The development and analysis of various aspects of this class of schemes will be given along with the motivations behind many of the choices. Various acceleration and efficiency modifications such as matrix reduction, diagonalization and flux split schemes will be presented.

DNS of Flows over Periodic Hills using a Discontinuous-Galerkin Spectral-Element Method

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2014-01-01

Direct numerical simulation (DNS) of turbulent compressible flows is performed using a higher-order space-time discontinuous-Galerkin finite-element method. The numerical scheme is validated by performing DNS of the evolution of the Taylor-Green vortex and turbulent flow in a channel. The higher-order method is shown to provide increased accuracy relative to low-order methods at a given number of degrees of freedom. The turbulent flow over a periodic array of hills in a channel is simulated at Reynolds number 10,595 using an 8th-order scheme in space and a 4th-order scheme in time. These results are validated against previous large eddy simulation (LES) results. A preliminary analysis provides insight into how these detailed simulations can be used to improve Reynoldsaveraged Navier-Stokes (RANS) modeling

Error reduction program: A progress report

NASA Technical Reports Server (NTRS)

Syed, S. A.

1984-01-01

Five finite differences schemes were evaluated for minimum numerical diffusion in an effort to identify and incorporate the best error reduction scheme into a 3D combustor performance code. Based on this evaluated, two finite volume method schemes were selected for further study. Both the quadratic upstream differencing scheme (QUDS) and the bounded skew upstream differencing scheme two (BSUDS2) were coded into a two dimensional computer code and their accuracy and stability determined by running several test cases. It was found that BSUDS2 was more stable than QUDS. It was also found that the accuracy of both schemes is dependent on the angle that the streamline make with the mesh with QUDS being more accurate at smaller angles and BSUDS2 more accurate at larger angles. The BSUDS2 scheme was selected for extension into three dimensions.

Quality of Recovery Evaluation of the Protection Schemes for Fiber-Wireless Access Networks

NASA Astrophysics Data System (ADS)

Fu, Minglei; Chai, Zhicheng; Le, Zichun

2016-03-01

With the rapid development of fiber-wireless (FiWi) access network, the protection schemes have got more and more attention due to the risk of huge data loss when failures occur. However, there are few studies on the performance evaluation of the FiWi protection schemes by the unified evaluation criterion. In this paper, quality of recovery (QoR) method was adopted to evaluate the performance of three typical protection schemes (MPMC scheme, OBOF scheme and RPMF scheme) against the segment-level failure in FiWi access network. The QoR models of the three schemes were derived in terms of availability, quality of backup path, recovery time and redundancy. To compare the performance of the three protection schemes comprehensively, five different classes of network services such as emergency service, prioritized elastic service, conversational service, etc. were utilized by means of assigning different QoR weights. Simulation results showed that, for the most service cases, RPMF scheme was proved to be the best solution to enhance the survivability when planning the FiWi access network.

Research in computational fluid dynamics and analysis of algorithms

NASA Technical Reports Server (NTRS)

Gottlieb, David

1992-01-01

Recently, higher-order compact schemes have seen increasing use in the DNS (Direct Numerical Simulations) of the Navier-Stokes equations. Although they do not have the spatial resolution of spectral methods, they offer significant increases in accuracy over conventional second order methods. They can be used on any smooth grid, and do not have an overly restrictive CFL dependence as compared with the O(N(exp -2)) CFL dependence observed in Chebyshev spectral methods on finite domains. In addition, they are generally more robust and less costly than spectral methods. The issue of the relative cost of higher-order schemes (accuracy weighted against physical and numerical cost) is a far more complex issue, depending ultimately on what features of the solution are sought and how accurately they must be resolved. In any event, the further development of the underlying stability theory of these schemes is important. The approach of devising suitable boundary clusters and then testing them with various stability techniques (such as finding the norm) is entirely the wrong approach when dealing with high-order methods. Very seldom are high-order boundary closures stable, making them difficult to isolate. An alternative approach is to begin with a norm which satisfies all the stability criteria for the hyperbolic system, and look for the boundary closure forms which will match the norm exactly. This method was used recently by Strand to isolate stable boundary closure schemes for the explicit central fourth- and sixth-order schemes. The norm used was an energy norm mimicking the norm for the differential equations. Further research should be devoted to BC for high order schemes in order to make sure that the results obtained are reliable. The compact fourth order and sixth order finite difference scheme had been incorporated into a code to simulate flow past circular cylinders. This code will serve as a verification of the full spectral codes. A detailed stability analysis by Carpenter (from the fluid Mechanics Division) and Gottlieb gave analytic conditions for stability as well as asymptotic stability. This had been incorporated in the code in form of stable boundary conditions. Effects of the cylinder rotations had been studied. The results differ from the known theoretical results. We are in the middle of analyzing the results. A detailed analysis of the effects of the heating of the cylinder on the shedding frequency had been studied using the above schemes. It has been found that the shedding frequency decreases when the wire was heated. Experimental work is being carried out to affirm this result.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Stable and low diffusive hybrid upwind splitting methods

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1992-01-01

A new concept for upwinding is introduced, named the hybrid upwind splitting (HUS), which is achieved by combining the basically distinct flux vector splitting (FVS) and the flux difference splitting (FDS) approaches. The HUS approach yields upwind methods which share the robustness of the FVS schemes in the capture of nonlinear waves and the accuracy of some of the FDS schemes. Numerical illustrations are presented proving the relevance of the HUS methods for viscous calculations.

A numerical scheme to solve unstable boundary value problems

NASA Technical Reports Server (NTRS)

Kalnay Derivas, E.

1975-01-01

A new iterative scheme for solving boundary value problems is presented. It consists of the introduction of an artificial time dependence into a modified version of the system of equations. Then explicit forward integrations in time are followed by explicit integrations backwards in time. The method converges under much more general conditions than schemes based in forward time integrations (false transient schemes). In particular it can attain a steady state solution of an elliptical system of equations even if the solution is unstable, in which case other iterative schemes fail to converge. The simplicity of its use makes it attractive for solving large systems of nonlinear equations.

Design of algorithms for a dispersive hyperbolic problem

NASA Technical Reports Server (NTRS)

Roe, Philip L.; Arora, Mohit

1991-01-01

In order to develop numerical schemes for stiff problems, a model of relaxing heat flow is studied. To isolate those errors unavoidably associated with discretization, a method of characteristics is developed, containing three free parameters depending on the stiffness ratio. It is shown that such 'decoupled' schemes do not take into account the interaction between the wave families, and hence result in incorrect wavespeeds. Schemes can differ by up to two orders of magnitude in their rms errors, even while maintaining second-order accuracy. 'Coupled' schemes which account for the interactions are developed to obtain two additional free parameters. Numerical results are given for several decoupled and coupled schemes.

Method and apparatus for conversion of carbonaceous materials to liquid fuel

DOEpatents

Lux, Kenneth W.; Namazian, Mehdi; Kelly, John T.

2015-12-01

Embodiments of the invention relates to conversion of hydrocarbon material including but not limited to coal and biomass to a synthetic liquid transportation fuel. The invention includes the integration of a non-catalytic first reaction scheme, which converts carbonaceous materials into a solid product that includes char and ash and a gaseous product; a non-catalytic second reaction scheme, which converts a portion of the gaseous product from the first reaction scheme to light olefins and liquid byproducts; a traditional gas-cleanup operations; and the third reaction scheme to combine the olefins from the second reaction scheme to produce a targeted fuel like liquid transportation fuels.

The Nature of All "Inappropriate Referrals" Made to a Countywide Physical Activity Referral Scheme: Implications for Practice

ERIC Educational Resources Information Center

Johnston, Lynne Halley; Warwick, Jane; De Ste Croix, Mark; Crone, Diane; Sldford, Adrienne

2005-01-01

Objective: The aim of this study was to evaluate the impact of a centralised referral mechanism (CRM) upon the number and type of "inappropriate referrals" made to a countywide physical activity referral scheme. Design: Case study. Method: Phase 1: Hierarchical Content Analysis of 458 "inappropriate referrals" made to a countywide scheme over a…

Scheme for Implementing Teleporting an Arbitrary Tripartite Entangled State in Cavity QED

NASA Astrophysics Data System (ADS)

Wang, Xue-Wen; Peng, Zhao-Hui

2009-10-01

We propose to teleport an arbitrary tripartite entangled state in cavity QED. In this scheme, the five-qubit Brown state is chosen as the quantum channel. It has been shown that the teleportation protocol can be completed perfectly with two different measurement methods. In the future, our scheme might be realizable based on present experimental technology.

Quantum-secret-sharing scheme based on local distinguishability of orthogonal multiqudit entangled states

NASA Astrophysics Data System (ADS)

Wang, Jingtao; Li, Lixiang; Peng, Haipeng; Yang, Yixian

2017-02-01

In this study, we propose the concept of judgment space to investigate the quantum-secret-sharing scheme based on local distinguishability (called LOCC-QSS). Because of the proposing of this conception, the property of orthogonal mutiqudit entangled states under restricted local operation and classical communication (LOCC) can be described more clearly. According to these properties, we reveal that, in the previous (k ,n )-threshold LOCC-QSS scheme, there are two required conditions for the selected quantum states to resist the unambiguous attack: (i) their k -level judgment spaces are orthogonal, and (ii) their (k -1 )-level judgment spaces are equal. Practically, if k

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-07-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

An Orbit And Dispersion Correction Scheme for the PEP II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Y.; Donald, M.; Shoaee, H.

2011-09-01

To achieve optimum luminosity in a storage ring it is vital to control the residual vertical dispersion. In the original PEP storage ring, a scheme to control the residual dispersion function was implemented using the ring orbit as the controlling element. The 'best' orbit not necessarily giving the lowest vertical dispersion. A similar scheme has been implemented in both the on-line control code and in the simulation code LEGO. The method involves finding the response matrices (sensitivity of orbit/dispersion at each Beam-Position-Monitor (BPM) to each orbit corrector) and solving in a least squares sense for minimum orbit, dispersion function ormore » both. The optimum solution is usually a subset of the full least squares solution. A scheme of simultaneously correcting the orbits and dispersion has been implemented in the simulation code and on-line control system for PEP-II. The scheme is based on the eigenvector decomposition method. An important ingredient of the scheme is to choose the optimum eigenvectors that minimize the orbit, dispersion and corrector strength. Simulations indicate this to be a very effective way to control the vertical residual dispersion.« less

Chapman-Enskog Analyses on the Gray Lattice Boltzmann Equation Method for Fluid Flow in Porous Media

NASA Astrophysics Data System (ADS)

Chen, Chen; Li, Like; Mei, Renwei; Klausner, James F.

2018-03-01

The gray lattice Boltzmann equation (GLBE) method has recently been used to simulate fluid flow in porous media. It employs a partial bounce-back of populations (through a fractional coefficient θ, which represents the fraction of populations being reflected by the solid phase) in the evolution equation to account for the linear drag of the medium. Several particular GLBE schemes have been proposed in the literature and these schemes are very easy to implement; but there exists uncertainty about the need for redefining the macroscopic velocity as there has been no systematic analysis to recover the Brinkman equation from the various GLBE schemes. Rigorous Chapman-Enskog analyses are carried out to show that the momentum equation recovered from these schemes can satisfy Brinkman equation to second order in ɛ only if θ = O( ɛ ) in which ɛ is the ratio of the lattice spacing to the characteristic length of physical dimension. The need for redefining macroscopic velocity is shown to be scheme-dependent. When a body force is encountered such as the gravitational force or that caused by a pressure gradient, different forms of forcing redefinitions are required for each GLBE scheme.

Performance of Low Dissipative High Order Shock-Capturing Schemes for Shock-Turbulence Interactions

NASA Technical Reports Server (NTRS)

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

1998-01-01

Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

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.

Multigrid Acceleration of Time-Accurate DNS of Compressible Turbulent Flow

NASA Technical Reports Server (NTRS)

Broeze, Jan; Geurts, Bernard; Kuerten, Hans; Streng, Martin

1996-01-01

An efficient scheme for the direct numerical simulation of 3D transitional and developed turbulent flow is presented. Explicit and implicit time integration schemes for the compressible Navier-Stokes equations are compared. The nonlinear system resulting from the implicit time discretization is solved with an iterative method and accelerated by the application of a multigrid technique. Since we use central spatial discretizations and no artificial dissipation is added to the equations, the smoothing method is less effective than in the more traditional use of multigrid in steady-state calculations. Therefore, a special prolongation method is needed in order to obtain an effective multigrid method. This simulation scheme was studied in detail for compressible flow over a flat plate. In the laminar regime and in the first stages of turbulent flow the implicit method provides a speed-up of a factor 2 relative to the explicit method on a relatively coarse grid. At increased resolution this speed-up is enhanced correspondingly.

A class of high resolution explicit and implicit shock-capturing methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1989-01-01

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1991-01-01

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

Critical analysis of the Bennett-Riedel attack on secure cryptographic key distributions via the Kirchhoff-Law-Johnson-noise scheme.

PubMed

Kish, Laszlo B; Abbott, Derek; Granqvist, Claes G

2013-01-01

Recently, Bennett and Riedel (BR) (http://arxiv.org/abs/1303.7435v1) argued that thermodynamics is not essential in the Kirchhoff-law-Johnson-noise (KLJN) classical physical cryptographic exchange method in an effort to disprove the security of the KLJN scheme. They attempted to demonstrate this by introducing a dissipation-free deterministic key exchange method with two batteries and two switches. In the present paper, we first show that BR's scheme is unphysical and that some elements of its assumptions violate basic protocols of secure communication. All our analyses are based on a technically unlimited Eve with infinitely accurate and fast measurements limited only by the laws of physics and statistics. For non-ideal situations and at active (invasive) attacks, the uncertainly principle between measurement duration and statistical errors makes it impossible for Eve to extract the key regardless of the accuracy or speed of her measurements. To show that thermodynamics and noise are essential for the security, we crack the BR system with 100% success via passive attacks, in ten different ways, and demonstrate that the same cracking methods do not function for the KLJN scheme that employs Johnson noise to provide security underpinned by the Second Law of Thermodynamics. We also present a critical analysis of some other claims by BR; for example, we prove that their equations for describing zero security do not apply to the KLJN scheme. Finally we give mathematical security proofs for each BR-attack against the KLJN scheme and conclude that the information theoretic (unconditional) security of the KLJN method has not been successfully challenged.

Designing single- and multiple-shell sampling schemes for diffusion MRI using spherical code.

PubMed

Cheng, Jian; Shen, Dinggang; Yap, Pew-Thian

2014-01-01

In diffusion MRI (dMRI), determining an appropriate sampling scheme is crucial for acquiring the maximal amount of information for data reconstruction and analysis using the minimal amount of time. For single-shell acquisition, uniform sampling without directional preference is usually favored. To achieve this, a commonly used approach is the Electrostatic Energy Minimization (EEM) method introduced in dMRI by Jones et al. However, the electrostatic energy formulation in EEM is not directly related to the goal of optimal sampling-scheme design, i.e., achieving large angular separation between sampling points. A mathematically more natural approach is to consider the Spherical Code (SC) formulation, which aims to achieve uniform sampling by maximizing the minimal angular difference between sampling points on the unit sphere. Although SC is well studied in the mathematical literature, its current formulation is limited to a single shell and is not applicable to multiple shells. Moreover, SC, or more precisely continuous SC (CSC), currently can only be applied on the continuous unit sphere and hence cannot be used in situations where one or several subsets of sampling points need to be determined from an existing sampling scheme. In this case, discrete SC (DSC) is required. In this paper, we propose novel DSC and CSC methods for designing uniform single-/multi-shell sampling schemes. The DSC and CSC formulations are solved respectively by Mixed Integer Linear Programming (MILP) and a gradient descent approach. A fast greedy incremental solution is also provided for both DSC and CSC. To our knowledge, this is the first work to use SC formulation for designing sampling schemes in dMRI. Experimental results indicate that our methods obtain larger angular separation and better rotational invariance than the generalized EEM (gEEM) method currently used in the Human Connectome Project (HCP).

Critical Analysis of the Bennett–Riedel Attack on Secure Cryptographic Key Distributions via the Kirchhoff-Law–Johnson-Noise Scheme

PubMed Central

Kish, Laszlo B.; Abbott, Derek; Granqvist, Claes G.

2013-01-01

Recently, Bennett and Riedel (BR) (http://arxiv.org/abs/1303.7435v1) argued that thermodynamics is not essential in the Kirchhoff-law–Johnson-noise (KLJN) classical physical cryptographic exchange method in an effort to disprove the security of the KLJN scheme. They attempted to demonstrate this by introducing a dissipation-free deterministic key exchange method with two batteries and two switches. In the present paper, we first show that BR's scheme is unphysical and that some elements of its assumptions violate basic protocols of secure communication. All our analyses are based on a technically unlimited Eve with infinitely accurate and fast measurements limited only by the laws of physics and statistics. For non-ideal situations and at active (invasive) attacks, the uncertainly principle between measurement duration and statistical errors makes it impossible for Eve to extract the key regardless of the accuracy or speed of her measurements. To show that thermodynamics and noise are essential for the security, we crack the BR system with 100% success via passive attacks, in ten different ways, and demonstrate that the same cracking methods do not function for the KLJN scheme that employs Johnson noise to provide security underpinned by the Second Law of Thermodynamics. We also present a critical analysis of some other claims by BR; for example, we prove that their equations for describing zero security do not apply to the KLJN scheme. Finally we give mathematical security proofs for each BR-attack against the KLJN scheme and conclude that the information theoretic (unconditional) security of the KLJN method has not been successfully challenged. PMID:24358129

Influence diagnostics in meta-regression model.

PubMed

Shi, Lei; Zuo, ShanShan; Yu, Dalei; Zhou, Xiaohua

2017-09-01

This paper studies the influence diagnostics in meta-regression model including case deletion diagnostic and local influence analysis. We derive the subset deletion formulae for the estimation of regression coefficient and heterogeneity variance and obtain the corresponding influence measures. The DerSimonian and Laird estimation and maximum likelihood estimation methods in meta-regression are considered, respectively, to derive the results. Internal and external residual and leverage measure are defined. The local influence analysis based on case-weights perturbation scheme, responses perturbation scheme, covariate perturbation scheme, and within-variance perturbation scheme are explored. We introduce a method by simultaneous perturbing responses, covariate, and within-variance to obtain the local influence measure, which has an advantage of capable to compare the influence magnitude of influential studies from different perturbations. An example is used to illustrate the proposed methodology. Copyright © 2017 John Wiley & Sons, Ltd.

Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.

2004-01-01

A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.

A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri

2018-04-01

In this paper we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.

Comparative Study on High-Order Positivity-preserving WENO Schemes

NASA Technical Reports Server (NTRS)

Kotov, Dmitry V.; Yee, Helen M.; Sjogreen, Bjorn Axel

2013-01-01

The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more di cult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium ow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case (LeVeque & Yee 1990) as well as for the case consisting of two species and one reaction (Wang et al. 2012). For further information concerning this issue see (LeVeque & Yee 1990; Griffiths et al. 1992; Lafon & Yee 1996; Yee et al. 2012). This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

Nonlinear Aeroacoustics Computations by the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a recently developed numerical method for conservation laws. Despite its second order accuracy in space and time, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide range of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its truly multi-dimensional, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for computational aeroacoustics (CAA). In nature, the method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its careful treatment of the surface fluxes and geometry, it is different from the existing schemes. Currently, the CE/SE scheme has been developed to a matured stage that a 3-D unstructured CE/SE Navier-Stokes solver is already available. However, in the present review paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen and sketched in section 2. Then applications of the 2-D and 3-D CE/SE schemes to linear, and in particular, nonlinear aeroacoustics are depicted in sections 3, 4, and 5 to demonstrate its robustness and capability.

A gas kinetic scheme for hybrid simulation of partially rarefied flows

NASA Astrophysics Data System (ADS)

Colonia, S.; Steijl, R.; Barakos, G.

2017-06-01

Approaches to predict flow fields that display rarefaction effects incur a cost in computational time and memory considerably higher than methods commonly employed for continuum flows. For this reason, to simulate flow fields where continuum and rarefied regimes coexist, hybrid techniques have been introduced. In the present work, analytically defined gas-kinetic schemes based on the Shakhov and Rykov models for monoatomic and diatomic gas flows, respectively, are proposed and evaluated with the aim to be used in the context of hybrid simulations. This should reduce the region where more expensive methods are needed by extending the validity of the continuum formulation. Moreover, since for high-speed rare¦ed gas flows it is necessary to take into account the nonequilibrium among the internal degrees of freedom, the extension of the approach to employ diatomic gas models including rotational relaxation process is a mandatory first step towards realistic simulations. Compared to previous works of Xu and coworkers, the presented scheme is de¦ned directly on the basis of kinetic models which involve a Prandtl number correction. Moreover, the methods are defined fully analytically instead of making use of Taylor expansion for the evaluation of the required derivatives. The scheme has been tested for various test cases and Mach numbers proving to produce reliable predictions in agreement with other approaches for near-continuum flows. Finally, the performance of the scheme, in terms of memory and computational time, compared to discrete velocity methods makes it a compelling alternative in place of more complex methods for hybrid simulations of weakly rarefied flows.

A new method suitable for calculating accurately wetting temperature over a wide range of conditions: Based on the adaptation of continuation algorithm to classical DFT

NASA Astrophysics Data System (ADS)

Zhou, Shiqi

2017-11-01

A new scheme is put forward to determine the wetting temperature (Tw) by utilizing the adaptation of arc-length continuation algorithm to classical density functional theory (DFT) used originally by Frink and Salinger, and its advantages are summarized into four points: (i) the new scheme is applicable whether the wetting occurs near a planar or a non-planar surface, whereas a zero contact angle method is considered only applicable to a perfectly flat solid surface, as demonstrated previously and in this work, and essentially not fit for non-planar surface. (ii) The new scheme is devoid of an uncertainty, which plagues a pre-wetting extrapolation method and originates from an unattainability of the infinitely thick film in the theoretical calculation. (iii) The new scheme can be similarly and easily applied to extreme instances characterized by lower temperatures and/or higher surface attraction force field, which, however, can not be dealt with by the pre-wetting extrapolation method because of the pre-wetting transition being mixed with many layering transitions and the difficulty in differentiating varieties of the surface phase transitions. (iv) The new scheme still works in instance wherein the wetting transition occurs close to the bulk critical temperature; however, this case completely can not be managed by the pre-wetting extrapolation method because near the bulk critical temperature the pre-wetting region is extremely narrow, and no enough pre-wetting data are available for use of the extrapolation procedure.

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

NASA Technical Reports Server (NTRS)

Helenbrook, B. T.; Atkins, H. L.

2006-01-01

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

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.

Parametrization of Combined Quantum Mechanical and Molecular Mechanical Methods: Bond-Tuned Link Atoms.

PubMed

Wu, Xin-Ping; Gagliardi, Laura; Truhlar, Donald G

2018-05-30

Combined quantum mechanical and molecular mechanical (QM/MM) methods are the most powerful available methods for high-level treatments of subsystems of very large systems. The treatment of the QM-MM boundary strongly affects the accuracy of QM/MM calculations. For QM/MM calculations having covalent bonds cut by the QM-MM boundary, it has been proposed previously to use a scheme with system-specific tuned fluorine link atoms. Here, we propose a broadly parametrized scheme where the parameters of the tuned F link atoms depend only on the type of bond being cut. In the proposed new scheme, the F link atom is tuned for systems with a certain type of cut bond at the QM-MM boundary instead of for a specific target system, and the resulting link atoms are call bond-tuned link atoms. In principle, the bond-tuned link atoms can be as convenient as the popular H link atoms, and they are especially well adapted for high-throughput and accurate QM/MM calculations. Here, we present the parameters for several kinds of cut bonds along with a set of validation calculations that confirm that the proposed bond-tuned link-atom scheme can be as accurate as the system-specific tuned F link-atom scheme.

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

NASA Astrophysics Data System (ADS)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

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.

Projecting future precipitation and temperature at sites with diverse climate through multiple statistical downscaling schemes

NASA Astrophysics Data System (ADS)

Vallam, P.; Qin, X. S.

2017-10-01

Anthropogenic-driven climate change would affect the global ecosystem and is becoming a world-wide concern. Numerous studies have been undertaken to determine the future trends of meteorological variables at different scales. Despite these studies, there remains significant uncertainty in the prediction of future climates. To examine the uncertainty arising from using different schemes to downscale the meteorological variables for the future horizons, projections from different statistical downscaling schemes were examined. These schemes included statistical downscaling method (SDSM), change factor incorporated with LARS-WG, and bias corrected disaggregation (BCD) method. Global circulation models (GCMs) based on CMIP3 (HadCM3) and CMIP5 (CanESM2) were utilized to perturb the changes in the future climate. Five study sites (i.e., Alice Springs, Edmonton, Frankfurt, Miami, and Singapore) with diverse climatic conditions were chosen for examining the spatial variability of applying various statistical downscaling schemes. The study results indicated that the regions experiencing heavy precipitation intensities were most likely to demonstrate the divergence between the predictions from various statistical downscaling methods. Also, the variance computed in projecting the weather extremes indicated the uncertainty derived from selection of downscaling tools and climate models. This study could help gain an improved understanding about the features of different downscaling approaches and the overall downscaling uncertainty.

A pseudospectra-based approach to non-normal stability of embedded boundary methods

NASA Astrophysics Data System (ADS)

Rapaka, Narsimha; Samtaney, Ravi

2017-11-01

We present non-normal linear stability of embedded boundary (EB) methods employing pseudospectra and resolvent norms. Stability of the discrete linear wave equation is characterized in terms of the normalized distance of the EB to the nearest ghost node (α) in one and two dimensions. An important objective is that the CFL condition based on the Cartesian grid spacing remains unaffected by the EB. We consider various discretization methods including both central and upwind-biased schemes. Stability is guaranteed when α <=αmax ranges between 0.5 and 0.77 depending on the discretization scheme. Also, the stability characteristics remain the same in both one and two dimensions. Sharper limits on the sufficient conditions for stability are obtained based on the pseudospectral radius (the Kreiss constant) than the restrictive limits based on the usual singular value decomposition analysis. We present a simple and robust reclassification scheme for the ghost cells (``hybrid ghost cells'') to ensure Lax stability of the discrete systems. This has been tested successfully for both low and high order discretization schemes with transient growth of at most O (1). Moreover, we present a stable, fourth order EB reconstruction scheme. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1394-01.

Multicomponent-flow analyses by multimode method of characteristics

USGS Publications Warehouse

Lai, Chintu

1994-01-01

For unsteady open-channel flows having N interacting unknown variables, a system of N mutually independent, partial differential equations can be used to describe the flow-field. The system generally belongs to marching-type problems and permits transformation into characteristic equations that are associated with N distinct characteristics directions. Because characteristics can be considered 'wave' or 'disturbance' propagation, a fluvial system so described can be viewed as adequately definable using these N component waves. A numerical algorithm to solve the N families of characteristics can then be introduced for formulation of an N-component flow-simulation model. The multimode method of characteristics (MMOC), a new numerical scheme that has a combined capacity of several specified-time-interval (STI) schemes of the method of characteristics, makes numerical modeling of such N-component riverine flows feasible and attainable. Merging different STI schemes yields different kinds of MMOC schemes, for which two kinds are displayed herein. With the MMOC, each characteristics is dynamically treated by an appropriate numerical mode, which should lead to an effective and suitable global simulation, covering various types of unsteady flow. The scheme is always linearly stable and its numerical accuracy can be systematically analyzed. By increasing the N value, one can develop a progressively sophisticated model that addresses increasingly complex river-mechanics problems.

Unconditionally stable, second-order accurate schemes for solid state phase transformations driven by mechano-chemical spinodal decomposition

DOE PAGES

Sagiyama, Koki; Rudraraju, Shiva; Garikipati, Krishna

2016-09-13

Here, we consider solid state phase transformations that are caused by free energy densities with domains of non-convexity in strain-composition space; we refer to the non-convex domains as mechano-chemical spinodals. The non-convexity with respect to composition and strain causes segregation into phases with different crystal structures. We work on an existing model that couples the classical Cahn-Hilliard model with Toupin’s theory of gradient elasticity at finite strains. Both systems are represented by fourth-order, nonlinear, partial differential equations. The goal of this work is to develop unconditionally stable, second-order accurate time-integration schemes, motivated by the need to carry out large scalemore » computations of dynamically evolving microstructures in three dimensions. We also introduce reduced formulations naturally derived from these proposed schemes for faster computations that are still second-order accurate. Although our method is developed and analyzed here for a specific class of mechano-chemical problems, one can readily apply the same method to develop unconditionally stable, second-order accurate schemes for any problems for which free energy density functions are multivariate polynomials of solution components and component gradients. Apart from an analysis and construction of methods, we present a suite of numerical results that demonstrate the schemes in action.« less

External quality assurance as a revalidation method for pathologists in pediatric histopathology: Comparison of four international programs

PubMed Central

Sergi, Consolato; Mikuz, Gregor

2008-01-01

Aim External quality assurance (EQA) is an extremely valuable resource for clinical pathologists to maintain high standards, improve diagnostic skills, and possibly revalidate medical license. The aim of this study was to participate in and compare four international slide survey programs (UK, IAP-Germany, USA-Canada, Australasia) in pediatric histopathology for clinical pathologists with the aim to use it as a revalidation method. Methods The following parameters were evaluated: number of circulations per year, number of slides, membership requirement, proof of significant pediatric pathology work, open to overseas participants, laboratory accreditation, issue of continuing professional development certificates and credits, slides discussion meeting, use of digital images, substandard performance letter, and anonymity of responses. Results The UK scheme, which has sampling procedure over several time frames (2 circulations/year, 30 slides), partial confidentiality, and multiple sources of data and assessors, can be used as a model for revalidation. The US-Canadian and Australasian schemes only partially fulfill the revalidation requirements. The IAP scheme appears to be essentially an educational program and may be unsuitable for revalidation. Conclusion The purposes and programs of EQA schemes vary worldwide. In order for it to be used for revalidation, it is advisable that EQA schemes are immediately unified. PMID:19014480

Selectively strippable paint schemes

NASA Astrophysics Data System (ADS)

Stein, R.; Thumm, D.; Blackford, Roger W.

1993-03-01

In order to meet the requirements of more environmentally acceptable paint stripping processes many different removal methods are under evaluation. These new processes can be divided into mechanical and chemical methods. ICI has developed a paint scheme with intermediate coat and fluid resistant polyurethane topcoat which can be stripped chemically in a short period of time with methylene chloride free and phenol free paint strippers.

Accurate Adaptive Level Set Method and Sharpening Technique for Three Dimensional Deforming Interfaces

NASA Technical Reports Server (NTRS)

Kim, Hyoungin; Liou, Meng-Sing

2011-01-01

In this paper, we demonstrate improved accuracy of the level set method for resolving deforming interfaces by proposing two key elements: (1) accurate level set solutions on adapted Cartesian grids by judiciously choosing interpolation polynomials in regions of different grid levels and (2) enhanced reinitialization by an interface sharpening procedure. The level set equation is solved using a fifth order WENO scheme or a second order central differencing scheme depending on availability of uniform stencils at each grid point. Grid adaptation criteria are determined so that the Hamiltonian functions at nodes adjacent to interfaces are always calculated by the fifth order WENO scheme. This selective usage between the fifth order WENO and second order central differencing schemes is confirmed to give more accurate results compared to those in literature for standard test problems. In order to further improve accuracy especially near thin filaments, we suggest an artificial sharpening method, which is in a similar form with the conventional re-initialization method but utilizes sign of curvature instead of sign of the level set function. Consequently, volume loss due to numerical dissipation on thin filaments is remarkably reduced for the test problems

Rapid Parameterization Schemes for Aircraft Shape Optimization

NASA Technical Reports Server (NTRS)

Li, Wu

2012-01-01

A rapid shape parameterization tool called PROTEUS is developed for aircraft shape optimization. This tool can be applied directly to any aircraft geometry that has been defined in PLOT3D format, with the restriction that each aircraft component must be defined by only one data block. PROTEUS has eight types of parameterization schemes: planform, wing surface, twist, body surface, body scaling, body camber line, shifting/scaling, and linear morphing. These parametric schemes can be applied to two types of components: wing-type surfaces (e.g., wing, canard, horizontal tail, vertical tail, and pylon) and body-type surfaces (e.g., fuselage, pod, and nacelle). These schemes permit the easy setup of commonly used shape modification methods, and each customized parametric scheme can be applied to the same type of component for any configuration. This paper explains the mathematics for these parametric schemes and uses two supersonic configurations to demonstrate the application of these schemes.

A two-stage spectrum sensing scheme based on energy detection and a novel multitaper method

NASA Astrophysics Data System (ADS)

Qi, Pei-Han; Li, Zan; Si, Jiang-Bo; Xiong, Tian-Yi

2015-04-01

Wideband spectrum sensing has drawn much attention in recent years since it provides more opportunities to the secondary users. However, wideband spectrum sensing requires a long time and a complex mechanism at the sensing terminal. A two-stage wideband spectrum sensing scheme is considered to proceed spectrum sensing with low time consumption and high performance to tackle this predicament. In this scheme, a novel multitaper spectrum sensing (MSS) method is proposed to mitigate the poor performance of energy detection (ED) in the low signal-to-noise ratio (SNR) region. The closed-form expression of the decision threshold is derived based on the Neyman-Pearson criterion and the probability of detection in the Rayleigh fading channel is analyzed. An optimization problem is formulated to maximize the probability of detection of the proposed two-stage scheme and the average sensing time of the two-stage scheme is analyzed. Numerical results validate the efficiency of MSS and show that the two-stage spectrum sensing scheme enjoys higher performance in the low SNR region and lower time cost in the high SNR region than the single-stage scheme. Project supported by the National Natural Science Foundation of China (Grant No. 61301179), the China Postdoctoral Science Foundation (Grant No. 2014M550479), and the Doctorial Programs Foundation of the Ministry of Education, China (Grant No. 20110203110011).

A Higher Order Iterative Method for Computing the Drazin Inverse

PubMed Central

Soleymani, F.; Stanimirović, Predrag S.

2013-01-01

A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper. PMID:24222747

Finite difference methods for reducing numerical diffusion in TEACH-type calculations. [Teaching Elliptic Axisymmetric Characteristics Heuristically

NASA Technical Reports Server (NTRS)

Syed, S. A.; Chiappetta, L. M.

1985-01-01

A methodological evaluation for two-finite differencing schemes for computer-aided gas turbine design is presented. The two computational schemes include; a Bounded Skewed Finite Differencing Scheme (BSUDS); and a Quadratic Upwind Differencing Scheme (QSDS). In the evaluation, the derivations of the schemes were incorporated into two-dimensional and three-dimensional versions of the Teaching Axisymmetric Characteristics Heuristically (TEACH) computer code. Assessments were made according to performance criteria for the solution of problems of turbulent, laminar, and coannular turbulent flow. The specific performance criteria used in the evaluation were simplicity, accuracy, and computational economy. It is found that the BSUDS scheme performed better with respect to the criteria than the QUDS. Some of the reasons for the more successful performance BSUDS are discussed.

Importance sampling variance reduction for the Fokker–Planck rarefied gas particle method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Collyer, B.S., E-mail: benjamin.collyer@gmail.com; London Mathematical Laboratory, 14 Buckingham Street, London WC2N 6DF; Connaughton, C.

The Fokker–Planck approximation to the Boltzmann equation, solved numerically by stochastic particle schemes, is used to provide estimates for rarefied gas flows. This paper presents a variance reduction technique for a stochastic particle method that is able to greatly reduce the uncertainty of the estimated flow fields when the characteristic speed of the flow is small in comparison to the thermal velocity of the gas. The method relies on importance sampling, requiring minimal changes to the basic stochastic particle scheme. We test the importance sampling scheme on a homogeneous relaxation, planar Couette flow and a lid-driven-cavity flow, and find thatmore » our method is able to greatly reduce the noise of estimated quantities. Significantly, we find that as the characteristic speed of the flow decreases, the variance of the noisy estimators becomes independent of the characteristic speed.« less

Supersonic nonlinear potential analysis

NASA Technical Reports Server (NTRS)

Siclari, M. J.

1984-01-01

The NCOREL computer code was established to compute supersonic flow fields of wings and bodies. The method encompasses an implicit finite difference transonic relaxation method to solve the full potential equation in a spherical coordinate system. Two basic topic to broaden the applicability and usefulness of the present method which is encompassed within the computer code NCOREL for the treatment of supersonic flow problems were studied. The first topic is that of computing efficiency. Accelerated schemes are in use for transonic flow problems. One such scheme is the approximate factorization (AF) method and an AF scheme to the supersonic flow problem is developed. The second topic is the computation of wake flows. The proper modeling of wake flows is important for multicomponent configurations such as wing-body and multiple lifting surfaces where the wake of one lifting surface has a pronounced effect on a downstream body or other lifting surfaces.

A novel Kalman filter based video image processing scheme for two-photon fluorescence microscopy

NASA Astrophysics Data System (ADS)

Sun, Wenqing; Huang, Xia; Li, Chunqiang; Xiao, Chuan; Qian, Wei

2016-03-01

Two-photon fluorescence microscopy (TPFM) is a perfect optical imaging equipment to monitor the interaction between fast moving viruses and hosts. However, due to strong unavoidable background noises from the culture, videos obtained by this technique are too noisy to elaborate this fast infection process without video image processing. In this study, we developed a novel scheme to eliminate background noises, recover background bacteria images and improve video qualities. In our scheme, we modified and implemented the following methods for both host and virus videos: correlation method, round identification method, tree-structured nonlinear filters, Kalman filters, and cell tracking method. After these procedures, most of noises were eliminated and host images were recovered with their moving directions and speed highlighted in the videos. From the analysis of the processed videos, 93% bacteria and 98% viruses were correctly detected in each frame on average.

Computational plasticity algorithm for particle dynamics simulations

NASA Astrophysics Data System (ADS)

Krabbenhoft, K.; Lyamin, A. V.; Vignes, C.

2018-01-01

The problem of particle dynamics simulation is interpreted in the framework of computational plasticity leading to an algorithm which is mathematically indistinguishable from the common implicit scheme widely used in the finite element analysis of elastoplastic boundary value problems. This algorithm provides somewhat of a unification of two particle methods, the discrete element method and the contact dynamics method, which usually are thought of as being quite disparate. In particular, it is shown that the former appears as the special case where the time stepping is explicit while the use of implicit time stepping leads to the kind of schemes usually labelled contact dynamics methods. The framing of particle dynamics simulation within computational plasticity paves the way for new approaches similar (or identical) to those frequently employed in nonlinear finite element analysis. These include mixed implicit-explicit time stepping, dynamic relaxation and domain decomposition schemes.

Electronic excitation of molecules in solution calculated using the symmetry-adapted cluster–configuration interaction method in the polarizable continuum model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fukuda, Ryoichi, E-mail: fukuda@ims.ac.jp; Ehara, Masahiro; Elements Strategy Initiative for Catalysts and Batteries

2015-12-31

The effects from solvent environment are specific to the electronic states; therefore, a computational scheme for solvent effects consistent with the electronic states is necessary to discuss electronic excitation of molecules in solution. The PCM (polarizable continuum model) SAC (symmetry-adapted cluster) and SAC-CI (configuration interaction) methods are developed for such purposes. The PCM SAC-CI adopts the state-specific (SS) solvation scheme where solvent effects are self-consistently considered for every ground and excited states. For efficient computations of many excited states, we develop a perturbative approximation for the PCM SAC-CI method, which is called corrected linear response (cLR) scheme. Our test calculationsmore » show that the cLR PCM SAC-CI is a very good approximation of the SS PCM SAC-CI method for polar and nonpolar solvents.« less

A novel evaluation method for building construction project based on integrated information entropy with reliability theory.

PubMed

Bai, Xiao-ping; Zhang, Xi-wei

2013-01-01

Selecting construction schemes of the building engineering project is a complex multiobjective optimization decision process, in which many indexes need to be selected to find the optimum scheme. Aiming at this problem, this paper selects cost, progress, quality, and safety as the four first-order evaluation indexes, uses the quantitative method for the cost index, uses integrated qualitative and quantitative methodologies for progress, quality, and safety indexes, and integrates engineering economics, reliability theories, and information entropy theory to present a new evaluation method for building construction project. Combined with a practical case, this paper also presents detailed computing processes and steps, including selecting all order indexes, establishing the index matrix, computing score values of all order indexes, computing the synthesis score, sorting all selected schemes, and making analysis and decision. Presented method can offer valuable references for risk computing of building construction projects.

A joint tracking method for NSCC based on WLS algorithm

NASA Astrophysics Data System (ADS)

Luo, Ruidan; Xu, Ying; Yuan, Hong

2017-12-01

Navigation signal based on compound carrier (NSCC), has the flexible multi-carrier scheme and various scheme parameters configuration, which enables it to possess significant efficiency of navigation augmentation in terms of spectral efficiency, tracking accuracy, multipath mitigation capability and anti-jamming reduction compared with legacy navigation signals. Meanwhile, the typical scheme characteristics can provide auxiliary information for signal synchronism algorithm design. This paper, based on the characteristics of NSCC, proposed a kind of joint tracking method utilizing Weighted Least Square (WLS) algorithm. In this method, the LS algorithm is employed to jointly estimate each sub-carrier frequency shift with the frequency-Doppler linear relationship, by utilizing the known sub-carrier frequency. Besides, the weighting matrix is set adaptively according to the sub-carrier power to ensure the estimation accuracy. Both the theory analysis and simulation results illustrate that the tracking accuracy and sensitivity of this method outperforms the single-carrier algorithm with lower SNR.

A new uniformly valid asymptotic integration algorithm for elasto-plastic creep and unified viscoplastic theories including continuum damage

NASA Technical Reports Server (NTRS)

Chulya, Abhisak; Walker, Kevin P.

1991-01-01

A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.

A new uniformly valid asymptotic integration algorithm for elasto-plastic-creep and unified viscoplastic theories including continuum damage

NASA Technical Reports Server (NTRS)

Chulya, A.; Walker, K. P.

1989-01-01

A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.

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

NASA Astrophysics Data System (ADS)

Jiang, Jiamin; Younis, Rami M.

2017-10-01

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

Introducing the MIT Regional Climate Model (MRCM)

NASA Astrophysics Data System (ADS)

Eltahir, Elfatih A. B.; Winter, Jonathn M.; Marcella, Marc P.; Gianotti, Rebecca L.; Im, Eun-Soon

2013-04-01

During the last decade researchers at MIT have worked on improving the skill of Regional Climate Model version 3 (RegCM3) in simulating climate over different regions through the incorporation of new physical schemes or modification of original schemes. The MIT Regional Climate Model (MRCM) features several modifications over RegCM3 including coupling of Integrated Biosphere Simulator (IBIS), a new surface albedo assignment method, a new convective cloud and rainfall auto-conversion scheme, and a modified boundary layer height and cloud scheme. Here, we introduce the MRCM and briefly describe the major model modifications relative to RegCM3 and their impact on the model performance. The most significant difference relative to the RegCM3 original configuration is coupling the Integrated Biosphere Simulator (IBIS) land-surface scheme (Winter et al., 2009). Based on the simulations using IBIS over the North America, the Maritime Continent, Southwest Asia and West Africa, we demonstrate that the use of IBIS as the land surface scheme results in better representation of surface energy and water budgets in comparison to BATS. Furthermore, the addition of a new irrigation scheme to IBIS makes it possible to investigate the effects of irrigation over any region. Also a new surface albedo assignment method used together with IBIS brings further improvement in simulations of surface radiation (Marcella and Eltahir, 2013). Another important feature of the MRCM is the introduction of a new convective cloud and rainfall auto-conversion scheme (Gianotti and Eltahir, 2013). This modification brings more physical realism into an important component of the model, and succeeds in simulating convective-radiative feedback improving model performance across several radiation fields and rainfall characteristics. Other features of MRCM such as the modified boundary layer height and cloud scheme, and the improvements in the dust emission and transport representations will be discussed.

Cheating prevention in visual cryptography.

PubMed

Hu, Chih-Ming; Tzeng, Wen-Guey

2007-01-01

Visual cryptography (VC) is a method of encrypting a secret image into shares such that stacking a sufficient number of shares reveals the secret image. Shares are usually presented in transparencies. Each participant holds a transparency. Most of the previous research work on VC focuses on improving two parameters: pixel expansion and contrast. In this paper, we studied the cheating problem in VC and extended VC. We considered the attacks of malicious adversaries who may deviate from the scheme in any way. We presented three cheating methods and applied them on attacking existent VC or extended VC schemes. We improved one cheat-preventing scheme. We proposed a generic method that converts a VCS to another VCS that has the property of cheating prevention. The overhead of the conversion is near optimal in both contrast degression and pixel expansion.

Performance analysis of cross-seeding WDM-PON system using transfer matrix method

NASA Astrophysics Data System (ADS)

Simatupang, Joni Welman; Pukhrambam, Puspa Devi; Huang, Yen-Ru

2016-12-01

In this paper, a model based on the transfer matrix method is adopted to analyze the effects of Rayleigh backscattering and Fresnel multiple reflections on a cross-seeding WDM-PON system. As part of analytical approximation methods, this time-independent model is quite simple but very efficient when it is applied to various WDM-PON transmission systems, including the cross-seeding scheme. The cross seeding scheme is most beneficial for systems with low loop-back ONU gain or low reflection loss at the drop fiber for upstream data in bidirectional transmission. However for downstream data transmission, multiple reflections power could destroy the usefulness of the cross-seeding scheme when the reflectivity is high enough and the RN is positioned near OLT or close to ONU.

Using an interference spectrum as a short-range absolute rangefinder with fiber and wideband source

NASA Astrophysics Data System (ADS)

Hsieh, Tsung-Han; Han, Pin

2018-06-01

Recently, a new type of displacement instrument using spectral-interference has been found, which utilizes fiber and a wideband light source to produce an interference spectrum. In this work, we develop a method that measures the absolute air-gap distance by taking wavelengths at two interference spectra minima. The experimental results agree with the theoretical calculations. It is also utilized to produce and control the spectral switch, which is much easier than other previous methods using other control mechanisms. A scanning mode of this scheme for stepped surface measurement is suggested, which is verified by a standard thickness gauge test. Our scheme is different to one available on the market that may use a curve-fitting method, and some comparisons are made between our scheme and that one.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

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

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

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

DUAL STATE-PARAMETER UPDATING SCHEME ON A CONCEPTUAL HYDROLOGIC MODEL USING SEQUENTIAL MONTE CARLO FILTERS

NASA Astrophysics Data System (ADS)

Noh, Seong Jin; Tachikawa, Yasuto; Shiiba, Michiharu; Kim, Sunmin

Applications of data assimilation techniques have been widely used to improve upon the predictability of hydrologic modeling. Among various data assimilation techniques, sequential Monte Carlo (SMC) filters, known as "particle filters" provide the capability to handle non-linear and non-Gaussian state-space models. This paper proposes a dual state-parameter updating scheme (DUS) based on SMC methods to estimate both state and parameter variables of a hydrologic model. We introduce a kernel smoothing method for the robust estimation of uncertain model parameters in the DUS. The applicability of the dual updating scheme is illustrated using the implementation of the storage function model on a middle-sized Japanese catchment. We also compare performance results of DUS combined with various SMC methods, such as SIR, ASIR and RPF.

Evaluation of the impact of observations on blended sea surface winds in a two-dimensional variational scheme using degrees of freedom

NASA Astrophysics Data System (ADS)

Wang, Ting; Xiang, Jie; Fei, Jianfang; Wang, Yi; Liu, Chunxia; Li, Yuanxiang

2017-12-01

This paper presents an evaluation of the observational impacts on blended sea surface winds from a two-dimensional variational data assimilation (2D-Var) scheme. We begin by briefly introducing the analysis sensitivity with respect to observations in variational data assimilation systems and its relationship with the degrees of freedom for signal (DFS), and then the DFS concept is applied to the 2D-Var sea surface wind blending scheme. Two methods, a priori and a posteriori, are used to estimate the DFS of the zonal ( u) and meridional ( v) components of winds in the 2D-Var blending scheme. The a posteriori method can obtain almost the same results as the a priori method. Because only by-products of the blending scheme are used for the a posteriori method, the computation time is reduced significantly. The magnitude of the DFS is critically related to the observational and background error statistics. Changing the observational and background error variances can affect the DFS value. Because the observation error variances are assumed to be uniform, the observational influence at each observational location is related to the background error variance, and the observations located at the place where there are larger background error variances have larger influences. The average observational influence of u and v with respect to the analysis is about 40%, implying that the background influence with respect to the analysis is about 60%.

High order accurate and low dissipation method for unsteady compressible viscous flow computation on helicopter rotor in forward flight

NASA Astrophysics Data System (ADS)

Xu, Li; Weng, Peifen

2014-02-01

An improved fifth-order weighted essentially non-oscillatory (WENO-Z) scheme combined with the moving overset grid technique has been developed to compute unsteady compressible viscous flows on the helicopter rotor in forward flight. In order to enforce periodic rotation and pitching of the rotor and relative motion between rotor blades, the moving overset grid technique is extended, where a special judgement standard is presented near the odd surface of the blade grid during search donor cells by using the Inverse Map method. The WENO-Z scheme is adopted for reconstructing left and right state values with the Roe Riemann solver updating the inviscid fluxes and compared with the monotone upwind scheme for scalar conservation laws (MUSCL) and the classical WENO scheme. Since the WENO schemes require a six point stencil to build the fifth-order flux, the method of three layers of fringes for hole boundaries and artificial external boundaries is proposed to carry out flow information exchange between chimera grids. The time advance on the unsteady solution is performed by the full implicit dual time stepping method with Newton type LU-SGS subiteration, where the solutions of pseudo steady computation are as the initial fields of the unsteady flow computation. Numerical results on non-variable pitch rotor and periodic variable pitch rotor in forward flight reveal that the approach can effectively capture vortex wake with low dissipation and reach periodic solutions very soon.

A Fast and Accurate Method of Radiation Hydrodynamics Calculation in Spherical Symmetry

NASA Astrophysics Data System (ADS)

Stamer, Torsten; Inutsuka, Shu-ichiro

2018-06-01

We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation, and it is accurate for optically thin, thick, and intermediate systems. In the limit of a homogeneously distributed extinction coefficient, our method is very accurate and exceptionally fast. We combine this fast method with a slower but more generally applicable method to describe realistic problems. We perform various test calculations, including a simplified protostellar collapse simulation. We also discuss possible future improvements.

Improved finite difference schemes for transonic potential calculations

NASA Technical Reports Server (NTRS)

Hafez, M.; Osher, S.; Whitlow, W., Jr.

1984-01-01

Engquist and Osher (1980) have introduced a finite difference scheme for solving the transonic small disturbance equation, taking into account cases in which only compression shocks are admitted. Osher et al. (1983) studied a class of schemes for the full potential equation. It is proved that these schemes satisfy a new discrete 'entropy inequality' which rules out expansion shocks. However, the conducted analysis is restricted to steady two-dimensional flows. The present investigation is concerned with the adoption of a heuristic approach. The full potential equation in conservation form is solved with the aid of a modified artificial density method, based on flux biasing. It is shown that, with the current scheme, expansion shocks are not possible.

A numerical study of the axisymmetric Couette-Taylor problem using a fast high-resolution second-order central scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kupferman, R.

The author presents a numerical study of the axisymmetric Couette-Taylor problem using a finite difference scheme. The scheme is based on a staggered version of a second-order central-differencing method combined with a discrete Hodge projection. The use of central-differencing operators obviates the need to trace the characteristic flow associated with the hyperbolic terms. The result is a simple and efficient scheme which is readily adaptable to other geometries and to more complicated flows. The scheme exhibits competitive performance in terms of accuracy, resolution, and robustness. The numerical results agree accurately with linear stability theory and with previous numerical studies.

The constant displacement scheme for tracking particles in heterogeneous aquifers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wen, X.H.; Gomez-Hernandez, J.J.

1996-01-01

Simulation of mass transport by particle tracking or random walk in highly heterogeneous media may be inefficient from a computational point of view if the traditional constant time step scheme is used. A new scheme which adjusts automatically the time step for each particle according to the local pore velocity, so that each particle always travels a constant distance, is shown to be computationally faster for the same degree of accuracy than the constant time step method. Using the constant displacement scheme, transport calculations in a 2-D aquifer model, with nature log-transmissivity variance of 4, can be 8.6 times fastermore » than using the constant time step scheme.« less

ONU Power Saving Scheme for EPON System

NASA Astrophysics Data System (ADS)

Mukai, Hiroaki; Tano, Fumihiko; Tanaka, Masaki; Kozaki, Seiji; Yamanaka, Hideaki

PON (Passive Optical Network) achieves FTTH (Fiber To The Home) economically, by sharing an optical fiber among plural subscribers. Recently, global climate change has been recognized as a serious near term problem. Power saving techniques for electronic devices are important. In PON system, the ONU (Optical Network Unit) power saving scheme has been studied and defined in XG-PON. In this paper, we propose an ONU power saving scheme for EPON. Then, we present an analysis of the power reduction effect and the data transmission delay caused by the ONU power saving scheme. According to the analysis, we propose an efficient provisioning method for the ONU power saving scheme which is applicable to both of XG-PON and EPON.

Multigrid schemes for viscous hypersonic flows

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Radespiel, R.

1993-01-01

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 two 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).

General calibration methodology for a combined Horton-SCS infiltration scheme in flash flood modeling

NASA Astrophysics Data System (ADS)

Gabellani, S.; Silvestro, F.; Rudari, R.; Boni, G.

2008-12-01

Flood forecasting undergoes a constant evolution, becoming more and more demanding about the models used for hydrologic simulations. The advantages of developing distributed or semi-distributed models have currently been made clear. Now the importance of using continuous distributed modeling emerges. A proper schematization of the infiltration process is vital to these types of models. Many popular infiltration schemes, reliable and easy to implement, are too simplistic for the development of continuous hydrologic models. On the other hand, the unavailability of detailed and descriptive information on soil properties often limits the implementation of complete infiltration schemes. In this work, a combination between the Soil Conservation Service Curve Number method (SCS-CN) and a method derived from Horton equation is proposed in order to overcome the inherent limits of the two schemes. The SCS-CN method is easily applicable on large areas, but has structural limitations. The Horton-like methods present parameters that, though measurable to a point, are difficult to achieve a reliable estimate at catchment scale. The objective of this work is to overcome these limits by proposing a calibration procedure which maintains the large applicability of the SCS-CN method as well as the continuous description of the infiltration process given by the Horton's equation suitably modified. The estimation of the parameters of the modified Horton method is carried out using a formal analogy with the SCS-CN method under specific conditions. Some applications, at catchment scale within a distributed model, are presented.

A single-stage flux-corrected transport algorithm for high-order finite-volume methods

DOE PAGES

Chaplin, Christopher; Colella, Phillip

2017-05-08

We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. Here, we modify the classical algorithm by introducing a new computation for solution bounds at smooth extrema, as well as improving the preconstraint on the high-order fluxes. We compute the high-order fluxes via a method-of-lines approach with fourth-order Runge-Kutta as the time integrator. For computing low-order fluxes, we select the corner-transport upwind method due to its improved stability over donor-cell upwind. Several spatial differencing schemes are investigated for the high-order flux computation, including centered- differencemore » and upwind schemes. We show that the upwind schemes perform well on account of the dissipation of high-wavenumber components. The new limiter method retains high-order accuracy for smooth solutions and accurately captures fronts in discontinuous solutions. Further, we need only apply the limiter once per complete time step.« less

An upwind method for the solution of the 3D Euler and Navier-Stokes equations on adaptively refined meshes

NASA Astrophysics Data System (ADS)

Aftosmis, Michael J.

1992-10-01

A new node based upwind scheme for the solution of the 3D Navier-Stokes equations on adaptively refined meshes is presented. The method uses a second-order upwind TVD scheme to integrate the convective terms, and discretizes the viscous terms with a new compact central difference technique. Grid adaptation is achieved through directional division of hexahedral cells in response to evolving features as the solution converges. The method is advanced in time with a multistage Runge-Kutta time stepping scheme. Two- and three-dimensional examples establish the accuracy of the inviscid and viscous discretization. These investigations highlight the ability of the method to produce crisp shocks, while accurately and economically resolving viscous layers. The representation of these and other structures is shown to be comparable to that obtained by structured methods. Further 3D examples demonstrate the ability of the adaptive algorithm to effectively locate and resolve multiple scale features in complex 3D flows with many interacting, viscous, and inviscid structures.

Error and Complexity Analysis for a Collocation-Grid-Projection Plus Precorrected-FFT Algorithm for Solving Potential Integral Equations with LaPlace or Helmholtz Kernels

NASA Technical Reports Server (NTRS)

Phillips, J. R.

1996-01-01

In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.

Round-robin differential-phase-shift quantum key distribution with heralded pair-coherent sources

NASA Astrophysics Data System (ADS)

Wang, Le; Zhao, Shengmei

2017-04-01

Round-robin differential-phase-shift (RRDPS) quantum key distribution (QKD) scheme provides an effective way to overcome the signal disturbance from the transmission process. However, most RRDPS-QKD schemes use weak coherent pulses (WCPs) as the replacement of the perfect single-photon source. Considering the heralded pair-coherent source (HPCS) can efficiently remove the shortcomings of WCPs, we propose a RRDPS-QKD scheme with HPCS in this paper. Both infinite-intensity decoy-state method and practical three-intensity decoy-state method are adopted to discuss the tight bound of the key rate of the proposed scheme. The results show that HPCS is a better candidate for the replacement of the perfect single-photon source, and both the key rate and the transmission distance are greatly increased in comparison with those results with WCPs when the length of the pulse trains is small. Simultaneously, the performance of the proposed scheme using three-intensity decoy states is close to that result using infinite-intensity decoy states when the length of pulse trains is small.

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

NASA Astrophysics Data System (ADS)

Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

2017-07-01

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

A Secure Trust Establishment Scheme for Wireless Sensor Networks

PubMed Central

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

2014-01-01

Trust establishment is an important tool to improve cooperation and enhance security in wireless sensor networks. The core of trust establishment is trust estimation. If a trust estimation method is not robust against attack and misbehavior, the trust values produced will be meaningless, and system performance will be degraded. We present a novel trust estimation method that is robust against on-off attacks and persistent malicious behavior. Moreover, in order to aggregate recommendations securely, we propose using a modified one-step M-estimator scheme. The novelty of the proposed scheme arises from combining past misbehavior with current status in a comprehensive way. Specifically, we introduce an aggregated misbehavior component in trust estimation, which assists in detecting an on-off attack and persistent malicious behavior. In order to determine the current status of the node, we employ previous trust values and current measured misbehavior components. These components are combined to obtain a robust trust value. Theoretical analyses and evaluation results show that our scheme performs better than other trust schemes in terms of detecting an on-off attack and persistent misbehavior. PMID:24451471

Quantum money with nearly optimal error tolerance

NASA Astrophysics Data System (ADS)

Amiri, Ryan; Arrazola, Juan Miguel

2017-06-01

We present a family of quantum money schemes with classical verification which display a number of benefits over previous proposals. Our schemes are based on hidden matching quantum retrieval games and they tolerate noise up to 23 % , which we conjecture reaches 25 % asymptotically as the dimension of the underlying hidden matching states is increased. Furthermore, we prove that 25 % is the maximum tolerable noise for a wide class of quantum money schemes with classical verification, meaning our schemes are almost optimally noise tolerant. We use methods in semidefinite programming to prove security in a substantially different manner to previous proposals, leading to two main advantages: first, coin verification involves only a constant number of states (with respect to coin size), thereby allowing for smaller coins; second, the reusability of coins within our scheme grows linearly with the size of the coin, which is known to be optimal. Last, we suggest methods by which the coins in our protocol could be implemented using weak coherent states and verified using existing experimental techniques, even in the presence of detector inefficiencies.

A third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

PubMed Central

Yousaf, Muhammad; Ghaffar, Tayabia; Qamar, Shamsul

2015-01-01

The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems. PMID:26070067

Correlation-based motion vector processing with adaptive interpolation scheme for motion-compensated frame interpolation.

PubMed

Huang, Ai-Mei; Nguyen, Truong

2009-04-01

In this paper, we address the problems of unreliable motion vectors that cause visual artifacts but cannot be detected by high residual energy or bidirectional prediction difference in motion-compensated frame interpolation. A correlation-based motion vector processing method is proposed to detect and correct those unreliable motion vectors by explicitly considering motion vector correlation in the motion vector reliability classification, motion vector correction, and frame interpolation stages. Since our method gradually corrects unreliable motion vectors based on their reliability, we can effectively discover the areas where no motion is reliable to be used, such as occlusions and deformed structures. We also propose an adaptive frame interpolation scheme for the occlusion areas based on the analysis of their surrounding motion distribution. As a result, the interpolated frames using the proposed scheme have clearer structure edges and ghost artifacts are also greatly reduced. Experimental results show that our interpolated results have better visual quality than other methods. In addition, the proposed scheme is robust even for those video sequences that contain multiple and fast motions.

Accuracy of maximum likelihood and least-squares estimates in the lidar slope method with noisy data.

PubMed

Eberhard, Wynn L

2017-04-01

The maximum likelihood estimator (MLE) is derived for retrieving the extinction coefficient and zero-range intercept in the lidar slope method in the presence of random and independent Gaussian noise. Least-squares fitting, weighted by the inverse of the noise variance, is equivalent to the MLE. Monte Carlo simulations demonstrate that two traditional least-squares fitting schemes, which use different weights, are less accurate. Alternative fitting schemes that have some positive attributes are introduced and evaluated. The principal factors governing accuracy of all these schemes are elucidated. Applying these schemes to data with Poisson rather than Gaussian noise alters accuracy little, even when the signal-to-noise ratio is low. Methods to estimate optimum weighting factors in actual data are presented. Even when the weighting estimates are coarse, retrieval accuracy declines only modestly. Mathematical tools are described for predicting retrieval accuracy. Least-squares fitting with inverse variance weighting has optimum accuracy for retrieval of parameters from single-wavelength lidar measurements when noise, errors, and uncertainties are Gaussian distributed, or close to optimum when only approximately Gaussian.

A Reverse Localization Scheme for Underwater Acoustic Sensor Networks

PubMed Central

Moradi, Marjan; Rezazadeh, Javad; Ismail, Abdul Samad

2012-01-01

Underwater Wireless Sensor Networks (UWSNs) provide new opportunities to observe and predict the behavior of aquatic environments. In some applications like target tracking or disaster prevention, sensed data is meaningless without location information. In this paper, we propose a novel 3D centralized, localization scheme for mobile underwater wireless sensor network, named Reverse Localization Scheme or RLS in short. RLS is an event-driven localization method triggered by detector sensors for launching localization process. RLS is suitable for surveillance applications that require very fast reactions to events and could report the location of the occurrence. In this method, mobile sensor nodes report the event toward the surface anchors as soon as they detect it. They do not require waiting to receive location information from anchors. Simulation results confirm that the proposed scheme improves the energy efficiency and reduces significantly localization response time with a proper level of accuracy in terms of mobility model of water currents. Major contributions of this method lie on reducing the numbers of message exchange for localization, saving the energy and decreasing the average localization response time. PMID:22666034

A reverse localization scheme for underwater acoustic sensor networks.

PubMed

Moradi, Marjan; Rezazadeh, Javad; Ismail, Abdul Samad

2012-01-01

Underwater Wireless Sensor Networks (UWSNs) provide new opportunities to observe and predict the behavior of aquatic environments. In some applications like target tracking or disaster prevention, sensed data is meaningless without location information. In this paper, we propose a novel 3D centralized, localization scheme for mobile underwater wireless sensor network, named Reverse Localization Scheme or RLS in short. RLS is an event-driven localization method triggered by detector sensors for launching localization process. RLS is suitable for surveillance applications that require very fast reactions to events and could report the location of the occurrence. In this method, mobile sensor nodes report the event toward the surface anchors as soon as they detect it. They do not require waiting to receive location information from anchors. Simulation results confirm that the proposed scheme improves the energy efficiency and reduces significantly localization response time with a proper level of accuracy in terms of mobility model of water currents. Major contributions of this method lie on reducing the numbers of message exchange for localization, saving the energy and decreasing the average localization response time.

Counter-Based Broadcast Scheme Considering Reachability, Network Density, and Energy Efficiency for Wireless Sensor Networks.

PubMed

Jung, Ji-Young; Seo, Dong-Yoon; Lee, Jung-Ryun

2018-01-04

A wireless sensor network (WSN) is emerging as an innovative method for gathering information that will significantly improve the reliability and efficiency of infrastructure systems. Broadcast is a common method to disseminate information in WSNs. A variety of counter-based broadcast schemes have been proposed to mitigate the broadcast-storm problems, using the count threshold value and a random access delay. However, because of the limited propagation of the broadcast-message, there exists a trade-off in a sense that redundant retransmissions of the broadcast-message become low and energy efficiency of a node is enhanced, but reachability become low. Therefore, it is necessary to study an efficient counter-based broadcast scheme that can dynamically adjust the random access delay and count threshold value to ensure high reachability, low redundant of broadcast-messages, and low energy consumption of nodes. Thus, in this paper, we first measure the additional coverage provided by a node that receives the same broadcast-message from two neighbor nodes, in order to achieve high reachability with low redundant retransmissions of broadcast-messages. Second, we propose a new counter-based broadcast scheme considering the size of the additional coverage area, distance between the node and the broadcasting node, remaining battery of the node, and variations of the node density. Finally, we evaluate performance of the proposed scheme compared with the existing counter-based broadcast schemes. Simulation results show that the proposed scheme outperforms the existing schemes in terms of saved rebroadcasts, reachability, and total energy consumption.

Fast auto-focus scheme based on optical defocus fitting model

NASA Astrophysics Data System (ADS)

Wang, Yeru; Feng, Huajun; Xu, Zhihai; Li, Qi; Chen, Yueting; Cen, Min

2018-04-01

An optical defocus fitting model-based (ODFM) auto-focus scheme is proposed. Considering the basic optical defocus principle, the optical defocus fitting model is derived to approximate the potential-focus position. By this accurate modelling, the proposed auto-focus scheme can make the stepping motor approach the focal plane more accurately and rapidly. Two fitting positions are first determined for an arbitrary initial stepping motor position. Three images (initial image and two fitting images) at these positions are then collected to estimate the potential-focus position based on the proposed ODFM method. Around the estimated potential-focus position, two reference images are recorded. The auto-focus procedure is then completed by processing these two reference images and the potential-focus image to confirm the in-focus position using a contrast based method. Experimental results prove that the proposed scheme can complete auto-focus within only 5 to 7 steps with good performance even under low-light condition.

Hyperbolic/parabolic development for the GIM-STAR code. [flow fields in supersonic inlets

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Stalnaker, J. F.; Ratliff, A. W.

1980-01-01

Flow fields in supersonic inlet configurations were computed using the eliptic GIM code on the STAR computer. Spillage flow under the lower cowl was calculated to be 33% of the incoming stream. The shock/boundary layer interaction on the upper propulsive surface was computed including separation. All shocks produced by the flow system were captured. Linearized block implicit (LBI) schemes were examined to determine their application to the GIM code. Pure explicit methods have stability limitations and fully implicit schemes are inherently inefficient; however, LBI schemes show promise as an effective compromise. A quasiparabolic version of the GIM code was developed using elastical parabolized Navier-Stokes methods combined with quasitime relaxation. This scheme is referred to as quasiparabolic although it applies equally well to hyperbolic supersonic inviscid flows. Second order windward differences are used in the marching coordinate and either explicit or linear block implicit time relaxation can be incorporated.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dyachenko, Sergey A.; Zlotnik, Anatoly; Korotkevich, Alexander O.

Here, we develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme ismore » unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.« less

Design of a Variational Multiscale Method for Turbulent Compressible Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo Tibor; Murman, Scott M.

2013-01-01

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

Deterministic multidimensional nonuniform gap sampling.

PubMed

Worley, Bradley; Powers, Robert

2015-12-01

Born from empirical observations in nonuniformly sampled multidimensional NMR data relating to gaps between sampled points, the Poisson-gap sampling method has enjoyed widespread use in biomolecular NMR. While the majority of nonuniform sampling schemes are fully randomly drawn from probability densities that vary over a Nyquist grid, the Poisson-gap scheme employs constrained random deviates to minimize the gaps between sampled grid points. We describe a deterministic gap sampling method, based on the average behavior of Poisson-gap sampling, which performs comparably to its random counterpart with the additional benefit of completely deterministic behavior. We also introduce a general algorithm for multidimensional nonuniform sampling based on a gap equation, and apply it to yield a deterministic sampling scheme that combines burst-mode sampling features with those of Poisson-gap schemes. Finally, we derive a relationship between stochastic gap equations and the expectation value of their sampling probability densities. Copyright © 2015 Elsevier Inc. All rights reserved.

The Space-Time Conservation Element and Solution Element Method-A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 2; Numerical Simulation of Shock Waves and Contact Discontinuities

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung

1998-01-01

Without resorting to special treatment for each individual test case, the 1D and 2D CE/SE shock-capturing schemes described previously (in Part I) are used to simulate flows involving phenomena such as shock waves, contact discontinuities, expansion waves and their interactions. Five 1D and six 2D problems are considered to examine the capability and robustness of these schemes. Despite their simple logical structures and low computational cost (for the 2D CE/SE shock-capturing scheme, the CPU time is about 2 micro-secs per mesh point per marching step on a Cray C90 machine), the numerical results, when compared with experimental data, exact solutions or numerical solutions by other methods, indicate that these schemes can accurately resolve shock and contact discontinuities consistently.

Stabilized Finite Elements in FUN3D

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Newman, James C.; Karman, Steve L.

2017-01-01

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation.

PubMed

Yoshida, Hiroaki; Kobayashi, Takayuki; Hayashi, Hidemitsu; Kinjo, Tomoyuki; Washizu, Hitoshi; Fukuzawa, Kenji

2014-07-01

A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme.

Numerical Investigation of a Model Scramjet Combustor Using DDES

NASA Astrophysics Data System (ADS)

Shin, Junsu; Sung, Hong-Gye

2017-04-01

Non-reactive flows moving through a model scramjet were investigated using a delayed detached eddy simulation (DDES), which is a hybrid scheme combining Reynolds averaged Navier-Stokes scheme and a large eddy simulation. The three dimensional Navier-Stokes equations were solved numerically on a structural grid using finite volume methods. An in-house was developed. This code used a monotonic upstream-centered scheme for conservation laws (MUSCL) with an advection upstream splitting method by pressure weight function (AUSMPW+) for space. In addition, a 4th order Runge-Kutta scheme was used with preconditioning for time integration. The geometries and boundary conditions of a scramjet combustor operated by DLR, a German aerospace center, were considered. The profiles of the lower wall pressure and axial velocity obtained from a time-averaged solution were compared with experimental results. Also, the mixing efficiency and total pressure recovery factor were provided in order to inspect the performance of the combustor.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

NASA Astrophysics Data System (ADS)

Chen, Jing-Bo

2014-06-01

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

On the application of subcell resolution to conservation laws with stiff source terms

NASA Technical Reports Server (NTRS)

Chang, Shih-Hung

1989-01-01

LeVeque and Yee recently investigated a one-dimensional scalar conservation law with stiff source terms modeling the reacting flow problems and discovered that for the very stiff case most of the current finite difference methods developed for non-reacting flows would produce wrong solutions when there is a propagating discontinuity. A numerical scheme, essentially nonoscillatory/subcell resolution - characteristic direction (ENO/SRCD), is proposed for solving conservation laws with stiff source terms. This scheme is a modification of Harten's ENO scheme with subcell resolution, ENO/SR. The locations of the discontinuities and the characteristic directions are essential in the design. Strang's time-splitting method is used and time evolutions are done by advancing along the characteristics. Numerical experiment using this scheme shows excellent results on the model problem of LeVeque and Yee. Comparisons of the results of ENO, ENO/SR, and ENO/SRCD are also presented.

Matching by linear programming and successive convexification.

PubMed

Jiang, Hao; Drew, Mark S; Li, Ze-Nian

2007-06-01

We present a novel convex programming scheme to solve matching problems, focusing on the challenging problem of matching in a large search range and with cluttered background. Matching is formulated as metric labeling with L1 regularization terms, for which we propose a novel linear programming relaxation method and an efficient successive convexification implementation. The unique feature of the proposed relaxation scheme is that a much smaller set of basis labels is used to represent the original label space. This greatly reduces the size of the searching space. A successive convexification scheme solves the labeling problem in a coarse to fine manner. Importantly, the original cost function is reconvexified at each stage, in the new focus region only, and the focus region is updated so as to refine the searching result. This makes the method well-suited for large label set matching. Experiments demonstrate successful applications of the proposed matching scheme in object detection, motion estimation, and tracking.

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2015-01-01

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Measurement scheme for purity based on two two-body gates

NASA Astrophysics Data System (ADS)

Nakazato, H.; Tanaka, T.; Yuasa, K.; Florio, G.; Pascazio, S.

2012-04-01

A scheme for measuring the purity of a quantum system with a finite number of levels is presented. The method makes use of two swap gates and hinges only on measurements performed on a reference system, prepared in a certain pure state and coupled with the target system. Neither tomographic methods, with the complete reconstruction of the state, nor interferometric setups are needed.

ICASE Semiannual Report, October 1, 1992 through March 31, 1993

DTIC Science & Technology

1993-06-01

NUMERICAL MATHEMATICS Saul Abarbanel Further results have been obtained regarding long time integration of high order compact finite difference schemes...overall accuracy. These problems are common to all numerical methods: finite differences , finite elements and spectral methods. It should be noted that...fourth order finite difference scheme. * In the same case, the D6 wavelets provide a sixth order finite difference , noncompact formula. * The wavelets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Podoshvedov, S. A., E-mail: podoshvedov@mail.ru

A method to generate Schroedinger cat states in free propagating optical fields based on the use of displaced states (or displacement operators) is developed. Some optical schemes with photon-added coherent states are studied. The schemes are modifications of the general method based on a sequence of displacements and photon additions or subtractions adjusted to generate Schroedinger cat states of a larger size. The effects of detection inefficiency are taken into account.

Robot-Arm Dynamic Control by Computer

NASA Technical Reports Server (NTRS)

Bejczy, Antal K.; Tarn, Tzyh J.; Chen, Yilong J.

1987-01-01

Feedforward and feedback schemes linearize responses to control inputs. Method for control of robot arm based on computed nonlinear feedback and state tranformations to linearize system and decouple robot end-effector motions along each of cartesian axes augmented with optimal scheme for correction of errors in workspace. Major new feature of control method is: optimal error-correction loop directly operates on task level and not on joint-servocontrol level.

An effective and secure key-management scheme for hierarchical access control in E-medicine system.

PubMed

Odelu, Vanga; Das, Ashok Kumar; Goswami, Adrijit

2013-04-01

Recently several hierarchical access control schemes are proposed in the literature to provide security of e-medicine systems. However, most of them are either insecure against 'man-in-the-middle attack' or they require high storage and computational overheads. Wu and Chen proposed a key management method to solve dynamic access control problems in a user hierarchy based on hybrid cryptosystem. Though their scheme improves computational efficiency over Nikooghadam et al.'s approach, it suffers from large storage space for public parameters in public domain and computational inefficiency due to costly elliptic curve point multiplication. Recently, Nikooghadam and Zakerolhosseini showed that Wu-Chen's scheme is vulnerable to man-in-the-middle attack. In order to remedy this security weakness in Wu-Chen's scheme, they proposed a secure scheme which is again based on ECC (elliptic curve cryptography) and efficient one-way hash function. However, their scheme incurs huge computational cost for providing verification of public information in the public domain as their scheme uses ECC digital signature which is costly when compared to symmetric-key cryptosystem. In this paper, we propose an effective access control scheme in user hierarchy which is only based on symmetric-key cryptosystem and efficient one-way hash function. We show that our scheme reduces significantly the storage space for both public and private domains, and computational complexity when compared to Wu-Chen's scheme, Nikooghadam-Zakerolhosseini's scheme, and other related schemes. Through the informal and formal security analysis, we further show that our scheme is secure against different attacks and also man-in-the-middle attack. Moreover, dynamic access control problems in our scheme are also solved efficiently compared to other related schemes, making our scheme is much suitable for practical applications of e-medicine systems.

The solution of the optimization problem of small energy complexes using linear programming methods

NASA Astrophysics Data System (ADS)

Ivanin, O. A.; Director, L. B.

2016-11-01

Linear programming methods were used for solving the optimization problem of schemes and operation modes of distributed generation energy complexes. Applicability conditions of simplex method, applied to energy complexes, including installations of renewable energy (solar, wind), diesel-generators and energy storage, considered. The analysis of decomposition algorithms for various schemes of energy complexes was made. The results of optimization calculations for energy complexes, operated autonomously and as a part of distribution grid, are presented.

An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs

PubMed Central

Guo, Jianqiang; Wang, Wansheng

2014-01-01

This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for vanilla call option and for European butterfly spread are provided. It turns out that the proposed scheme is efficient and reliable. PMID:24895653

An unconditionally stable, positivity-preserving splitting scheme for nonlinear Black-Scholes equation with transaction costs.

PubMed

Guo, Jianqiang; Wang, Wansheng

2014-01-01

This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for vanilla call option and for European butterfly spread are provided. It turns out that the proposed scheme is efficient and reliable.

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

NASA Technical Reports Server (NTRS)

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

2013-01-01

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

Investigation of the Use of Erasures in a Concatenated Coding Scheme

NASA Technical Reports Server (NTRS)

Kwatra, S. C.; Marriott, Philip J.

1997-01-01

A new method for declaring erasures in a concatenated coding scheme is investigated. This method is used with the rate 1/2 K = 7 convolutional code and the (255, 223) Reed Solomon code. Errors and erasures Reed Solomon decoding is used. The erasure method proposed uses a soft output Viterbi algorithm and information provided by decoded Reed Solomon codewords in a deinterleaving frame. The results show that a gain of 0.3 dB is possible using a minimum amount of decoding trials.

Analysis of drift correction in different simulated weighing schemes

NASA Astrophysics Data System (ADS)

Beatrici, A.; Rebelo, A.; Quintão, D.; Cacais, F. L.; Loayza, V. M.

2015-10-01

In the calibration of high accuracy mass standards some weighing schemes are used to reduce or eliminate the zero drift effects in mass comparators. There are different sources for the drift and different methods for its treatment. By using numerical methods, drift functions were simulated and a random term was included in each function. The comparison between the results obtained from ABABAB and ABBA weighing series was carried out. The results show a better efficacy of ABABAB method for drift with smooth variation and small randomness.

An RBF-FD closest point method for solving PDEs on surfaces

NASA Astrophysics Data System (ADS)

Petras, A.; Ling, L.; Ruuth, S. J.

2018-10-01

Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman (2008) [17]) is an embedding method for solving PDEs on surfaces using standard finite difference schemes. In this paper, we formulate an explicit closest point method using finite difference schemes derived from radial basis functions (RBF-FD). Unlike the orthogonal gradients method (Piret (2012) [22]), our proposed method uses RBF centers on regular grid nodes. This formulation not only reduces the computational cost but also avoids the ill-conditioning from point clustering on the surface and is more natural to couple with a grid based manifold evolution algorithm (Leung and Zhao (2009) [26]). When compared to the standard finite difference discretization of the closest point method, the proposed method requires a smaller computational domain surrounding the surface, resulting in a decrease in the number of sampling points on the surface. In addition, higher-order schemes can easily be constructed by increasing the number of points in the RBF-FD stencil. Applications to a variety of examples are provided to illustrate the numerical convergence of the method.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs) depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration scheme and the appropriate time step should possibly take into account the typical altitude ranges as well as the total length of the simulations to achieve the most efficient simulations. However, trying to summarize, we recommend the third-order Runge-Kutta method with a time step of 170 s or the midpoint scheme with a time step of 100 s for efficient simulations of up to 10 days of simulation time for the specific ECMWF high-resolution data set considered in this study. Purely stratospheric simulations can use significantly larger time steps of 800 and 1100 s for the midpoint scheme and the third-order Runge-Kutta method, respectively.

WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions

NASA Astrophysics Data System (ADS)

Tsoutsanis, P.; Titarev, V. A.; Drikakis, D.

2011-02-01

The paper extends weighted essentially non-oscillatory (WENO) methods to three dimensional mixed-element unstructured meshes, comprising tetrahedral, hexahedral, prismatic and pyramidal elements. Numerical results illustrate the convergence rates and non-oscillatory properties of the schemes for various smooth and discontinuous solutions test cases and the compressible Euler equations on various types of grids. Schemes of up to fifth order of spatial accuracy are considered.

CONDIF - A modified central-difference scheme for convective flows

NASA Technical Reports Server (NTRS)

Runchal, Akshai K.

1987-01-01

The paper presents a method, called CONDIF, which modifies the CDS (central-difference scheme) by introducing a controlled amount of numerical diffusion based on the local gradients. The numerical diffusion can be adjusted to be negligibly low for most problems. CONDIF results are significantly more accurate than those obtained from the hybrid scheme when the Peclet number is very high and the flow is at large angles to the grid.

Effective scheme of photolysis of GFP in live cell as revealed with confocal fluorescence microscopy

NASA Astrophysics Data System (ADS)

Glazachev, Yu I.; Orlova, D. Y.; Řezníčková, P.; Bártová, E.

2018-05-01

We proposed an effective kinetics scheme of photolysis of green fluorescent protein (GFP) observed in live cells with a commercial confocal fluorescence microscope. We investigated the photolysis of GFP-tagged heterochromatin protein, HP1β-GFP, in live nucleus with the pulse position modulation approach, which has several advantages over the classical pump-and-probe method. At the basis of the proposed scheme lies a process of photoswitching from the native fluorescence state to the intermediate fluorescence state, which has a lower fluorescence yield and recovers back to native state in the dark. This kinetics scheme includes four effective parameters (photoswitching, reverse switching, photodegradation rate constants, and relative brightness of the intermediate state) and covers the time scale from dozens of milliseconds to minutes of the experimental fluorescence kinetics. Additionally, the applicability of the scheme was demonstrated in the cases of continuous irradiation and the classical pump-and-probe approach using numerical calculations and analytical solutions. An interesting finding of experimental data analysis was that the overall photodegradation of GFP proceeds dominantly from the intermediate state, and demonstrated approximately the second-order reaction versus irradiation power. As a practical example, the proposed scheme elucidates the artifacts of fluorescence recovery after the photobleaching method, and allows us to propose some suggestions on how to diminish them.

Effective scheme of photolysis of GFP in live cell as revealed with confocal fluorescence microscopy.

PubMed

Glazachev, Yu I; Orlova, D Y; Řezníčková, P; Bártová, E

2018-03-23

We proposed an effective kinetics scheme of photolysis of green fluorescent protein (GFP) observed in live cells with a commercial confocal fluorescence microscope. We investigated the photolysis of GFP-tagged heterochromatin protein, HP1β-GFP, in live nucleus with the pulse position modulation approach, which has several advantages over the classical pump-and-probe method. At the basis of the proposed scheme lies a process of photoswitching from the native fluorescence state to the intermediate fluorescence state, which has a lower fluorescence yield and recovers back to native state in the dark. This kinetics scheme includes four effective parameters (photoswitching, reverse switching, photodegradation rate constants, and relative brightness of the intermediate state) and covers the time scale from dozens of milliseconds to minutes of the experimental fluorescence kinetics. Additionally, the applicability of the scheme was demonstrated in the cases of continuous irradiation and the classical pump-and-probe approach using numerical calculations and analytical solutions. An interesting finding of experimental data analysis was that the overall photodegradation of GFP proceeds dominantly from the intermediate state, and demonstrated approximately the second-order reaction versus irradiation power. As a practical example, the proposed scheme elucidates the artifacts of fluorescence recovery after the photobleaching method, and allows us to propose some suggestions on how to diminish them.

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coquel, Frédéric, E-mail: frederic.coquel@cmap.polytechnique.fr; Hérard, Jean-Marc, E-mail: jean-marc.herard@edf.fr; Saleh, Khaled, E-mail: saleh@math.univ-lyon1.fr

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

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.

Optimizing congestion and emissions via tradable credit charge and reward scheme without initial credit allocations

NASA Astrophysics Data System (ADS)

Zhu, Wenlong; Ma, Shoufeng; Tian, Junfang

2017-01-01

This paper investigates the revenue-neutral tradable credit charge and reward scheme without initial credit allocations that can reassign network traffic flow patterns to optimize congestion and emissions. First, we prove the existence of the proposed schemes and further decentralize the minimum emission flow pattern to user equilibrium. Moreover, we design the solving method of the proposed credit scheme for minimum emission problem. Second, we investigate the revenue-neutral tradable credit charge and reward scheme without initial credit allocations for bi-objectives to obtain the Pareto system optimum flow patterns of congestion and emissions; and present the corresponding solutions are located in the polyhedron constituted by some inequalities and equalities system. Last, numerical example based on a simple traffic network is adopted to obtain the proposed credit schemes and verify they are revenue-neutral.

Building fast well-balanced two-stage numerical schemes for a model of two-phase flows

NASA Astrophysics Data System (ADS)

Thanh, Mai Duc

2014-06-01

We present a set of well-balanced two-stage schemes for an isentropic model of two-phase flows arisen from the modeling of deflagration-to-detonation transition in granular materials. The first stage is to absorb the source term in nonconservative form into equilibria. Then in the second stage, these equilibria will be composed into a numerical flux formed by using a convex combination of the numerical flux of a stable Lax-Friedrichs-type scheme and the one of a higher-order Richtmyer-type scheme. Numerical schemes constructed in such a way are expected to get the interesting property: they are fast and stable. Tests show that the method works out until the parameter takes on the value CFL, and so any value of the parameter between zero and this value is expected to work as well. All the schemes in this family are shown to capture stationary waves and preserves the positivity of the volume fractions. The special values of the parameter 0,1/2,1/(1+CFL), and CFL in this family define the Lax-Friedrichs-type, FAST1, FAST2, and FAST3 schemes, respectively. These schemes are shown to give a desirable accuracy. The errors and the CPU time of these schemes and the Roe-type scheme are calculated and compared. The constructed schemes are shown to be well-balanced and faster than the Roe-type scheme.

Development of Mycoplasma synoviae (MS) core genome multilocus sequence typing (cgMLST) scheme.

PubMed

Ghanem, Mostafa; El-Gazzar, Mohamed

2018-05-01

Mycoplasma synoviae (MS) is a poultry pathogen with reported increased prevalence and virulence in recent years. MS strain identification is essential for prevention, control efforts and epidemiological outbreak investigations. Multiple multilocus based sequence typing schemes have been developed for MS, yet the resolution of these schemes could be limited for outbreak investigation. The cost of whole genome sequencing became close to that of sequencing the seven MLST targets; however, there is no standardized method for typing MS strains based on whole genome sequences. In this paper, we propose a core genome multilocus sequence typing (cgMLST) scheme as a standardized and reproducible method for typing MS based whole genome sequences. A diverse set of 25 MS whole genome sequences were used to identify 302 core genome genes as cgMLST targets (35.5% of MS genome) and 44 whole genome sequences of MS isolates from six countries in four continents were used for typing applying this scheme. cgMLST based phylogenetic trees displayed a high degree of agreement with core genome SNP based analysis and available epidemiological information. cgMLST allowed evaluation of two conventional MLST schemes of MS. The high discriminatory power of cgMLST allowed differentiation between samples of the same conventional MLST type. cgMLST represents a standardized, accurate, highly discriminatory, and reproducible method for differentiation between MS isolates. Like conventional MLST, it provides stable and expandable nomenclature, allowing for comparing and sharing the typing results between different laboratories worldwide. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes

NASA Astrophysics Data System (ADS)

Clark, Martyn P.; Kavetski, Dmitri

2010-10-01

A major neglected weakness of many current hydrological models is the numerical method used to solve the governing model equations. This paper thoroughly evaluates several classes of time stepping schemes in terms of numerical reliability and computational efficiency in the context of conceptual hydrological modeling. Numerical experiments are carried out using 8 distinct time stepping algorithms and 6 different conceptual rainfall-runoff models, applied in a densely gauged experimental catchment, as well as in 12 basins with diverse physical and hydroclimatic characteristics. Results show that, over vast regions of the parameter space, the numerical errors of fixed-step explicit schemes commonly used in hydrology routinely dwarf the structural errors of the model conceptualization. This substantially degrades model predictions, but also, disturbingly, generates fortuitously adequate performance for parameter sets where numerical errors compensate for model structural errors. Simply running fixed-step explicit schemes with shorter time steps provides a poor balance between accuracy and efficiency: in some cases daily-step adaptive explicit schemes with moderate error tolerances achieved comparable or higher accuracy than 15 min fixed-step explicit approximations but were nearly 10 times more efficient. From the range of simple time stepping schemes investigated in this work, the fixed-step implicit Euler method and the adaptive explicit Heun method emerge as good practical choices for the majority of simulation scenarios. In combination with the companion paper, where impacts on model analysis, interpretation, and prediction are assessed, this two-part study vividly highlights the impact of numerical errors on critical performance aspects of conceptual hydrological models and provides practical guidelines for robust numerical implementation.

Low Dissipative High Order Shock-Capturing Methods Using Characteristic-Based Filters

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sandham, N. D.; Djomehri, M. J.

1998-01-01

An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Oisson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.

Low Dissipative High Order Shock-Capturing Methods using Characteristic-Based Filters

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sandham, N. D.; Djomehri, M. J.

1998-01-01

An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Olsson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.

One lens optical correlation: application to face recognition.

PubMed

Jridi, Maher; Napoléon, Thibault; Alfalou, Ayman

2018-03-20

Despite its extensive use, the traditional 4f Vander Lugt Correlator optical setup can be further simplified. We propose a lightweight correlation scheme where the decision is taken in the Fourier plane. For this purpose, the Fourier plane is adapted and used as a decision plane. Then, the offline phase and the decision metric are re-examined in order to keep a reasonable recognition rate. The benefits of the proposed approach are numerous: (1) it overcomes the constraints related to the use of a second lens; (2) the optical correlation setup is simplified; (3) the multiplication with the correlation filter can be done digitally, which offers a higher adaptability according to the application. Moreover, the digital counterpart of the correlation scheme is lightened since with the proposed scheme we get rid of the inverse Fourier transform (IFT) calculation (i.e., decision directly in the Fourier domain without resorting to IFT). To assess the performance of the proposed approach, an insight into digital hardware resources saving is provided. The proposed method involves nearly 100 times fewer arithmetic operators. Moreover, from experimental results in the context of face verification-based correlation, we demonstrate that the proposed scheme provides comparable or better accuracy than the traditional method. One interesting feature of the proposed scheme is that it could greatly outperform the traditional scheme for face identification application in terms of sensitivity to face orientation. The proposed method is found to be digital/optical implementation-friendly, which facilitates its integration on a very broad range of scenarios.

Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.

PubMed

Suk, Heejun

2016-07-01

MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the Lagrangian concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes. © 2016, National Ground Water Association.

Critical study of higher order numerical methods for solving the boundary-layer equations

NASA Technical Reports Server (NTRS)

Wornom, S. F.

1978-01-01

A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.

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

NASA Astrophysics Data System (ADS)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 by directly approximating the integer-order derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 < α < 1 for any fixed tn > 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

A multistage approach to improve performance of computer-aided detection of pulmonary embolisms depicted on CT images: preliminary investigation.

PubMed

Park, Sang Cheol; Chapman, Brian E; Zheng, Bin

2011-06-01

This study developed a computer-aided detection (CAD) scheme for pulmonary embolism (PE) detection and investigated several approaches to improve CAD performance. In the study, 20 computed tomography examinations with various lung diseases were selected, which include 44 verified PE lesions. The proposed CAD scheme consists of five basic steps: 1) lung segmentation; 2) PE candidate extraction using an intensity mask and tobogganing region growing; 3) PE candidate feature extraction; 4) false-positive (FP) reduction using an artificial neural network (ANN); and 5) a multifeature-based k-nearest neighbor for positive/negative classification. In this study, we also investigated the following additional methods to improve CAD performance: 1) grouping 2-D detected features into a single 3-D object; 2) selecting features with a genetic algorithm (GA); and 3) limiting the number of allowed suspicious lesions to be cued in one examination. The results showed that 1) CAD scheme using tobogganing, an ANN, and grouping method achieved the maximum detection sensitivity of 79.2%; 2) the maximum scoring method achieved the superior performance over other scoring fusion methods; 3) GA was able to delete "redundant" features and further improve CAD performance; and 4) limiting the maximum number of cued lesions in an examination reduced FP rate by 5.3 times. Combining these approaches, CAD scheme achieved 63.2% detection sensitivity with 18.4 FP lesions per examination. The study suggested that performance of CAD schemes for PE detection depends on many factors that include 1) optimizing the 2-D region grouping and scoring methods; 2) selecting the optimal feature set; and 3) limiting the number of allowed cueing lesions per examination.

An intercomparison of methods for solving the stochastic collection equation with a focus on cloud radar Doppler spectra in drizzling stratocumulus

NASA Astrophysics Data System (ADS)

Lee, H.; Fridlind, A. M.; Ackerman, A. S.; Kollias, P.

2017-12-01

Cloud radar Doppler spectra provide rich information for evaluating the fidelity of particle size distributions from cloud models. The intrinsic simplifications of bulk microphysics schemes generally preclude the generation of plausible Doppler spectra, unlike bin microphysics schemes, which develop particle size distributions more organically at substantial computational expense. However, bin microphysics schemes face the difficulty of numerical diffusion leading to overly rapid large drop formation, particularly while solving the stochastic collection equation (SCE). Because such numerical diffusion can cause an even greater overestimation of radar reflectivity, an accurate method for solving the SCE is essential for bin microphysics schemes to accurately simulate Doppler spectra. While several methods have been proposed to solve the SCE, here we examine those of Berry and Reinhardt (1974, BR74), Jacobson et al. (1994, J94), and Bott (2000, B00). Using a simple box model to simulate drop size distribution evolution during precipitation formation with a realistic kernel, it is shown that each method yields a converged solution as the resolution of the drop size grid increases. However, the BR74 and B00 methods yield nearly identical size distributions in time, whereas the J94 method produces consistently larger drops throughout the simulation. In contrast to an earlier study, the performance of the B00 method is found to be satisfactory; it converges at relatively low resolution and long time steps, and its computational efficiency is the best among the three methods considered here. Finally, a series of idealized stratocumulus large-eddy simulations are performed using the J94 and B00 methods. The reflectivity size distributions and Doppler spectra obtained from the different SCE solution methods are presented and compared with observations.

Comparitive Study of High-Order Positivity-Preserving WENO Schemes

NASA Technical Reports Server (NTRS)

Kotov, D. V.; Yee, H. C.; Sjogreen, B.

2014-01-01

In gas dynamics and magnetohydrodynamics flows, physically, the density ? and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order Weighted Essentially Non-Oscillatory (WENO) schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative ? may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more di cult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium ow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case as well as for the case consisting of two species and one reaction.. This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

An almost symmetric Strang splitting scheme for nonlinear evolution equations☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2014-01-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun

1993-01-01

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

An improved PCA method with application to boiler leak detection.

PubMed

Sun, Xi; Marquez, Horacio J; Chen, Tongwen; Riaz, Muhammad

2005-07-01

Principal component analysis (PCA) is a popular fault detection technique. It has been widely used in process industries, especially in the chemical industry. In industrial applications, achieving a sensitive system capable of detecting incipient faults, which maintains the false alarm rate to a minimum, is a crucial issue. Although a lot of research has been focused on these issues for PCA-based fault detection and diagnosis methods, sensitivity of the fault detection scheme versus false alarm rate continues to be an important issue. In this paper, an improved PCA method is proposed to address this problem. In this method, a new data preprocessing scheme and a new fault detection scheme designed for Hotelling's T2 as well as the squared prediction error are developed. A dynamic PCA model is also developed for boiler leak detection. This new method is applied to boiler water/steam leak detection with real data from Syncrude Canada's utility plant in Fort McMurray, Canada. Our results demonstrate that the proposed method can effectively reduce false alarm rate, provide effective and correct leak alarms, and give early warning to operators.

Force analysis of magnetic bearings with power-saving controls

NASA Technical Reports Server (NTRS)

Johnson, Dexter; Brown, Gerald V.; Inman, Daniel J.

1992-01-01

Most magnetic bearing control schemes use a bias current with a superimposed control current to linearize the relationship between the control current and the force it delivers. For most operating conditions, the existence of the bias current requires more power than alternative methods that do not use conventional bias. Two such methods are examined which diminish or eliminate bias current. In the typical bias control scheme it is found that for a harmonic control force command into a voltage limited transconductance amplifier, the desired force output is obtained only up to certain combinations of force amplitude and frequency. Above these values, the force amplitude is reduced and a phase lag occurs. The power saving alternative control schemes typically exhibit such deficiencies at even lower command frequencies and amplitudes. To assess the severity of these effects, a time history analysis of the force output is performed for the bias method and the alternative methods. Results of the analysis show that the alternative approaches may be viable. The various control methods examined were mathematically modeled using nondimensionalized variables to facilitate comparison of the various methods.

High-order scheme for the source-sink term in a one-dimensional water temperature model

PubMed Central

Jing, Zheng; Kang, Ling

2017-01-01

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data. PMID:28264005

High-order scheme for the source-sink term in a one-dimensional water temperature model.

PubMed

Jing, Zheng; Kang, Ling

2017-01-01

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data.

Viscous flow computations using a second-order upwind differencing scheme

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1988-01-01

In the present computations of a wide range of fluid flow problems by means of the primitive variables-incorporating Navier-Stokes equations, a mixed second-order upwinding scheme approximates the convective terms of the transport equations and the scheme's accuracy is verified for convection-dominated high Re number flow problems. An adaptive dissipation scheme is used as a monotonic supersonic shock flow capture mechanism. Many benchmark fluid flow problems, including the compressible and incompressible, laminar and turbulent, over a wide range of M and Re numbers, are presently studied to verify the accuracy and robustness of this numerical method.

Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

NASA Technical Reports Server (NTRS)

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

1993-01-01

We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

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.

Program scheme using common source lines in channel stacked NAND flash memory with layer selection by multilevel operation

NASA Astrophysics Data System (ADS)

Kim, Do-Bin; Kwon, Dae Woong; Kim, Seunghyun; Lee, Sang-Ho; Park, Byung-Gook

2018-02-01

To obtain high channel boosting potential and reduce a program disturbance in channel stacked NAND flash memory with layer selection by multilevel (LSM) operation, a new program scheme using boosted common source line (CSL) is proposed. The proposed scheme can be achieved by applying proper bias to each layer through its own CSL. Technology computer-aided design (TCAD) simulations are performed to verify the validity of the new method in LSM. Through TCAD simulation, it is revealed that the program disturbance characteristics is effectively improved by the proposed scheme.

A concatenated coding scheme for error control

NASA Technical Reports Server (NTRS)

Lin, S.

1985-01-01

A concatenated coding scheme for error contol in data communications was analyzed. The inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if either the inner code decoder fails to make a successful decoding or the outer code decoder detects the presence of errors after the inner code decoding. Probability of undetected error of the proposed scheme is derived. An efficient method for computing this probability is presented. Throughout efficiency of the proposed error control scheme incorporated with a selective repeat ARQ retransmission strategy is analyzed.

Identification of material constants for piezoelectric transformers by three-dimensional, finite-element method and a design-sensitivity method.

PubMed

Joo, Hyun-Woo; Lee, Chang-Hwan; Rho, Jong-Seok; Jung, Hyun-Kyo

2003-08-01

In this paper, an inversion scheme for piezoelectric constants of piezoelectric transformers is proposed. The impedance of piezoelectric transducers is calculated using a three-dimensional finite element method. The validity of this is confirmed experimentally. The effects of material coefficients on piezoelectric transformers are investigated numerically. Six material coefficient variables for piezoelectric transformers were selected, and a design sensitivity method was adopted as an inversion scheme. The validity of the proposed method was confirmed by step-up ratio calculations. The proposed method is applied to the analysis of a sample piezoelectric transformer, and its resonance characteristics are obtained by numerically combined equivalent circuit method.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

The application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems is discussed. The methods consist of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line-, or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to that of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Crystal structure prediction supported by incomplete experimental data

NASA Astrophysics Data System (ADS)

Tsujimoto, Naoto; Adachi, Daiki; Akashi, Ryosuke; Todo, Synge; Tsuneyuki, Shinji

2018-05-01

We propose an efficient theoretical scheme for structure prediction on the basis of the idea of combining methods, which optimize theoretical calculation and experimental data simultaneously. In this scheme, we formulate a cost function based on a weighted sum of interatomic potential energies and a penalty function which is defined with partial experimental data totally insufficient for conventional structure analysis. In particular, we define the cost function using "crystallinity" formulated with only peak positions within the small range of the x-ray-diffraction pattern. We apply this method to well-known polymorphs of SiO2 and C with up to 108 atoms in the simulation cell and show that it reproduces the correct structures efficiently with very limited information of diffraction peaks. This scheme opens a new avenue for determining and predicting structures that are difficult to determine by conventional methods.

Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Ju, E-mail: jliu@ices.utexas.edu; Gomez, Hector; Evans, John A.

2013-09-01

We propose a new methodology for the numerical solution of the isothermal Navier–Stokes–Korteweg equations. Our methodology is based on a semi-discrete Galerkin method invoking functional entropy variables, a generalization of classical entropy variables, and a new time integration scheme. We show that the resulting fully discrete scheme is unconditionally stable-in-energy, second-order time-accurate, and mass-conservative. We utilize isogeometric analysis for spatial discretization and verify the aforementioned properties by adopting the method of manufactured solutions and comparing coarse mesh solutions with overkill solutions. Various problems are simulated to show the capability of the method. Our methodology provides a means of constructing unconditionallymore » stable numerical schemes for nonlinear non-convex hyperbolic systems of conservation laws.« less

Finite-element lattice Boltzmann simulations of contact line dynamics

NASA Astrophysics Data System (ADS)

Matin, Rastin; Krzysztof Misztal, Marek; Hernández-García, Anier; Mathiesen, Joachim

2018-01-01

The lattice Boltzmann method has become one of the standard techniques for simulating a wide range of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the traditional lattice Boltzmann method to regular lattices. Alternative off-lattice Boltzmann schemes exist for both single- and multiphase flows that decouple the velocity discretization from the underlying spatial grid. The current study extends the applicability of these off-lattice methods by introducing a finite element formulation that enables simulating contact line dynamics for partially wetting fluids. This work exemplifies the implementation of the scheme and furthermore presents benchmark experiments that show the scheme reduces spurious currents at the liquid-vapor interface by at least two orders of magnitude compared to a nodal implementation and allows for predicting the equilibrium states accurately in the range of moderate contact angles.

A new hybrid numerical scheme for modelling elastodynamics in unbounded media with near-source heterogeneities

NASA Astrophysics Data System (ADS)

Hajarolasvadi, Setare; Elbanna, Ahmed E.

2017-11-01

The finite difference (FD) and the spectral boundary integral (SBI) methods have been used extensively to model spontaneously-propagating shear cracks in a variety of engineering and geophysical applications. In this paper, we propose a new modelling approach in which these two methods are combined through consistent exchange of boundary tractions and displacements. Benefiting from the flexibility of FD and the efficiency of SBI methods, the proposed hybrid scheme will solve a wide range of problems in a computationally efficient way. We demonstrate the validity of the approach using two examples for dynamic rupture propagation: one in the presence of a low-velocity layer and the other in which off-fault plasticity is permitted. We discuss possible potential uses of the hybrid scheme in earthquake cycle simulations as well as an exact absorbing boundary condition.

On processed splitting methods and high-order actions in path-integral Monte Carlo simulations.

PubMed

Casas, Fernando

2010-10-21

Processed splitting methods are particularly well adapted to carry out path-integral Monte Carlo (PIMC) simulations: since one is mainly interested in estimating traces of operators, only the kernel of the method is necessary to approximate the thermal density matrix. Unfortunately, they suffer the same drawback as standard, nonprocessed integrators: kernels of effective order greater than two necessarily involve some negative coefficients. This problem can be circumvented, however, by incorporating modified potentials into the composition, thus rendering schemes of higher effective order. In this work we analyze a family of fourth-order schemes recently proposed in the PIMC setting, paying special attention to their linear stability properties, and justify their observed behavior in practice. We also propose a new fourth-order scheme requiring the same computational cost but with an enlarged stability interval.

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2014-01-01

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

A computerized scheme for lung nodule detection in multiprojection chest radiography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo Wei; Li Qiang; Boyce, Sarah J.

2012-04-15

Purpose: Our previous study indicated that multiprojection chest radiography could significantly improve radiologists' performance for lung nodule detection in clinical practice. In this study, the authors further verify that multiprojection chest radiography can greatly improve the performance of a computer-aided diagnostic (CAD) scheme. Methods: Our database consisted of 59 subjects, including 43 subjects with 45 nodules and 16 subjects without nodules. The 45 nodules included 7 real and 38 simulated ones. The authors developed a conventional CAD scheme and a new fusion CAD scheme to detect lung nodules. The conventional CAD scheme consisted of four steps for (1) identification ofmore » initial nodule candidates inside lungs, (2) nodule candidate segmentation based on dynamic programming, (3) extraction of 33 features from nodule candidates, and (4) false positive reduction using a piecewise linear classifier. The conventional CAD scheme processed each of the three projection images of a subject independently and discarded the correlation information between the three images. The fusion CAD scheme included the four steps in the conventional CAD scheme and two additional steps for (5) registration of all candidates in the three images of a subject, and (6) integration of correlation information between the registered candidates in the three images. The integration step retained all candidates detected at least twice in the three images of a subject and removed those detected only once in the three images as false positives. A leave-one-subject-out testing method was used for evaluation of the performance levels of the two CAD schemes. Results: At the sensitivities of 70%, 65%, and 60%, our conventional CAD scheme reported 14.7, 11.3, and 8.6 false positives per image, respectively, whereas our fusion CAD scheme reported 3.9, 1.9, and 1.2 false positives per image, and 5.5, 2.8, and 1.7 false positives per patient, respectively. The low performance of the conventional CAD scheme may be attributed to the high noise level in chest radiography, and the small size and low contrast of most nodules. Conclusions: This study indicated that the fusion of correlation information in multiprojection chest radiography can markedly improve the performance of CAD scheme for lung nodule detection.« less

TSOS and TSOS-FK hybrid methods for modelling the propagation of seismic waves

NASA Astrophysics Data System (ADS)

Ma, Jian; Yang, Dinghui; Tong, Ping; Ma, Xiao

2018-05-01

We develop a new time-space optimized symplectic (TSOS) method for numerically solving elastic wave equations in heterogeneous isotropic media. We use the phase-preserving symplectic partitioned Runge-Kutta method to evaluate the time derivatives and optimized explicit finite-difference (FD) schemes to discretize the space derivatives. We introduce the averaged medium scheme into the TSOS method to further increase its capability of dealing with heterogeneous media and match the boundary-modified scheme for implementing free-surface boundary conditions and the auxiliary differential equation complex frequency-shifted perfectly matched layer (ADE CFS-PML) non-reflecting boundaries with the TSOS method. A comparison of the TSOS method with analytical solutions and standard FD schemes indicates that the waveform generated by the TSOS method is more similar to the analytic solution and has a smaller error than other FD methods, which illustrates the efficiency and accuracy of the TSOS method. Subsequently, we focus on the calculation of synthetic seismograms for teleseismic P- or S-waves entering and propagating in the local heterogeneous region of interest. To improve the computational efficiency, we successfully combine the TSOS method with the frequency-wavenumber (FK) method and apply the ADE CFS-PML to absorb the scattered waves caused by the regional heterogeneity. The TSOS-FK hybrid method is benchmarked against semi-analytical solutions provided by the FK method for a 1-D layered model. Several numerical experiments, including a vertical cross-section of the Chinese capital area crustal model, illustrate that the TSOS-FK hybrid method works well for modelling waves propagating in complex heterogeneous media and remains stable for long-time computation. These numerical examples also show that the TSOS-FK method can tackle the converted and scattered waves of the teleseismic plane waves caused by local heterogeneity. Thus, the TSOS and TSOS-FK methods proposed in this study present an essential tool for the joint inversion of local, regional, and teleseismic waveform data.

An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems.

PubMed

Joyce, Duncan; Parnell, William J; Assier, Raphaël C; Abrahams, I David

2017-05-01

In Parnell & Abrahams (2008 Proc. R. Soc. A 464 , 1461-1482. (doi:10.1098/rspa.2007.0254)), a homogenization scheme was developed that gave rise to explicit forms for the effective antiplane shear moduli of a periodic unidirectional fibre-reinforced medium where fibres have non-circular cross section. The explicit expressions are rational functions in the volume fraction. In that scheme, a (non-dilute) approximation was invoked to determine leading-order expressions. Agreement with existing methods was shown to be good except at very high volume fractions. Here, the theory is extended in order to determine higher-order terms in the expansion. Explicit expressions for effective properties can be derived for fibres with non-circular cross section, without recourse to numerical methods. Terms appearing in the expressions are identified as being associated with the lattice geometry of the periodic fibre distribution, fibre cross-sectional shape and host/fibre material properties. Results are derived in the context of antiplane elasticity but the analogy with the potential problem illustrates the broad applicability of the method to, e.g. thermal, electrostatic and magnetostatic problems. The efficacy of the scheme is illustrated by comparison with the well-established method of asymptotic homogenization where for fibres of general cross section, the associated cell problem must be solved by some computational scheme.

An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems

PubMed Central

Joyce, Duncan

2017-01-01

In Parnell & Abrahams (2008 Proc. R. Soc. A 464, 1461–1482. (doi:10.1098/rspa.2007.0254)), a homogenization scheme was developed that gave rise to explicit forms for the effective antiplane shear moduli of a periodic unidirectional fibre-reinforced medium where fibres have non-circular cross section. The explicit expressions are rational functions in the volume fraction. In that scheme, a (non-dilute) approximation was invoked to determine leading-order expressions. Agreement with existing methods was shown to be good except at very high volume fractions. Here, the theory is extended in order to determine higher-order terms in the expansion. Explicit expressions for effective properties can be derived for fibres with non-circular cross section, without recourse to numerical methods. Terms appearing in the expressions are identified as being associated with the lattice geometry of the periodic fibre distribution, fibre cross-sectional shape and host/fibre material properties. Results are derived in the context of antiplane elasticity but the analogy with the potential problem illustrates the broad applicability of the method to, e.g. thermal, electrostatic and magnetostatic problems. The efficacy of the scheme is illustrated by comparison with the well-established method of asymptotic homogenization where for fibres of general cross section, the associated cell problem must be solved by some computational scheme. PMID:28588412

Artificial dissipation and central difference schemes for the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, Eli

1987-01-01

An artificial dissipation model, including boundary treatment, that is employed in many central difference schemes for solving the Euler and Navier-Stokes equations is discussed. Modifications of this model such as the eigenvalue scaling suggested by upwind differencing are examined. Multistage time stepping schemes with and without a multigrid method are used to investigate the effects of changes in the dissipation model on accuracy and convergence. Improved accuracy for inviscid and viscous airfoil flow is obtained with the modified eigenvalue scaling. Slower convergence rates are experienced with the multigrid method using such scaling. The rate of convergence is improved by applying a dissipation scaling function that depends on mesh cell aspect ratio.

An implict LU scheme for the Euler equations applied to arbitrary cascades. [new method of factoring

NASA Technical Reports Server (NTRS)

Buratynski, E. K.; Caughey, D. A.

1984-01-01

An implicit scheme for solving the Euler equations is derived and demonstrated. The alternating-direction implicit (ADI) technique is modified, using two implicit-operator factors corresponding to lower-block-diagonal (L) or upper-block-diagonal (U) algebraic systems which can be easily inverted. The resulting LU scheme is implemented in finite-volume mode and applied to 2D subsonic and transonic cascade flows with differing degrees of geometric complexity. The results are presented graphically and found to be in good agreement with those of other numerical and analytical approaches. The LU method is also 2.0-3.4 times faster than ADI, suggesting its value in calculating 3D problems.