Meshless Lagrangian SPH method applied to isothermal lid-driven cavity flow at low-Re numbers

NASA Astrophysics Data System (ADS)

Fraga Filho, C. A. D.; Chacaltana, J. T. A.; Pinto, W. J. N.

2018-01-01

SPH is a recent particle method applied in the cavities study, without many results available in the literature. The lid-driven cavity flow is a classic problem of the fluid mechanics, extensively explored in the literature and presenting a considerable complexity. The aim of this paper is to present a solution from the Lagrangian viewpoint for this problem. The discretization of the continuum domain is performed using the Lagrangian particles. The physical laws of mass, momentum and energy conservation are presented by the Navier-Stokes equations. A serial numerical code, written in Fortran programming language, has been used to perform the numerical simulations. The application of the SPH and comparison with the literature (mesh methods and a meshless collocation method) have been done. The positions of the primary vortex centre and the non-dimensional velocity profiles passing through the geometric centre of the cavity have been analysed. The numerical Lagrangian results showed a good agreement when compared to the results found in the literature, specifically for { Re} < 100.00 . Suggestions for improvements in the SPH model presented are listed, in the search for better results for flows with higher Reynolds numbers.

Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

NASA Astrophysics Data System (ADS)

Liu, L. H.; Tan, J. Y.

2007-02-01

A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media.

Progress on the DPASS project

NASA Astrophysics Data System (ADS)

Galkin, Sergei A.; Bogatu, I. N.; Svidzinski, V. A.

2015-11-01

A novel project to develop Disruption Prediction And Simulation Suite (DPASS) of comprehensive computational tools to predict, model, and analyze disruption events in tokamaks has been recently started at FAR-TECH Inc. DPASS will eventually address the following aspects of the disruption problem: MHD, plasma edge dynamics, plasma-wall interaction, generation and losses of runaway electrons. DPASS uses the 3-D Disruption Simulation Code (DSC-3D) as a core tool and will have a modular structure. DSC is a one fluid non-linear, time-dependent 3D MHD code to simulate dynamics of tokamak plasma surrounded by pure vacuum B-field in the real geometry of a conducting tokamak vessel. DSC utilizes the adaptive meshless technique with adaptation to the moving plasma boundary, with accurate magnetic flux conservation and resolution of the plasma surface current. DSC has also an option to neglect the plasma inertia to eliminate fast magnetosonic scale. This option can be turned on/off as needed. During Phase I of the project, two modules will be developed: the computational module for modeling the massive gas injection and main plasma respond; and the module for nanoparticle plasma jet injection as an innovative disruption mitigation scheme. We will report on this development progress. Work is supported by the US DOE SBIR grant # DE-SC0013727.

A-posteriori error estimation for the finite point method with applications to compressible flow

NASA Astrophysics Data System (ADS)

Ortega, Enrique; Flores, Roberto; Oñate, Eugenio; Idelsohn, Sergio

2017-08-01

An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

Biomechanical Model for Computing Deformations for Whole-Body Image Registration: A Meshless Approach

PubMed Central

Li, Mao; Miller, Karol; Joldes, Grand Roman; Kikinis, Ron; Wittek, Adam

2016-01-01

Patient-specific biomechanical models have been advocated as a tool for predicting deformations of soft body organs/tissue for medical image registration (aligning two sets of images) when differences between the images are large. However, complex and irregular geometry of the body organs makes generation of patient-specific biomechanical models very time consuming. Meshless discretisation has been proposed to solve this challenge. However, applications so far have been limited to 2-D models and computing single organ deformations. In this study, 3-D comprehensive patient-specific non-linear biomechanical models implemented using Meshless Total Lagrangian Explicit Dynamics (MTLED) algorithms are applied to predict a 3-D deformation field for whole-body image registration. Unlike a conventional approach which requires dividing (segmenting) the image into non-overlapping constituents representing different organs/tissues, the mechanical properties are assigned using the Fuzzy C-Means (FCM) algorithm without the image segmentation. Verification indicates that the deformations predicted using the proposed meshless approach are for practical purposes the same as those obtained using the previously validated finite element models. To quantitatively evaluate the accuracy of the predicted deformations, we determined the spatial misalignment between the registered (i.e. source images warped using the predicted deformations) and target images by computing the edge-based Hausdorff distance. The Hausdorff distance-based evaluation determines that our meshless models led to successful registration of the vast majority of the image features. PMID:26791945

GANDALF - Graphical Astrophysics code for N-body Dynamics And Lagrangian Fluids

NASA Astrophysics Data System (ADS)

Hubber, D. A.; Rosotti, G. P.; Booth, R. A.

2018-01-01

GANDALF is a new hydrodynamics and N-body dynamics code designed for investigating planet formation, star formation and star cluster problems. GANDALF is written in C++, parallelized with both OPENMP and MPI and contains a PYTHON library for analysis and visualization. The code has been written with a fully object-oriented approach to easily allow user-defined implementations of physics modules or other algorithms. The code currently contains implementations of smoothed particle hydrodynamics, meshless finite-volume and collisional N-body schemes, but can easily be adapted to include additional particle schemes. We present in this paper the details of its implementation, results from the test suite, serial and parallel performance results and discuss the planned future development. The code is freely available as an open source project on the code-hosting website github at https://github.com/gandalfcode/gandalf and is available under the GPLv2 license.

A high-order staggered meshless method for elliptic problems

DOE PAGES

Trask, Nathaniel; Perego, Mauro; Bochev, Pavel Blagoveston

2017-03-21

Here, we present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that specification of the dual metric attributes is implicit in the method's construction. Our method combines a topological gradient operator on the local primal grid with a generalized moving least squares approximation of the divergence on the local dual grid. We show that the resulting approximation of the div-grad operator maintains polynomial reproduction to arbitrary orders and yields a meshless method, which attainsmore » $$O(h^{m})$$ convergence in both $L^2$- and $H^1$-norms, similar to mixed finite element methods. We demonstrate this convergence on curvilinear domains using manufactured solutions in two and three dimensions. Application of the new method to problems with discontinuous coefficients reveals solutions that are qualitatively similar to those of compatible mesh-based discretizations.« less

Biomechanical model for computing deformations for whole-body image registration: A meshless approach.

PubMed

Li, Mao; Miller, Karol; Joldes, Grand Roman; Kikinis, Ron; Wittek, Adam

2016-12-01

Patient-specific biomechanical models have been advocated as a tool for predicting deformations of soft body organs/tissue for medical image registration (aligning two sets of images) when differences between the images are large. However, complex and irregular geometry of the body organs makes generation of patient-specific biomechanical models very time-consuming. Meshless discretisation has been proposed to solve this challenge. However, applications so far have been limited to 2D models and computing single organ deformations. In this study, 3D comprehensive patient-specific nonlinear biomechanical models implemented using meshless Total Lagrangian explicit dynamics algorithms are applied to predict a 3D deformation field for whole-body image registration. Unlike a conventional approach that requires dividing (segmenting) the image into non-overlapping constituents representing different organs/tissues, the mechanical properties are assigned using the fuzzy c-means algorithm without the image segmentation. Verification indicates that the deformations predicted using the proposed meshless approach are for practical purposes the same as those obtained using the previously validated finite element models. To quantitatively evaluate the accuracy of the predicted deformations, we determined the spatial misalignment between the registered (i.e. source images warped using the predicted deformations) and target images by computing the edge-based Hausdorff distance. The Hausdorff distance-based evaluation determines that our meshless models led to successful registration of the vast majority of the image features. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

A Novel Haptic Interactive Approach to Simulation of Surgery Cutting Based on Mesh and Meshless Models

PubMed Central

Liu, Peter X.; Lai, Pinhua; Xu, Shaoping; Zou, Yanni

2018-01-01

In the present work, the majority of implemented virtual surgery simulation systems have been based on either a mesh or meshless strategy with regard to soft tissue modelling. To take full advantage of the mesh and meshless models, a novel coupled soft tissue cutting model is proposed. Specifically, the reconstructed virtual soft tissue consists of two essential components. One is associated with surface mesh that is convenient for surface rendering and the other with internal meshless point elements that is used to calculate the force feedback during cutting. To combine two components in a seamless way, virtual points are introduced. During the simulation of cutting, the Bezier curve is used to characterize smooth and vivid incision on the surface mesh. At the same time, the deformation of internal soft tissue caused by cutting operation can be treated as displacements of the internal point elements. Furthermore, we discussed and proved the stability and convergence of the proposed approach theoretically. The real biomechanical tests verified the validity of the introduced model. And the simulation experiments show that the proposed approach offers high computational efficiency and good visual effect, enabling cutting of soft tissue with high stability. PMID:29850006

Real-time deformation of human soft tissues: A radial basis meshless 3D model based on Marquardt's algorithm.

PubMed

Zhou, Jianyong; Luo, Zu; Li, Chunquan; Deng, Mi

2018-01-01

When the meshless method is used to establish the mathematical-mechanical model of human soft tissues, it is necessary to define the space occupied by human tissues as the problem domain and the boundary of the domain as the surface of those tissues. Nodes should be distributed in both the problem domain and on the boundaries. Under external force, the displacement of the node is computed by the meshless method to represent the deformation of biological soft tissues. However, computation by the meshless method consumes too much time, which will affect the simulation of real-time deformation of human tissues in virtual surgery. In this article, the Marquardt's Algorithm is proposed to fit the nodal displacement at the problem domain's boundary and obtain the relationship between surface deformation and force. When different external forces are applied, the deformation of soft tissues can be quickly obtained based on this relationship. The analysis and discussion show that the improved model equations with Marquardt's Algorithm not only can simulate the deformation in real-time but also preserve the authenticity of the deformation model's physical properties. Copyright © 2017 Elsevier B.V. All rights reserved.

Meshless Geometric Subdivision

DTIC Science & Technology

2004-10-01

Michelangelo Youthful data set is shown on the right. for p ∈ M and with boundary condition dM (q, q) = 0 is approximated by |∇dΩrP (p, ·)| = F̃ (p), (2...dealing with more complex geometry. We apply our meshless subdivision operator to a base point set of 10088 points generated from the Michelangelo ...acknowledge the permission to use the Michelangelo point sets granted by the Stanford Computer Graphics group. The Isis, 50% decimated and non

How to model supernovae in simulations of star and galaxy formation

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.; Wetzel, Andrew; Kereš, Dušan; Faucher-Giguère, Claude-André; Quataert, Eliot; Boylan-Kolchin, Michael; Murray, Norman; Hayward, Christopher C.; El-Badry, Kareem

2018-06-01

We study the implementation of mechanical feedback from supernovae (SNe) and stellar mass loss in galaxy simulations, within the Feedback In Realistic Environments (FIRE) project. We present the FIRE-2 algorithm for coupling mechanical feedback, which can be applied to any hydrodynamics method (e.g. fixed-grid, moving-mesh, and mesh-less methods), and black hole as well as stellar feedback. This algorithm ensures manifest conservation of mass, energy, and momentum, and avoids imprinting `preferred directions' on the ejecta. We show that it is critical to incorporate both momentum and thermal energy of mechanical ejecta in a self-consistent manner, accounting for SNe cooling radii when they are not resolved. Using idealized simulations of single SN explosions, we show that the FIRE-2 algorithm, independent of resolution, reproduces converged solutions in both energy and momentum. In contrast, common `fully thermal' (energy-dump) or `fully kinetic' (particle-kicking) schemes in the literature depend strongly on resolution: when applied at mass resolution ≳100 M⊙, they diverge by orders of magnitude from the converged solution. In galaxy-formation simulations, this divergence leads to orders-of-magnitude differences in galaxy properties, unless those models are adjusted in a resolution-dependent way. We show that all models that individually time-resolve SNe converge to the FIRE-2 solution at sufficiently high resolution (<100 M⊙). However, in both idealized single-SN simulations and cosmological galaxy-formation simulations, the FIRE-2 algorithm converges much faster than other sub-grid models without re-tuning parameters.

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.

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

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

Luo, Kang; Yi, Hong-Liang, E-mail: yihongliang@hit.edu.cn; Tan, He-Ping, E-mail: tanheping@hit.edu.cn

2014-05-15

Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it ismore » considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.« less

Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2017-04-01

We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent 'eddy diffusion'. We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.

Experimental and AI-based numerical modeling of contaminant transport in porous media

NASA Astrophysics Data System (ADS)

Nourani, Vahid; Mousavi, Shahram; Sadikoglu, Fahreddin; Singh, Vijay P.

2017-10-01

This study developed a new hybrid artificial intelligence (AI)-meshless approach for modeling contaminant transport in porous media. The key innovation of the proposed approach is that both black box and physically-based models are combined for modeling contaminant transport. The effectiveness of the approach was evaluated using experimental and real world data. Artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) were calibrated to predict temporal contaminant concentrations (CCs), and the effect of noisy and de-noised data on the model performance was evaluated. Then, considering the predicted CCs at test points (TPs, in experimental study) and piezometers (in Myandoab plain) as interior conditions, the multiquadric radial basis function (MQ-RBF), as a meshless approach which solves partial differential equation (PDE) of contaminant transport in porous media, was employed to estimate the CC values at any point within the study area where there was no TP or piezometer. Optimal values of the dispersion coefficient in the advection-dispersion PDE and shape coefficient of MQ-RBF were determined using the imperialist competitive algorithm. In temporal contaminant transport modeling, de-noised data enhanced the performance of ANN and ANFIS methods in terms of the determination coefficient, up to 6 and 5%, respectively, in the experimental study and up to 39 and 18%, respectively, in the field study. Results showed that the efficiency of ANFIS-meshless model was more than ANN-meshless model up to 2 and 13% in the experimental and field studies, respectively.

A GPU-accelerated implicit meshless method for compressible flows

NASA Astrophysics Data System (ADS)

Zhang, Jia-Le; Ma, Zhi-Hua; Chen, Hong-Quan; Cao, Cheng

2018-05-01

This paper develops a recently proposed GPU based two-dimensional explicit meshless method (Ma et al., 2014) by devising and implementing an efficient parallel LU-SGS implicit algorithm to further improve the computational efficiency. The capability of the original 2D meshless code is extended to deal with 3D complex compressible flow problems. To resolve the inherent data dependency of the standard LU-SGS method, which causes thread-racing conditions destabilizing numerical computation, a generic rainbow coloring method is presented and applied to organize the computational points into different groups by painting neighboring points with different colors. The original LU-SGS method is modified and parallelized accordingly to perform calculations in a color-by-color manner. The CUDA Fortran programming model is employed to develop the key kernel functions to apply boundary conditions, calculate time steps, evaluate residuals as well as advance and update the solution in the temporal space. A series of two- and three-dimensional test cases including compressible flows over single- and multi-element airfoils and a M6 wing are carried out to verify the developed code. The obtained solutions agree well with experimental data and other computational results reported in the literature. Detailed analysis on the performance of the developed code reveals that the developed CPU based implicit meshless method is at least four to eight times faster than its explicit counterpart. The computational efficiency of the implicit method could be further improved by ten to fifteen times on the GPU.

On the Conservation and Convergence to Weak Solutions of Global Schemes

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Shu, Chi-Wang

2001-01-01

In this paper we discuss the issue of conservation and convergence to weak solutions of several global schemes, including the commonly used compact schemes and spectral collocation schemes, for solving hyperbolic conservation laws. It is shown that such schemes, if convergent boundedly almost everywhere, will converge to weak solutions. The results are extensions of the classical Lax-Wendroff theorem concerning conservative schemes.

Experimental and AI-based numerical modeling of contaminant transport in porous media.

PubMed

Nourani, Vahid; Mousavi, Shahram; Sadikoglu, Fahreddin; Singh, Vijay P

2017-10-01

This study developed a new hybrid artificial intelligence (AI)-meshless approach for modeling contaminant transport in porous media. The key innovation of the proposed approach is that both black box and physically-based models are combined for modeling contaminant transport. The effectiveness of the approach was evaluated using experimental and real world data. Artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) were calibrated to predict temporal contaminant concentrations (CCs), and the effect of noisy and de-noised data on the model performance was evaluated. Then, considering the predicted CCs at test points (TPs, in experimental study) and piezometers (in Myandoab plain) as interior conditions, the multiquadric radial basis function (MQ-RBF), as a meshless approach which solves partial differential equation (PDE) of contaminant transport in porous media, was employed to estimate the CC values at any point within the study area where there was no TP or piezometer. Optimal values of the dispersion coefficient in the advection-dispersion PDE and shape coefficient of MQ-RBF were determined using the imperialist competitive algorithm. In temporal contaminant transport modeling, de-noised data enhanced the performance of ANN and ANFIS methods in terms of the determination coefficient, up to 6 and 5%, respectively, in the experimental study and up to 39 and 18%, respectively, in the field study. Results showed that the efficiency of ANFIS-meshless model was more than ANN-meshless model up to 2 and 13% in the experimental and field studies, respectively. Copyright © 2017. Published by Elsevier B.V.

Solving Reynolds Equation in the Head-Disk Interface of Hard Disk Drives by Using a Meshless Method

NASA Astrophysics Data System (ADS)

Bao-Jun, Shi; Ting-Yi, Yang; Jian, Zhang; Yun-Dong, Du

2010-05-01

With the decrease of the flying height of the magnetic head/slider in hard disk drives (HDDs), Reynolds equation, which is used to describe the pressure distribution of the air bearing film in HDDs, must be modified to account for the rarefaction effect. Meshless local Petrov-Galerkin (MLPG) method has been successfully used in some fields of solid mechanics and fluid mechanics and was proven to be an efficacious method. No meshes are needed in MLPG method either for the interpolation of the trial and test functions, or for the integration of the weak form of the related differential equation. We solve Reynolds equation in the head-disk interface (HDI) of HDDs by using MLPG method. The pressure distribution of the air baring film by using MLPG method is obtained and compared with the exact solution and that obtained by using a least square finite difference (LSFD) method. We also investigate effects of the bearing number on the pressure value and the center of pressure based on this meshless method for different film-thickness ratios.

Coupling Finite Element and Meshless Local Petrov-Galerkin Methods for Two-Dimensional Potential Problems

NASA Technical Reports Server (NTRS)

Chen, T.; Raju, I. S.

2002-01-01

A coupled finite element (FE) method and meshless local Petrov-Galerkin (MLPG) method for analyzing two-dimensional potential problems is presented in this paper. The analysis domain is subdivided into two regions, a finite element (FE) region and a meshless (MM) region. A single weighted residual form is written for the entire domain. Independent trial and test functions are assumed in the FE and MM regions. A transition region is created between the two regions. The transition region blends the trial and test functions of the FE and MM regions. The trial function blending is achieved using a technique similar to the 'Coons patch' method that is widely used in computer-aided geometric design. The test function blending is achieved by using either FE or MM test functions on the nodes in the transition element. The technique was evaluated by applying the coupled method to two potential problems governed by the Poisson equation. The coupled method passed all the patch test problems and gave accurate solutions for the problems studied.

An energy and potential enstrophy conserving scheme for the shallow water equations. [orography effects on atmospheric circulation

NASA Technical Reports Server (NTRS)

Arakawa, A.; Lamb, V. R.

1979-01-01

A three-dimensional finite difference scheme for the solution of the shallow water momentum equations which accounts for the conservation of potential enstrophy in the flow of a homogeneous incompressible shallow atmosphere over steep topography as well as for total energy conservation is presented. The scheme is derived to be consistent with a reasonable scheme for potential vorticity advection in a long-term integration for a general flow with divergent mass flux. Numerical comparisons of the characteristics of the present potential enstrophy-conserving scheme with those of a scheme that conserves potential enstrophy only for purely horizontal nondivergent flow are presented which demonstrate the reduction of computational noise in the wind field with the enstrophy-conserving scheme and its convergence even in relatively coarse grids.

Numerical viscosity and the entropy condition for conservative difference schemes

NASA Technical Reports Server (NTRS)

Tadmor, E.

1983-01-01

Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation. In particular, entropy satisfying convergence follows for E schemes - those containing more numerical viscosity than Godunov's scheme.

IMPROVED PERFORMANCES IN SUBSONIC FLOWS OF AN SPH SCHEME WITH GRADIENTS ESTIMATED USING AN INTEGRAL APPROACH

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

Valdarnini, R., E-mail: valda@sissa.it

In this paper, we present results from a series of hydrodynamical tests aimed at validating the performance of a smoothed particle hydrodynamics (SPH) formulation in which gradients are derived from an integral approach. We specifically investigate the code behavior with subsonic flows, where it is well known that zeroth-order inconsistencies present in standard SPH make it particularly problematic to correctly model the fluid dynamics. In particular, we consider the Gresho–Chan vortex problem, the growth of Kelvin–Helmholtz instabilities, the statistics of driven subsonic turbulence and the cold Keplerian disk problem. We compare simulation results for the different tests with those obtained,more » for the same initial conditions, using standard SPH. We also compare the results with the corresponding ones obtained previously with other numerical methods, such as codes based on a moving-mesh scheme or Godunov-type Lagrangian meshless methods. We quantify code performances by introducing error norms and spectral properties of the particle distribution, in a way similar to what was done in other works. We find that the new SPH formulation exhibits strongly reduced gradient errors and outperforms standard SPH in all of the tests considered. In fact, in terms of accuracy, we find good agreement between the simulation results of the new scheme and those produced using other recently proposed numerical schemes. These findings suggest that the proposed method can be successfully applied for many astrophysical problems in which the presence of subsonic flows previously limited the use of SPH, with the new scheme now being competitive in these regimes with other numerical methods.« less

A meshless EFG-based algorithm for 3D deformable modeling of soft tissue in real-time.

PubMed

Abdi, Elahe; Farahmand, Farzam; Durali, Mohammad

2012-01-01

The meshless element-free Galerkin method was generalized and an algorithm was developed for 3D dynamic modeling of deformable bodies in real time. The efficacy of the algorithm was investigated in a 3D linear viscoelastic model of human spleen subjected to a time-varying compressive force exerted by a surgical grasper. The model remained stable in spite of the considerably large deformations occurred. There was a good agreement between the results and those of an equivalent finite element model. The computational cost, however, was much lower, enabling the proposed algorithm to be effectively used in real-time applications.

Local participation in biodiversity conservation initiatives: a comparative analysis of different models in South East Mexico.

PubMed

Méndez-López, María Elena; García-Frapolli, Eduardo; Pritchard, Diana J; Sánchez González, María Consuelo; Ruiz-Mallén, Isabel; Porter-Bolland, Luciana; Reyes-Garcia, Victoria

2014-12-01

In Mexico, biodiversity conservation is primarily implemented through three schemes: 1) protected areas, 2) payment-based schemes for environmental services, and 3) community-based conservation, officially recognized in some cases as Indigenous and Community Conserved Areas. In this paper we compare levels of local participation across conservation schemes. Through a survey applied to 670 households across six communities in Southeast Mexico, we document local participation during the creation, design, and implementation of the management plan of different conservation schemes. To analyze the data, we first calculated the frequency of participation at the three different stages mentioned, then created a participation index that characterizes the presence and relative intensity of local participation for each conservation scheme. Results showed that there is a low level of local participation across all the conservation schemes explored in this study. Nonetheless, the payment for environmental services had the highest local participation while the protected areas had the least. Our findings suggest that local participation in biodiversity conservation schemes is not a predictable outcome of a specific (community-based) model, thus implying that other factors might be important in determining local participation. This has implications on future strategies that seek to encourage local involvement in conservation. Copyright © 2014 Elsevier Ltd. All rights reserved.

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.

2003-01-01

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

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.

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.

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.

SPH simulation of free surface flow over a sharp-crested weir

NASA Astrophysics Data System (ADS)

Ferrari, Angela

2010-03-01

In this paper the numerical simulation of a free surface flow over a sharp-crested weir is presented. Since in this case the usual shallow water assumptions are not satisfied, we propose to solve the problem using the full weakly compressible Navier-Stokes equations with the Tait equation of state for water. The numerical method used consists of the new meshless Smooth Particle Hydrodynamics (SPH) formulation proposed by Ferrari et al. (2009) [8], that accurately tracks the free surface profile and provides monotone pressure fields. Thus, the unsteady evolution of the complex moving material interface (free surface) can been properly solved. The simulations involving about half a million of fluid particles have been run in parallel on two of the most powerful High Performance Computing (HPC) facilities in Europe. The validation of the results has been carried out analysing the pressure field and comparing the free surface profiles obtained with the SPH scheme with experimental measurements available in literature [18]. A very good quantitative agreement has been obtained.

A 3D smoothed particle hydrodynamics model for erosional dam-break floods

NASA Astrophysics Data System (ADS)

Amicarelli, Andrea; Kocak, Bozhana; Sibilla, Stefano; Grabe, Jürgen

2017-11-01

A mesh-less smoothed particle hydrodynamics (SPH) model for bed-load transport on erosional dam-break floods is presented. This mixture model describes both the liquid phase and the solid granular material. The model is validated on the results from several experiments on erosional dam breaks. A comparison between the present model and a 2-phase SPH model for geotechnical applications (Gadget Soil; TUHH) is performed. A demonstrative 3D erosional dam break on complex topography is investigated. The present 3D mixture model is characterised by: no tuning parameter for the mixture viscosity; consistency with the Kinetic Theory of Granular Flow; ability to reproduce the evolution of the free surface and the bed-load transport layer; applicability to practical problems in civil engineering. The numerical developments of this study are represented by a new SPH scheme for bed-load transport, which is implemented in the SPH code SPHERA v.8.0 (RSE SpA), distributed as FOSS on GitHub.

Multi-scale Eulerian model within the new National Environmental Modeling System

NASA Astrophysics Data System (ADS)

Janjic, Zavisa; Janjic, Tijana; Vasic, Ratko

2010-05-01

The unified Non-hydrostatic Multi-scale Model on the Arakawa B grid (NMMB) is being developed at NCEP within the National Environmental Modeling System (NEMS). The finite-volume horizontal differencing employed in the model preserves important properties of differential operators and conserves a variety of basic and derived dynamical and quadratic quantities. Among these, conservation of energy and enstrophy improves the accuracy of nonlinear dynamics of the model. Within further model development, advection schemes of fourth order of formal accuracy have been developed. It is argued that higher order advection schemes should not be used in the thermodynamic equation in order to preserve consistency with the second order scheme used for computation of the pressure gradient force. Thus, the fourth order scheme is applied only to momentum advection. Three sophisticated second order schemes were considered for upgrade. Two of them, proposed in Janjic(1984), conserve energy and enstrophy, but with enstrophy calculated differently. One of them conserves enstrophy as computed by the most accurate second order Laplacian operating on stream function. The other scheme conserves enstrophy as computed from the B grid velocity. The third scheme (Arakawa 1972) is arithmetic mean of the former two. It does not conserve enstrophy strictly, but it conserves other quadratic quantities that control the nonlinear energy cascade. Linearization of all three schemes leads to the same second order linear advection scheme. The second order term of the truncation error of the linear advection scheme has a special form so that it can be eliminated by simply preconditioning the advected quantity. Tests with linear advection of a cone confirm the advantage of the fourth order scheme. However, if a localized, large amplitude and high wave-number pattern is present in initial conditions, the clear advantage of the fourth order scheme disappears. In real data runs, problems with noisy data may appear due to mountains. Thus, accuracy and formal accuracy may not be synonymous. The nonlinear fourth order schemes are quadratic conservative and reduce to the Arakawa Jacobian in case of non-divergent flow. In case of general flow the conservation properties of the new momentum advection schemes impose stricter constraint on the nonlinear cascade than the original second order schemes. However, for non-divergent flow, the conservation properties of the fourth order schemes cannot be proven in the same way as those of the original second order schemes. Therefore, nonlinear tests were carried out in order to check how well the fourth order schemes control the nonlinear energy cascade. In the tests nonlinear shallow water equations are solved in a rotating rectangular domain (Janjic, 1984). The domain is covered with only 17 x 17 grid points. A diagnostic quantity is used to monitor qualitative changes in the spectrum over 116 days of simulated time. All schemes maintained meaningful solutions throughout the test. Among the second order schemes, the best result was obtained with the scheme that conserved enstrophy as computed by the second order Laplacian of the stream function. It was closely followed by the Arakawa (1972) scheme, while the remaining scheme was distant third. The fourth order schemes ranked in the same order, and were competitive throughout the experiments with their second order counterparts in preventing accumulation of energy at small scales. Finally, the impact was examined of the fourth order momentum advection on global medium range forecasts. The 500 mb anomaly correlation coefficient is used as a measure of success of the forecasts. Arakawa, A., 1972: Design of the UCLA general circulation model. Tech. Report No. 7, Department of Meteorology, University of California, Los Angeles, 116 pp. Janjic, Z. I., 1984: Non-linear advection schemes and energy cascade on semi-staggered grids. Monthly Weather Review, 112, 1234-1245.

Reconciling global mammal prioritization schemes into a strategy.

PubMed

Rondinini, Carlo; Boitani, Luigi; Rodrigues, Ana S L; Brooks, Thomas M; Pressey, Robert L; Visconti, Piero; Baillie, Jonathan E M; Baisero, Daniele; Cabeza, Mar; Crooks, Kevin R; Di Marco, Moreno; Redford, Kent H; Andelman, Sandy A; Hoffmann, Michael; Maiorano, Luigi; Stuart, Simon N; Wilson, Kerrie A

2011-09-27

The huge conservation interest that mammals attract and the large datasets that have been collected on them have propelled a diversity of global mammal prioritization schemes, but no comprehensive global mammal conservation strategy. We highlight some of the potential discrepancies between the schemes presented in this theme issue, including: conservation of species or areas, reactive and proactive conservation approaches, conservation knowledge and action, levels of aggregation of indicators of trend and scale issues. We propose that recently collected global mammal data and many of the mammal prioritization schemes now available could be incorporated into a comprehensive global strategy for the conservation of mammals. The task of developing such a strategy should be coordinated by a super-partes, authoritative institution (e.g. the International Union for Conservation of Nature, IUCN). The strategy would facilitate funding agencies, conservation organizations and national institutions to rapidly identify a number of short-term and long-term global conservation priorities, and act complementarily to achieve them.

High-resolution schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Harten, A.

1982-01-01

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

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

Meshless Local Petrov-Galerkin Euler-Bernoulli Beam Problems: A Radial Basis Function Approach

NASA Technical Reports Server (NTRS)

Raju, I. S.; Phillips, D. R.; Krishnamurthy, T.

2003-01-01

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Compactly and noncompactly supported radial basis functions are considered. The non-compactly supported cubic radial basis function is found to perform very well. Results obtained from the radial basis MLPG method are comparable to those obtained using the conventional MLPG method for mixed boundary value problems and problems with discontinuous loading conditions.

Meshless Modeling of Deformable Shapes and their Motion

PubMed Central

Adams, Bart; Ovsjanikov, Maks; Wand, Michael; Seidel, Hans-Peter; Guibas, Leonidas J.

2010-01-01

We present a new framework for interactive shape deformation modeling and key frame interpolation based on a meshless finite element formulation. Starting from a coarse nodal sampling of an object’s volume, we formulate rigidity and volume preservation constraints that are enforced to yield realistic shape deformations at interactive frame rates. Additionally, by specifying key frame poses of the deforming shape and optimizing the nodal displacements while targeting smooth interpolated motion, our algorithm extends to a motion planning framework for deformable objects. This allows reconstructing smooth and plausible deformable shape trajectories in the presence of possibly moving obstacles. The presented results illustrate that our framework can handle complex shapes at interactive rates and hence is a valuable tool for animators to realistically and efficiently model and interpolate deforming 3D shapes. PMID:24839614

Supporting local diversity of habitats and species on farmland: a comparison of three wildlife-friendly schemes.

PubMed

Hardman, Chloe J; Harrison, Dominic P G; Shaw, Pete J; Nevard, Tim D; Hughes, Brin; Potts, Simon G; Norris, Ken

2016-02-01

Restoration and maintenance of habitat diversity have been suggested as conservation priorities in farmed landscapes, but how this should be achieved and at what scale are unclear. This study makes a novel comparison of the effectiveness of three wildlife-friendly farming schemes for supporting local habitat diversity and species richness on 12 farms in England.The schemes were: (i) Conservation Grade (Conservation Grade: a prescriptive, non-organic, biodiversity-focused scheme), (ii) organic agriculture and (iii) a baseline of Entry Level Stewardship (Entry Level Stewardship: a flexible widespread government scheme). Conservation Grade farms supported a quarter higher habitat diversity at the 100-m radius scale compared to Entry Level Stewardship farms. Conservation Grade and organic farms both supported a fifth higher habitat diversity at the 250-m radius scale compared to Entry Level Stewardship farms. Habitat diversity at the 100-m and 250-m scales significantly predicted species richness of butterflies and plants. Habitat diversity at the 100-m scale also significantly predicted species richness of birds in winter and solitary bees. There were no significant relationships between habitat diversity and species richness for bumblebees or birds in summer.Butterfly species richness was significantly higher on organic farms (50% higher) and marginally higher on Conservation Grade farms (20% higher), compared with farms in Entry Level Stewardship. Organic farms supported significantly more plant species than Entry Level Stewardship farms (70% higher) but Conservation Grade farms did not (10% higher). There were no significant differences between the three schemes for species richness of bumblebees, solitary bees or birds. Policy implications . The wildlife-friendly farming schemes which included compulsory changes in management, Conservation Grade and organic, were more effective at increasing local habitat diversity and species richness compared with the less prescriptive Entry Level Stewardship scheme. We recommend that wildlife-friendly farming schemes should aim to enhance and maintain high local habitat diversity, through mechanisms such as option packages, where farmers are required to deliver a combination of several habitats.

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

Eldred, Christopher; Randall, David

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

Convergence of generalized MUSCL schemes

NASA Technical Reports Server (NTRS)

Osher, S.

1984-01-01

Semi-discrete generalizations of the second order extension of Godunov's scheme, known as the MUSCL scheme, are constructed, starting with any three point E scheme. They are used to approximate scalar conservation laws in one space dimension. For convex conservation laws, each member of a wide class is proven to be a convergent approximation to the correct physical solution. Comparison with another class of high resolution convergent schemes is made.

On the convergence of difference approximations to scalar conservation laws

NASA Technical Reports Server (NTRS)

Osher, Stanley; Tadmor, Eitan

1988-01-01

A unified treatment is given for time-explicit, two-level, second-order-resolution (SOR), total-variation-diminishing (TVD) approximations to scalar conservation laws. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced to obtain results in terms of the latter. The existence of a cell entropy inequality is discussed, and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first-order accurate in general. Convergence for TVD-SOR schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

A Meshless Method Using Radial Basis Functions for Beam Bending Problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Phillips, D. R.; Krishnamurthy, T.

2004-01-01

A meshless local Petrov-Galerkin (MLPG) method that uses radial basis functions (RBFs) as trial functions in the study of Euler-Bernoulli beam problems is presented. RBFs, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as they are in the conventional MLPG method. Compactly and noncompactly supported RBFs are considered. Noncompactly supported cubic RBFs are found to be preferable. Patch tests, mixed boundary value problems, and problems with complex loading conditions are considered. Results obtained from the radial basis MLPG method are either of comparable or better accuracy than those obtained when using the conventional MLPG method.

Meshless Solution of the Problem on the Static Behavior of Thin and Thick Laminated Composite Beams

NASA Astrophysics Data System (ADS)

Xiang, S.; Kang, G. W.

2018-03-01

For the first time, the static behavior of laminated composite beams is analyzed using the meshless collocation method based on a thin-plate-spline radial basis function. In the approximation of a partial differential equation by using a radial basis function, the shape parameter has an important role in ensuring the numerical accuracy. The choice of a shape parameter in the thin plate spline radial basis function is easier than in other radial basis functions. The governing differential equations are derived based on Reddy's third-order shear deformation theory. Numerical results are obtained for symmetric cross-ply laminated composite beams with simple-simple and cantilever boundary conditions under a uniform load. The results found are compared with available published ones and demonstrate the accuracy of the present method.

A New Hybrid Viscoelastic Soft Tissue Model based on Meshless Method for Haptic Surgical Simulation

PubMed Central

Bao, Yidong; Wu, Dongmei; Yan, Zhiyuan; Du, Zhijiang

2013-01-01

This paper proposes a hybrid soft tissue model that consists of a multilayer structure and many spheres for surgical simulation system based on meshless. To improve accuracy of the model, tension is added to the three-parameter viscoelastic structure that connects the two spheres. By using haptic device, the three-parameter viscoelastic model (TPM) produces accurate deformationand also has better stress-strain, stress relaxation and creep properties. Stress relaxation and creep formulas have been obtained by mathematical formula derivation. Comparing with the experimental results of the real pig liver which were reported by Evren et al. and Amy et al., the curve lines of stress-strain, stress relaxation and creep of TPM are close to the experimental data of the real liver. Simulated results show that TPM has better real-time, stability and accuracy. PMID:24339837

On the convergence of difference approximations to scalar conservation laws

NASA Technical Reports Server (NTRS)

Osher, S.; Tadmor, E.

1985-01-01

A unified treatment of explicit in time, two level, second order resolution, total variation diminishing, approximations to scalar conservation laws are presented. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced and results in terms of the latter are obtained. The existence of a cell entropy inequality is discussed and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first order accurate in general. Convergence for total variation diminishing-second order resolution schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

Modeling and Analysis of Energy Conservation Scheme Based on Duty Cycling in Wireless Ad Hoc Sensor Network

PubMed Central

Chung, Yun Won; Hwang, Ho Young

2010-01-01

In sensor network, energy conservation is one of the most critical issues since sensor nodes should perform a sensing task for a long time (e.g., lasting a few years) but the battery of them cannot be replaced in most practical situations. For this purpose, numerous energy conservation schemes have been proposed and duty cycling scheme is considered the most suitable power conservation technique, where sensor nodes alternate between states having different levels of power consumption. In order to analyze the energy consumption of energy conservation scheme based on duty cycling, it is essential to obtain the probability of each state. In this paper, we analytically derive steady state probability of sensor node states, i.e., sleep, listen, and active states, based on traffic characteristics and timer values, i.e., sleep timer, listen timer, and active timer. The effect of traffic characteristics and timer values on the steady state probability and energy consumption is analyzed in detail. Our work can provide sensor network operators guideline for selecting appropriate timer values for efficient energy conservation. The analytical methodology developed in this paper can be extended to other energy conservation schemes based on duty cycling with different sensor node states, without much difficulty. PMID:22219676

Second- and third-order upwind difference schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Yang, J. Y.

1984-01-01

Second- and third-order two time-level five-point explicit upwind-difference schemes are described for the numerical solution of hyperbolic systems of conservation laws and applied to the Euler equations of inviscid gas dynamics. Nonliner smoothing techniques are used to make the schemes total variation diminishing. In the method both hyperbolicity and conservation properties of the hyperbolic conservation laws are combined in a very natural way by introducing a normalized Jacobian matrix of the hyperbolic system. Entropy satisfying shock transition operators which are consistent with the upwind differencing are locally introduced when transonic shock transition is detected. Schemes thus constructed are suitable for shockcapturing calculations. The stability and the global order of accuracy of the proposed schemes are examined. Numerical experiments for the inviscid Burgers equation and the compressible Euler equations in one and two space dimensions involving various situations of aerodynamic interest are included and compared.

Second-order accurate nonoscillatory schemes for scalar conservation laws

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

1989-01-01

Explicit finite difference schemes for the computation of weak solutions of nonlinear scalar conservation laws is presented and analyzed. These schemes are uniformly second-order accurate and nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time.

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.

Two-level schemes for the advection equation

NASA Astrophysics Data System (ADS)

Vabishchevich, Petr N.

2018-06-01

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

Generating spatially optimized habitat in a trade-off between social optimality and budget efficiency.

PubMed

Drechsler, Martin

2017-02-01

Auctions have been proposed as alternatives to payments for environmental services when spatial interactions and costs are better known to landowners than to the conservation agency (asymmetric information). Recently, an auction scheme was proposed that delivers optimal conservation in the sense that social welfare is maximized. I examined the social welfare and the budget efficiency delivered by this scheme, where social welfare represents the difference between the monetized ecological benefit and the conservation cost incurred to the landowners and budget efficiency is defined as maximizing the ecological benefit for a given conservation budget. For the analysis, I considered a stylized landscape with land patches that can be used for agriculture or conservation. The ecological benefit was measured by an objective function that increases with increasing number and spatial aggregation of conserved land patches. I compared the social welfare and the budget efficiency of the auction scheme with an agglomeration payment, a policy scheme that considers spatial interactions and that was proposed recently. The auction delivered a higher level of social welfare than the agglomeration payment. However, the agglomeration payment was more efficient budgetarily than the auction, so the comparative performances of the 2 schemes depended on the chosen policy criterion-social welfare or budget efficiency. Both policy criteria are relevant for conservation. Which one should be chosen depends on the problem at hand, for example, whether social preferences should be taken into account in the decision of how much money to invest in conservation or whether the available conservation budget is strictly limited. © 2016 Society for Conservation Biology.

Free Mesh Method: fundamental conception, algorithms and accuracy study

PubMed Central

YAGAWA, Genki

2011-01-01

The finite element method (FEM) has been commonly employed in a variety of fields as a computer simulation method to solve such problems as solid, fluid, electro-magnetic phenomena and so on. However, creation of a quality mesh for the problem domain is a prerequisite when using FEM, which becomes a major part of the cost of a simulation. It is natural that the concept of meshless method has evolved. The free mesh method (FMM) is among the typical meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, especially on parallel processors. FMM is an efficient node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm for the finite element calculations. In this paper, FMM and its variation are reviewed focusing on their fundamental conception, algorithms and accuracy. PMID:21558752

Simple Test Functions in Meshless Local Petrov-Galerkin Methods

NASA Technical Reports Server (NTRS)

Raju, Ivatury S.

2016-01-01

Two meshless local Petrov-Galerkin (MLPG) methods based on two different trial functions but that use a simple linear test function were developed for beam and column problems. These methods used generalized moving least squares (GMLS) and radial basis (RB) interpolation functions as trial functions. These two methods were tested on various patch test problems. Both methods passed the patch tests successfully. Then the methods were applied to various beam vibration problems and problems involving Euler and Beck's columns. Both methods yielded accurate solutions for all problems studied. The simple linear test function offers considerable savings in computing efforts as the domain integrals involved in the weak form are avoided. The two methods based on this simple linear test function method produced accurate results for frequencies and buckling loads. Of the two methods studied, the method with radial basis trial functions is very attractive as the method is simple, accurate, and robust.

Element free Galerkin formulation of composite beam with longitudinal slip

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

Ahmad, Dzulkarnain; Mokhtaram, Mokhtazul Haizad; Badli, Mohd Iqbal

2015-05-15

Behaviour between two materials in composite beam is assumed partially interact when longitudinal slip at its interfacial surfaces is considered. Commonly analysed by the mesh-based formulation, this study used meshless formulation known as Element Free Galerkin (EFG) method in the beam partial interaction analysis, numerically. As meshless formulation implies that the problem domain is discretised only by nodes, the EFG method is based on Moving Least Square (MLS) approach for shape functions formulation with its weak form is developed using variational method. The essential boundary conditions are enforced by Langrange multipliers. The proposed EFG formulation gives comparable results, after beenmore » verified by analytical solution, thus signify its application in partial interaction problems. Based on numerical test results, the Cubic Spline and Quartic Spline weight functions yield better accuracy for the EFG formulation, compares to other proposed weight functions.« less

Burton-Miller-type singular boundary method for acoustic radiation and scattering

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Gu, Yan

2014-08-01

This paper proposes the singular boundary method (SBM) in conjunction with Burton and Miller's formulation for acoustic radiation and scattering. The SBM is a strong-form collocation boundary discretization technique using the singular fundamental solutions, which is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors (SIFs) to eliminate the singularities of the fundamental solutions. Therefore, it avoids singular numerical integrals in the boundary element method (BEM) and circumvents the troublesome placement of the fictitious boundary in the method of fundamental solutions (MFS). In the present method, we derive the SIFs of exterior Helmholtz equation by means of the SIFs of exterior Laplace equation owing to the same order of singularities between the Laplace and Helmholtz fundamental solutions. In conjunction with the Burton-Miller formulation, the SBM enhances the quality of the solution, particularly in the vicinity of the corresponding interior eigenfrequencies. Numerical illustrations demonstrate efficiency and accuracy of the present scheme on some benchmark examples under 2D and 3D unbounded domains in comparison with the analytical solutions, the boundary element solutions and Dirichlet-to-Neumann finite element solutions.

Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables

NASA Astrophysics Data System (ADS)

Zanotti, Olindo; Dumbser, Michael

2016-01-01

We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are performed in primitive variables, rather than in conserved ones. To obtain a conservative method, the underlying finite volume scheme is still written in terms of the cell averages of the conserved quantities. Therefore, our new approach performs the spatial WENO reconstruction twice: the first WENO reconstruction is carried out on the known cell averages of the conservative variables. The WENO polynomials are then used at the cell centers to compute point values of the conserved variables, which are subsequently converted into point values of the primitive variables. This is the only place where the conversion from conservative to primitive variables is needed in the new scheme. Then, a second WENO reconstruction is performed on the point values of the primitive variables to obtain piecewise high order reconstruction polynomials of the primitive variables. The reconstruction polynomials are subsequently evolved in time with a novel space-time finite element predictor that is directly applied to the governing PDE written in primitive form. The resulting space-time polynomials of the primitive variables can then be directly used as input for the numerical fluxes at the cell boundaries in the underlying conservative finite volume scheme. Hence, the number of necessary conversions from the conserved to the primitive variables is reduced to just one single conversion at each cell center. We have verified the validity of the new approach over a wide range of hyperbolic systems, including the classical Euler equations of gas dynamics, the special relativistic hydrodynamics (RHD) and ideal magnetohydrodynamics (RMHD) equations, as well as the Baer-Nunziato model for compressible two-phase flows. In all cases we have noticed that the new ADER schemes provide less oscillatory solutions when compared to ADER finite volume schemes based on the reconstruction in conserved variables, especially for the RMHD and the Baer-Nunziato equations. For the RHD and RMHD equations, the overall accuracy is improved and the CPU time is reduced by about 25 %. Because of its increased accuracy and due to the reduced computational cost, we recommend to use this version of ADER as the standard one in the relativistic framework. At the end of the paper, the new approach has also been extended to ADER-DG schemes on space-time adaptive grids (AMR).

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.

Clumpy Disks as a Testbed for Feedback-regulated Galaxy Formation

NASA Astrophysics Data System (ADS)

Mayer, Lucio; Tamburello, Valentina; Lupi, Alessandro; Keller, Ben; Wadsley, James; Madau, Piero

2016-10-01

We study the dependence of fragmentation in massive gas-rich galaxy disks at z > 1 on stellar feedback schemes and hydrodynamical solvers, employing the GASOLINE2 SPH code and the lagrangian mesh-less code GIZMO in finite mass mode. Non-cosmological galaxy disk runs with the standard delayed-cooling blastwave feedback are compared with runs adopting a new superbubble feedback, which produces winds by modeling the detailed physics of supernova-driven bubbles and leads to efficient self-regulation of star formation. We find that, with blastwave feedback, massive star-forming clumps form in comparable number and with very similar masses in GASOLINE2 and GIZMO. Typical clump masses are in the range 107-108 M ⊙, lower than in most previous works, while giant clumps with masses above 109 M ⊙ are exceedingly rare. By contrast, superbubble feedback does not produce massive star-forming bound clumps as galaxies never undergo a phase of violent disk instability. In this scheme, only sporadic, unbound star-forming overdensities lasting a few tens of Myr can arise, triggered by non-linear perturbations from massive satellite companions. We conclude that there is severe tension between explaining massive star-forming clumps observed at z > 1 primarily as the result of disk fragmentation driven by gravitational instability and the prevailing view of feedback-regulated galaxy formation. The link between disk stability and star formation efficiency should thus be regarded as a key testing ground for galaxy formation theory.

Testing hydrodynamics schemes in galaxy disc simulations

NASA Astrophysics Data System (ADS)

Few, C. G.; Dobbs, C.; Pettitt, A.; Konstandin, L.

2016-08-01

We examine how three fundamentally different numerical hydrodynamics codes follow the evolution of an isothermal galactic disc with an external spiral potential. We compare an adaptive mesh refinement code (RAMSES), a smoothed particle hydrodynamics code (SPHNG), and a volume-discretized mesh-less code (GIZMO). Using standard refinement criteria, we find that RAMSES produces a disc that is less vertically concentrated and does not reach such high densities as the SPHNG or GIZMO runs. The gas surface density in the spiral arms increases at a lower rate for the RAMSES simulations compared to the other codes. There is also a greater degree of substructure in the SPHNG and GIZMO runs and secondary spiral arms are more pronounced. By resolving the Jeans length with a greater number of grid cells, we achieve more similar results to the Lagrangian codes used in this study. Other alterations to the refinement scheme (adding extra levels of refinement and refining based on local density gradients) are less successful in reducing the disparity between RAMSES and SPHNG/GIZMO. Although more similar, SPHNG displays different density distributions and vertical mass profiles to all modes of GIZMO (including the smoothed particle hydrodynamics version). This suggests differences also arise which are not intrinsic to the particular method but rather due to its implementation. The discrepancies between codes (in particular, the densities reached in the spiral arms) could potentially result in differences in the locations and time-scales for gravitational collapse, and therefore impact star formation activity in more complex galaxy disc simulations.

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.

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.

Meshless deformable models for 3D cardiac motion and strain analysis from tagged MRI.

PubMed

Wang, Xiaoxu; Chen, Ting; Zhang, Shaoting; Schaerer, Joël; Qian, Zhen; Huh, Suejung; Metaxas, Dimitris; Axel, Leon

2015-01-01

Tagged magnetic resonance imaging (TMRI) provides a direct and noninvasive way to visualize the in-wall deformation of the myocardium. Due to the through-plane motion, the tracking of 3D trajectories of the material points and the computation of 3D strain field call for the necessity of building 3D cardiac deformable models. The intersections of three stacks of orthogonal tagging planes are material points in the myocardium. With these intersections as control points, 3D motion can be reconstructed with a novel meshless deformable model (MDM). Volumetric MDMs describe an object as point cloud inside the object boundary and the coordinate of each point can be written in parametric functions. A generic heart mesh is registered on the TMRI with polar decomposition. A 3D MDM is generated and deformed with MR image tagging lines. Volumetric MDMs are deformed by calculating the dynamics function and minimizing the local Laplacian coordinates. The similarity transformation of each point is computed by assuming its neighboring points are making the same transformation. The deformation is computed iteratively until the control points match the target positions in the consecutive image frame. The 3D strain field is computed from the 3D displacement field with moving least squares. We demonstrate that MDMs outperformed the finite element method and the spline method with a numerical phantom. Meshless deformable models can track the trajectory of any material point in the myocardium and compute the 3D strain field of any particular area. The experimental results on in vivo healthy and patient heart MRI show that the MDM can fully recover the myocardium motion in three dimensions. Copyright © 2014. Published by Elsevier Inc.

Meshless deformable models for 3D cardiac motion and strain analysis from tagged MRI

PubMed Central

Wang, Xiaoxu; Chen, Ting; Zhang, Shaoting; Schaerer, Joël; Qian, Zhen; Huh, Suejung; Metaxas, Dimitris; Axel, Leon

2016-01-01

Tagged magnetic resonance imaging (TMRI) provides a direct and noninvasive way to visualize the in-wall deformation of the myocardium. Due to the through-plane motion, the tracking of 3D trajectories of the material points and the computation of 3D strain field call for the necessity of building 3D cardiac deformable models. The intersections of three stacks of orthogonal tagging planes are material points in the myocardium. With these intersections as control points, 3D motion can be reconstructed with a novel meshless deformable model (MDM). Volumetric MDMs describe an object as point cloud inside the object boundary and the coordinate of each point can be written in parametric functions. A generic heart mesh is registered on the TMRI with polar decomposition. A 3D MDM is generated and deformed with MR image tagging lines. Volumetric MDMs are deformed by calculating the dynamics function and minimizing the local Laplacian coordinates. The similarity transformation of each point is computed by assuming its neighboring points are making the same transformation. The deformation is computed iteratively until the control points match the target positions in the consecutive image frame. The 3D strain field is computed from the 3D displacement field with moving least squares. We demonstrate that MDMs outperformed the finite element method and the spline method with a numerical phantom. Meshless deformable models can track the trajectory of any material point in the myocardium and compute the 3D strain field of any particular area. The experimental results on in vivo healthy and patient heart MRI show that the MDM can fully recover the myocardium motion in three dimensions. PMID:25157446

A meshless approach to thermomechanics of DC casting of aluminium billets

NASA Astrophysics Data System (ADS)

Mavrič, B.; Šarler, B.

2016-03-01

The ability to model thermomechanics in DC casting is important due to the technological challenges caused by physical phenomena such as different ingot distortions, cracking, hot tearing and residual stress. Many thermomechanical models already exist and usually take into account three contributions: elastic, thermal expansion, and viscoplastic to model the mushy zone. These models are, in a vast majority, solved by the finite element method. In the present work the elastic model that accounts for linear thermal expansion is considered. The method used for solving the model is of a novel meshless type and extends our previous meshless attempts in solving fluid mechanics problems. The solution to the problem is constructed using collocation on the overlapping subdomains, which are composed of computational nodes. Multiquadric radial basis functions, augmented by monomials, are used for the displacement interpolation. The interpolation is constructed in such a manner that it readily satisfies the boundary conditions. The discretization results in construction of a global square sparse matrix representing the system of linear equations for the displacement field. The developed method has many advantages. The system of equations can be easily constructed and efficiently solved. There is no need to perform expensive meshing of the domain and the formulation of the method is similar in two and three dimensions. Since no meshing is required, the nodes can easily be added or removed, which allows for efficient adaption of the node arrangement density. The order of convergence, estimated through an analytically solvable test, can be adjusted through the number of interpolation nodes in the subdomain, with 6 nodes being enough for the second order convergence. Simulations of axisymmetric mechanical problems, associated with low frequency electromagnetic DC casting are presented.

The discrete one-sided Lipschitz condition for convex scalar conservation laws

NASA Technical Reports Server (NTRS)

Brenier, Yann; Osher, Stanley

1986-01-01

Physical solutions to convex scalar conservation laws satisfy a one-sided Lipschitz condition (OSLC) that enforces both the entropy condition and their variation boundedness. Consistency with this condition is therefore desirable for a numerical scheme and was proved for both the Godunov and the Lax-Friedrichs scheme--also, in a weakened version, for the Roe scheme, all of them being only first order accurate. A new, fully second order scheme is introduced here, which is consistent with the OSLC. The modified equation is considered and shows interesting features. Another second order scheme is then considered and numerical results are discussed.

A class of renormalised meshless Laplacians for boundary value problems

NASA Astrophysics Data System (ADS)

Basic, Josip; Degiuli, Nastia; Ban, Dario

2018-02-01

A meshless approach to approximating spatial derivatives on scattered point arrangements is presented in this paper. Three various derivations of approximate discrete Laplace operator formulations are produced using the Taylor series expansion and renormalised least-squares correction of the first spatial derivatives. Numerical analyses are performed for the introduced Laplacian formulations, and their convergence rate and computational efficiency are examined. The tests are conducted on regular and highly irregular scattered point arrangements. The results are compared to those obtained by the smoothed particle hydrodynamics method and the finite differences method on a regular grid. Finally, the strong form of various Poisson and diffusion equations with Dirichlet or Robin boundary conditions are solved in two and three dimensions by making use of the introduced operators in order to examine their stability and accuracy for boundary value problems. The introduced Laplacian operators perform well for highly irregular point distribution and offer adequate accuracy for mesh and mesh-free numerical methods that require frequent movement of the grid or point cloud.

High Performance Computing of Meshless Time Domain Method on Multi-GPU Cluster

NASA Astrophysics Data System (ADS)

Ikuno, Soichiro; Nakata, Susumu; Hirokawa, Yuta; Itoh, Taku

2015-01-01

High performance computing of Meshless Time Domain Method (MTDM) on multi-GPU using the supercomputer HA-PACS (Highly Accelerated Parallel Advanced system for Computational Sciences) at University of Tsukuba is investigated. Generally, the finite difference time domain (FDTD) method is adopted for the numerical simulation of the electromagnetic wave propagation phenomena. However, the numerical domain must be divided into rectangle meshes, and it is difficult to adopt the problem in a complexed domain to the method. On the other hand, MTDM can be easily adept to the problem because MTDM does not requires meshes. In the present study, we implement MTDM on multi-GPU cluster to speedup the method, and numerically investigate the performance of the method on multi-GPU cluster. To reduce the computation time, the communication time between the decomposed domain is hided below the perfect matched layer (PML) calculation procedure. The results of computation show that speedup of MTDM on 128 GPUs is 173 times faster than that of single CPU calculation.

Restoration of the contact surface in FORCE-type centred schemes I: Homogeneous two-dimensional shallow water equations

NASA Astrophysics Data System (ADS)

Canestrelli, Alberto; Toro, Eleuterio F.

2012-10-01

Recently, the FORCE centred scheme for conservative hyperbolic multi-dimensional systems has been introduced in [34] and has been applied to Euler and relativistic MHD equations, solved on unstructured meshes. In this work we propose a modification of the FORCE scheme, named FORCE-Contact, that provides improved resolution of contact and shear waves. This paper presents the technique in full detail as applied to the two-dimensional homogeneous shallow water equations. The improvements due to the new method are particularly evident when an additional equation is solved for a tracer, since the modified scheme exactly resolves isolated and steady contact discontinuities. The improvement is considerable also for slowly moving contact discontinuities, for shear waves and for steady states in meandering channels. For these types of flow fields, the numerical results provided by the new FORCE-Contact scheme are comparable with, and sometimes better than, the results obtained from upwind schemes, such as Roes scheme for example. In a companion paper, a similar approach to restoring the missing contact wave and preserving well-balanced properties for non-conservative one- and two-layer shallow water equations is introduced. However, the procedure is general and it is in principle applicable to other multidimensional hyperbolic systems in conservative and non-conservative form, such as the Euler equations for compressible gas dynamics.

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.

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

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

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

Recovery Schemes for Primitive Variables in General-relativistic Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Siegel, Daniel M.; Mösta, Philipp; Desai, Dhruv; Wu, Samantha

2018-05-01

General-relativistic magnetohydrodynamic (GRMHD) simulations are an important tool to study a variety of astrophysical systems such as neutron star mergers, core-collapse supernovae, and accretion onto compact objects. A conservative GRMHD scheme numerically evolves a set of conservation equations for “conserved” quantities and requires the computation of certain primitive variables at every time step. This recovery procedure constitutes a core part of any conservative GRMHD scheme and it is closely tied to the equation of state (EOS) of the fluid. In the quest to include nuclear physics, weak interactions, and neutrino physics, state-of-the-art GRMHD simulations employ finite-temperature, composition-dependent EOSs. While different schemes have individually been proposed, the recovery problem still remains a major source of error, failure, and inefficiency in GRMHD simulations with advanced microphysics. The strengths and weaknesses of the different schemes when compared to each other remain unclear. Here we present the first systematic comparison of various recovery schemes used in different dynamical spacetime GRMHD codes for both analytic and tabulated microphysical EOSs. We assess the schemes in terms of (i) speed, (ii) accuracy, and (iii) robustness. We find large variations among the different schemes and that there is not a single ideal scheme. While the computationally most efficient schemes are less robust, the most robust schemes are computationally less efficient. More robust schemes may require an order of magnitude more calls to the EOS, which are computationally expensive. We propose an optimal strategy of an efficient three-dimensional Newton–Raphson scheme and a slower but more robust one-dimensional scheme as a fall-back.

High order entropy conservative central schemes for wide ranges of compressible gas dynamics and MHD flows

NASA Astrophysics Data System (ADS)

Sjögreen, Björn; Yee, H. C.

2018-07-01

The Sjogreen and Yee [31] high order entropy conservative numerical method for compressible gas dynamics is extended to include discontinuities and also extended to equations of ideal magnetohydrodynamics (MHD). The basic idea is based on Tadmor's [40] original work for inviscid perfect gas flows. For the MHD four formulations of the MHD are considered: (a) the conservative MHD, (b) the Godunov [14] non-conservative form, (c) the Janhunen [19] - MHD with magnetic field source terms, and (d) a MHD with source terms by Brackbill and Barnes [5]. Three forms of the high order entropy numerical fluxes for the MHD in the finite difference framework are constructed. They are based on the extension of the low order form of Chandrashekar and Klingenberg [9], and two forms with modifications of the Winters and Gassner [49] numerical fluxes. For flows containing discontinuities and multiscale turbulence fluctuations the high order entropy conservative numerical fluxes as the new base scheme under the Yee and Sjogreen [31] and Kotov et al. [21,22] high order nonlinear filter approach is developed. The added nonlinear filter step on the high order centered entropy conservative spatial base scheme is only utilized at isolated computational regions, while maintaining high accuracy almost everywhere for long time integration of unsteady flows and DNS and LES of turbulence computations. Representative test cases for both smooth flows and problems containing discontinuities for the gas dynamics and the ideal MHD are included. The results illustrate the improved stability by using the high order entropy conservative numerical flux as the base scheme instead of the pure high order central scheme.

Effect of different sampling schemes on the spatial placement of conservation reserves in Utah, USA

USGS Publications Warehouse

Bassett, S.D.; Edwards, T.C.

2003-01-01

We evaluated the effect of three different sampling schemes used to organize spatially explicit biological information had on the spatial placement of conservation reserves in Utah, USA. The three sampling schemes consisted of a hexagon representation developed by the EPA/EMAP program (statistical basis), watershed boundaries (ecological), and the current county boundaries of Utah (socio-political). Four decision criteria were used to estimate effects, including amount of area, length of edge, lowest number of contiguous reserves, and greatest number of terrestrial vertebrate species covered. A fifth evaluation criterion was the effect each sampling scheme had on the ability of the modeled conservation reserves to cover the six major ecoregions found in Utah. Of the three sampling schemes, county boundaries covered the greatest number of species, but also created the longest length of edge and greatest number of reserves. Watersheds maximized species coverage using the least amount of area. Hexagons and watersheds provide the least amount of edge and fewest number of reserves. Although there were differences in area, edge and number of reserves among the sampling schemes, all three schemes covered all the major ecoregions in Utah and their inclusive biodiversity. ?? 2003 Elsevier Science Ltd. All rights reserved.

Path length differencing and energy conservation of the S[sub N] Boltzmann/Spencer-Lewis equation

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

Filippone, W.L.; Monahan, S.P.

It is shown that the S[sub N] Boltzmann/Spencer-Lewis equations conserve energy locally if and only if they satisfy particle balance and diamond differencing is used in path length. In contrast, the spatial differencing schemes have no bearing on the energy balance. Energy is conserved globally if it is conserved locally and the multigroup cross sections are energy conserving. Although the coupled electron-photon cross sections generated by CEPXS conserve particles and charge, they do not precisely conserve energy. It is demonstrated that these cross sections can be adjusted such that particles, charge, and energy are conserved. Finally, since a conventional negativemore » flux fixup destroys energy balance when applied to path legend, a modified fixup scheme that does not is presented.« less

Numerical treatment for solving two-dimensional space-fractional advection-dispersion equation using meshless method

NASA Astrophysics Data System (ADS)

Cheng, Rongjun; Sun, Fengxin; Wei, Qi; Wang, Jufeng

2018-02-01

Space-fractional advection-dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann-Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

The a(3) Scheme--A Fourth-Order Space-Time Flux-Conserving and Neutrally Stable CESE Solver

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

2008-01-01

The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a non-dissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To initiate a systematic CESE development of high order schemes, in this paper we provide a thorough discussion on the structure, consistency, stability, phase error, and accuracy of a new 4th-order space-time flux-conserving and neutrally stable CESE solver of an 1D scalar advection equation. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and three points at the lower time level. Because it is associated with three independent mesh variables (the numerical analogues of the dependent variable and its 1st-order and 2ndorder spatial derivatives, respectively) and three equations per mesh point, the new scheme is referred to as the a(3) scheme. Through the von Neumann analysis, it is shown that the a(3) scheme is stable if and only if the Courant number is less than 0.5. Moreover, it is established numerically that the a(3) scheme is 4th-order accurate.

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.

On recontamination and directional-bias problems in Monte Carlo simulation of PDF turbulence models. [probability density function

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.

1992-01-01

Turbulent combustion can not be simulated adequately by conventional moment closure turbulent models. The probability density function (PDF) method offers an attractive alternative: in a PDF model, the chemical source terms are closed and do not require additional models. Because the number of computational operations grows only linearly in the Monte Carlo scheme, it is chosen over finite differencing schemes. A grid dependent Monte Carlo scheme following J.Y. Chen and W. Kollmann has been studied in the present work. It was found that in order to conserve the mass fractions absolutely, one needs to add further restrictions to the scheme, namely alpha(sub j) + gamma(sub j) = alpha(sub j - 1) + gamma(sub j + 1). A new algorithm was devised that satisfied this restriction in the case of pure diffusion or uniform flow problems. Using examples, it is shown that absolute conservation can be achieved. Although for non-uniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.

Conservative properties of finite difference schemes for incompressible flow

NASA Technical Reports Server (NTRS)

Morinishi, Youhei

1995-01-01

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.

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.

CLUMPY DISKS AS A TESTBED FOR FEEDBACK-REGULATED GALAXY FORMATION

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

Mayer, Lucio; Tamburello, Valentina; Lupi, Alessandro

2016-10-10

We study the dependence of fragmentation in massive gas-rich galaxy disks at z >1 on stellar feedback schemes and hydrodynamical solvers, employing the GASOLINE2 SPH code and the lagrangian mesh-less code GIZMO in finite mass mode. Non-cosmological galaxy disk runs with the standard delayed-cooling blastwave feedback are compared with runs adopting a new superbubble feedback, which produces winds by modeling the detailed physics of supernova-driven bubbles and leads to efficient self-regulation of star formation. We find that, with blastwave feedback, massive star-forming clumps form in comparable number and with very similar masses in GASOLINE2 and GIZMO. Typical clump masses aremore » in the range 10{sup 7}–10{sup 8} M {sub ⊙}, lower than in most previous works, while giant clumps with masses above 10{sup 9} M {sub ⊙} are exceedingly rare. By contrast, superbubble feedback does not produce massive star-forming bound clumps as galaxies never undergo a phase of violent disk instability. In this scheme, only sporadic, unbound star-forming overdensities lasting a few tens of Myr can arise, triggered by non-linear perturbations from massive satellite companions. We conclude that there is severe tension between explaining massive star-forming clumps observed at z >1 primarily as the result of disk fragmentation driven by gravitational instability and the prevailing view of feedback-regulated galaxy formation. The link between disk stability and star formation efficiency should thus be regarded as a key testing ground for galaxy formation theory.« less

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.

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.

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.

Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

NASA Technical Reports Server (NTRS)

Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)

2000-01-01

This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates

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

Cheng, Juan, E-mail: cheng_juan@iapcm.ac.cn; Shu, Chi-Wang, E-mail: shu@dam.brown.edu

In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, basedmore » on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.« less

A consistent and conservative scheme for MHD flows with complex boundaries on an unstructured Cartesian adaptive system

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

Zhang, Jie; Ni, Ming-Jiu, E-mail: mjni@ucas.ac.cn

2014-01-01

The numerical simulation of Magnetohydrodynamics (MHD) flows with complex boundaries has been a topic of great interest in the development of a fusion reactor blanket for the difficulty to accurately simulate the Hartmann layers and side layers along arbitrary geometries. An adaptive version of a consistent and conservative scheme has been developed for simulating the MHD flows. Besides, the present study forms the first attempt to apply the cut-cell approach for irregular wall-bounded MHD flows, which is more flexible and conveniently implemented under adaptive mesh refinement (AMR) technique. It employs a Volume-of-Fluid (VOF) approach to represent the fluid–conducting wall interfacemore » that makes it possible to solve the fluid–solid coupling magnetic problems, emphasizing at how electric field solver is implemented when conductivity is discontinuous in cut-cell. For the irregular cut-cells, the conservative interpolation technique is applied to calculate the Lorentz force at cell-center. On the other hand, it will be shown how consistent and conservative scheme is implemented on fine/coarse mesh boundaries when using AMR technique. Then, the applied numerical schemes are validated by five test simulations and excellent agreement was obtained for all the cases considered, simultaneously showed good consistency and conservative properties.« less

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.

Priority setting for government investment in forestry conservation schemes-an example from New Zealand

Treesearch

Colin L. O' Loughlin

1991-01-01

In New Zealand responsibility for funding flood protection and erosion prevention and control projects rests largely with local regional authorities. However, in 1988 Central Government decided to provide direct funding for a major forestry conservation scheme in the erosion-susceptible East Coast region. Government's investment decision was influenced by a number...

The role of agri-environment schemes in conservation and environmental management.

PubMed

Batáry, Péter; Dicks, Lynn V; Kleijn, David; Sutherland, William J

2015-08-01

Over half of the European landscape is under agricultural management and has been for millennia. Many species and ecosystems of conservation concern in Europe depend on agricultural management and are showing ongoing declines. Agri-environment schemes (AES) are designed partly to address this. They are a major source of nature conservation funding within the European Union (EU) and the highest conservation expenditure in Europe. We reviewed the structure of current AES across Europe. Since a 2003 review questioned the overall effectiveness of AES for biodiversity, there has been a plethora of case studies and meta-analyses examining their effectiveness. Most syntheses demonstrate general increases in farmland biodiversity in response to AES, with the size of the effect depending on the structure and management of the surrounding landscape. This is important in the light of successive EU enlargement and ongoing reforms of AES. We examined the change in effect size over time by merging the data sets of 3 recent meta-analyses and found that schemes implemented after revision of the EU's agri-environmental programs in 2007 were not more effective than schemes implemented before revision. Furthermore, schemes aimed at areas out of production (such as field margins and hedgerows) are more effective at enhancing species richness than those aimed at productive areas (such as arable crops or grasslands). Outstanding research questions include whether AES enhance ecosystem services, whether they are more effective in agriculturally marginal areas than in intensively farmed areas, whether they are more or less cost-effective for farmland biodiversity than protected areas, and how much their effectiveness is influenced by farmer training and advice? The general lesson from the European experience is that AES can be effective for conserving wildlife on farmland, but they are expensive and need to be carefully designed and targeted. © 2015 The Authors. Conservation Biology published by Wiley Periodicals, Inc. on behalf of Society for Conservation Biology.

Comparative Study on High-Order Positivity-preserving WENO Schemes

NASA Technical Reports Server (NTRS)

Kotov, D. V.; Yee, H. C.; Sjogreen, B.

2013-01-01

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 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. 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 WENO schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is 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 difficult 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 flow 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.

Farmers value on-farm ecosystem services as important, but what are the impediments to participation in PES schemes?

PubMed

Page, Girija; Bellotti, Bill

2015-05-15

Optimal participation in market-based instruments such as PES (payment for ecosystem services) schemes is a necessary precondition for achieving large scale cost-effective conservation goals from agricultural landscapes. However farmers' willingness to participate in voluntary conservation programmes is influenced by psychological, financial and social factors and these need to be assessed on a case-by-case basis. In this research farmers' values towards on-farm ecosystem services, motivations and perceived impediments to participation in conservation programmes are identified in two local land services regions in Australia using surveys. Results indicated that irrespective of demographics such as age, gender, years farmed, area owned and annual gross farm income, farmers valued ecosystem services important for future sustainability. Non-financial motivations had significant associations with farmer's perceptions regarding attitudes and values towards the environment and participation in conservation-related programmes. Farmer factors such as lack of awareness and unavailability of adequate information were correlated with non-participation in conservation-based programmes. In the current political context, government uncertainty regarding schemes especially around carbon sequestration and reduction was the most frequently cited impediment that could deter participation. Future research that explores willingness of farmers towards participation in various types of PES programmes developed around carbon reduction, water quality provision and biodiversity conservation, and, duration of the contract and payment levels that are attractive to the farmers will provide insights for developing farmer-friendly PES schemes in the region. Copyright © 2015 Elsevier B.V. All rights reserved.

Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.

ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions

NASA Astrophysics Data System (ADS)

Toro, E. F.; Titarev, V. A.

2005-01-01

In this paper we develop non-linear ADER schemes for time-dependent scalar linear and non-linear conservation laws in one-, two- and three-space dimensions. Numerical results of schemes of up to fifth order of accuracy in both time and space illustrate that the designed order of accuracy is achieved in all space dimensions for a fixed Courant number and essentially non-oscillatory results are obtained for solutions with discontinuities. We also present preliminary results for two-dimensional non-linear systems.

Improving Simulated Soil Moisture Fields Through Assimilation of AMSR-E Soil Moisture Retrievals with an Ensemble Kalman Filter and a Mass Conservation Constraint

NASA Technical Reports Server (NTRS)

Li, Bailing; Toll, David; Zhan, Xiwu; Cosgrove, Brian

2011-01-01

Model simulated soil moisture fields are often biased due to errors in input parameters and deficiencies in model physics. Satellite derived soil moisture estimates, if retrieved appropriately, represent the spatial mean of soil moisture in a footprint area, and can be used to reduce model bias (at locations near the surface) through data assimilation techniques. While assimilating the retrievals can reduce model bias, it can also destroy the mass balance enforced by the model governing equation because water is removed from or added to the soil by the assimilation algorithm. In addition, studies have shown that assimilation of surface observations can adversely impact soil moisture estimates in the lower soil layers due to imperfect model physics, even though the bias near the surface is decreased. In this study, an ensemble Kalman filter (EnKF) with a mass conservation updating scheme was developed to assimilate the actual value of Advanced Microwave Scanning Radiometer (AMSR-E) soil moisture retrievals to improve the mean of simulated soil moisture fields by the Noah land surface model. Assimilation results using the conventional and the mass conservation updating scheme in the Little Washita watershed of Oklahoma showed that, while both updating schemes reduced the bias in the shallow root zone, the mass conservation scheme provided better estimates in the deeper profile. The mass conservation scheme also yielded physically consistent estimates of fluxes and maintained the water budget. Impacts of model physics on the assimilation results are discussed.

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

Zhang, Ch.; Gao, X. W.; Sladek, J.

This paper reports our recent research works on crack analysis in continuously non-homogeneous and linear elastic functionally graded materials. A meshless boundary element method is developed for this purpose. Numerical examples are presented and discussed to demonstrate the efficiency and the accuracy of the present numerical method, and to show the effects of the material gradation on the crack-opening-displacements and the stress intensity factors.

Economic growth and biodiversity loss in an age of tradable permits.

PubMed

Rosales, Jon

2006-08-01

Tradable permits are increasingly becoming part of environmental policy and conservation programs. The efficacy of tradable permit schemes in addressing the root cause of environmental decline-economic growth--will not be achieved unless the schemes cap economic activity based on ecological thresholds. Lessons can be learned from the largest tradable permit scheme to date, emissions trading now being implemented with the Kyoto Protocol. The Kyoto Protocol caps neither greenhouse gas emissions at a level that will achieve climate stability nor economic growth. If patterned after the Kyoto Protocol, cap-and-trade schemes for conservation will not ameliorate biodiversity loss either because they will not address economic growth. In response to these failures to cap economic growth, professional organizations concerned about biodiversity conservation should release position statements on economic growth and ecological thresholds. The statements can then be used by policy makers to infuse these positions into the local, national, and international environmental science-policy process when these schemes are being developed. Infusing language into the science-policy process that calls for capping economic activity based on ecological thresholds represents sound conservation science. Most importantly, position statements have a greater potential to ameliorate biodiversity loss if they are created and released than if this information remains within professional organizations because there is the potential for these ideas to be enacted into law and policy.

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

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.

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

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

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

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.

7 CFR 1410.60 - Scheme or device.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 10 2014-01-01 2014-01-01 false Scheme or device. 1410.60 Section 1410.60 Agriculture... AGRICULTURE LOANS, PURCHASES, AND OTHER OPERATIONS CONSERVATION RESERVE PROGRAM § 1410.60 Scheme or device. (a) If CCC determines that a person has employed a scheme or device to defeat the purposes of this part...

7 CFR 1410.60 - Scheme or device.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 7 Agriculture 10 2011-01-01 2011-01-01 false Scheme or device. 1410.60 Section 1410.60 Agriculture... AGRICULTURE LOANS, PURCHASES, AND OTHER OPERATIONS CONSERVATION RESERVE PROGRAM § 1410.60 Scheme or device. (a) If CCC determines that a person has employed a scheme or device to defeat the purposes of this part...

7 CFR 1410.60 - Scheme or device.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 7 Agriculture 10 2012-01-01 2012-01-01 false Scheme or device. 1410.60 Section 1410.60 Agriculture... AGRICULTURE LOANS, PURCHASES, AND OTHER OPERATIONS CONSERVATION RESERVE PROGRAM § 1410.60 Scheme or device. (a) If CCC determines that a person has employed a scheme or device to defeat the purposes of this part...

7 CFR 1410.60 - Scheme or device.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Scheme or device. 1410.60 Section 1410.60 Agriculture... AGRICULTURE LOANS, PURCHASES, AND OTHER OPERATIONS CONSERVATION RESERVE PROGRAM § 1410.60 Scheme or device. (a) If CCC determines that a person has employed a scheme or device to defeat the purposes of this part...

7 CFR 1410.60 - Scheme or device.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 7 Agriculture 10 2013-01-01 2013-01-01 false Scheme or device. 1410.60 Section 1410.60 Agriculture... AGRICULTURE LOANS, PURCHASES, AND OTHER OPERATIONS CONSERVATION RESERVE PROGRAM § 1410.60 Scheme or device. (a) If CCC determines that a person has employed a scheme or device to defeat the purposes of this part...

Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state

NASA Astrophysics Data System (ADS)

Lee, Bok Jik; Toro, Eleuterio F.; Castro, Cristóbal E.; Nikiforakis, Nikolaos

2013-08-01

For the numerical simulation of detonation of condensed phase explosives, a complex equation of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Cochran-Chan (C-C) EOS, are widely used. However, when a conservative scheme is used for solving the Euler equations with such equations of state, a spurious solution across the contact discontinuity, a well known phenomenon in multi-fluid systems, arises even for single materials. In this work, we develop a generalised Osher-type scheme in an adaptive primitive-conservative framework to overcome the aforementioned difficulties. Resulting numerical solutions are compared with the exact solutions and with the numerical solutions from the Godunov method in conjunction with the exact Riemann solver for the Euler equations with Mie-Grüneisen form of equations of state, such as the JWL and the C-C equations of state. The adaptive scheme is extended to second order and its empirical convergence rates are presented, verifying second order accuracy for smooth solutions. Through a suite of several tests problems in one and two space dimensions we illustrate the failure of conservative schemes and the capability of the methods of this paper to overcome the difficulties.

Cognitive Conflict, Peers, and Volume Conservation.

ERIC Educational Resources Information Center

Renshaw, Peter D.

This study investigates the effects of a training procedure on children's conservation. Volume conservation was induced in twenty-one 8-year-old non-conserving children by a procedure that combined two sources of conflict. First, the competing schemes used in making decisions on volumes were aroused; second, the non-conserver was made aware of a…

High resolution schemes and the entropy condition

NASA Technical Reports Server (NTRS)

Osher, S.; Chakravarthy, S.

1983-01-01

A systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five point band width, approximations to scalar conservation laws, is presented. These schemes are constructed to also satisfy a single discrete entropy inequality. Thus, in the convex flux case, convergence is proven to be the unique physically correct solution. For hyperbolic systems of conservation laws, this construction is used formally to extend the first author's first order accurate scheme, and show (under some minor technical hypotheses) that limit solutions satisfy an entropy inequality. Results concerning discrete shocks, a maximum principle, and maximal order of accuracy are obtained. Numerical applications are also presented.

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

Sustainable long-term conservation of rare cattle breeds using rotational AI sires

PubMed Central

Colleau, Jean-Jacques; Avon, Laurent

2008-01-01

The development of inbreeding in rotation breeding schemes, sequentially using artificial insemination (AI) sires over generations, was investigated for a full AI scheme. Asymptotic prediction formulae of inbreeding coefficients were established when the first rotation list of AI sires (possibly related) was in use. Simulated annealing provided the optimal rotation order of sires within this list, when the sires were related. These methods were also used for subsequent rotation lists, needed by the exhaustion of semen stores for the first bulls. Simulation was carried out starting with groups of independent sires, with different sizes. To generate a yearly inbreeding rate substantially lower than 0.05% (considered to be within reach by conventional conservation schemes using frequent replacements), the results obtained showed that the number of sires should be at least 10–15 and that the same sires should be used during at least 50 years. The ultimate objective was to examine the relevance of implementing rotation in breeding schemes on the actual rare French cattle breeds under conservation. The best candidate for such a test was the Villard-de-Lans breed (27 bulls and 73 000 doses for only 340 females) and it turned out to be the best performer with an inbreeding coefficient of only 7.4% after 500 years and five different sire lists. Due to the strong requirements on semen stores and on the stability of population size, actual implementation of this kind of conservation scheme was recommended only in special ('niche') cattle populations. PMID:18558074

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

NASA Astrophysics Data System (ADS)

Li, Haochen; Sun, Jianqiang

2012-09-01

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

Central Upwind Scheme for a Compressible Two-Phase Flow Model

PubMed Central

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

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme. PMID:26039242

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

PubMed

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

2015-01-01

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

Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1997-01-01

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton- Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics. These lecture notes are basically self-contained. It is our hope that with these notes and with the help of the quoted references, the reader can understand the algorithms and code them up for applications.

Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes

NASA Astrophysics Data System (ADS)

Chertock, Alina; Cui, Shumo; Kurganov, Alexander; Özcan, Şeyma Nur; Tadmor, Eitan

2018-04-01

We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium variables combined with a well-balanced central-upwind evolution in time, which is adapted to reduce the amount of numerical viscosity when the flow is at (near) steady-state regime. We show the performance of our newly developed central-upwind scheme and demonstrate importance of perfect balance between the fluxes and gravitational forces in a series of one- and two-dimensional examples.

A new flux-conserving numerical scheme for the steady, incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.

1994-01-01

This paper is concerned with the continued development of a new numerical method, the space-time solution element (STS) method, for solving conservation laws. The present work focuses on the two-dimensional, steady, incompressible Navier-Stokes equations. Using first an integral approach, and then a differential approach, the discrete flux conservation equations presented in a recent paper are rederived. Here a simpler method for determining the flux expressions at cell interfaces is given; a systematic and rigorous derivation of the conditions used to simulate the differential form of the governing conservation law(s) is provided; necessary and sufficient conditions for a discrete approximation to satisfy a conservation law in E2 are derived; and an estimate of the local truncation error is given. A specific scheme is then constructed for the solution of the thin airfoil boundary layer problem. Numerical results are presented which demonstrate the ability of the scheme to accurately resolve the developing boundary layer and wake regions using grids which are much coarser than those employed by other numerical methods. It is shown that ten cells in the cross-stream direction are sufficient to accurately resolve the developing airfoil boundary layer.

ACCURATE ORBITAL INTEGRATION OF THE GENERAL THREE-BODY PROBLEM BASED ON THE D'ALEMBERT-TYPE SCHEME

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

Minesaki, Yukitaka

2013-03-15

We propose an accurate orbital integration scheme for the general three-body problem that retains all conserved quantities except angular momentum. The scheme is provided by an extension of the d'Alembert-type scheme for constrained autonomous Hamiltonian systems. Although the proposed scheme is merely second-order accurate, it can precisely reproduce some periodic, quasiperiodic, and escape orbits. The Levi-Civita transformation plays a role in designing the scheme.

Involution and Difference Schemes for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.

In the present paper we consider the Navier-Stokes equations for the two-dimensional viscous incompressible fluid flows and apply to these equations our earlier designed general algorithmic approach to generation of finite-difference schemes. In doing so, we complete first the Navier-Stokes equations to involution by computing their Janet basis and discretize this basis by its conversion into the integral conservation law form. Then we again complete the obtained difference system to involution with eliminating the partial derivatives and extracting the minimal Gröbner basis from the Janet basis. The elements in the obtained difference Gröbner basis that do not contain partial derivatives of the dependent variables compose a conservative difference scheme. By exploiting arbitrariness in the numerical integration approximation we derive two finite-difference schemes that are similar to the classical scheme by Harlow and Welch. Each of the two schemes is characterized by a 5×5 stencil on an orthogonal and uniform grid. We also demonstrate how an inconsistent difference scheme with a 3×3 stencil is generated by an inappropriate numerical approximation of the underlying integrals.

The Predatory Bird Monitoring Scheme: identifying chemical risks to top predators in Britain.

PubMed

Walker, Lee A; Shore, Richard F; Turk, Anthony; Pereira, M Glória; Best, Jennifer

2008-09-01

The Predatory Bird Monitoring Scheme (PBMS) is a long term (>40 y), UK-wide, exposure monitoring scheme that determines the concentration of selected pesticides and pollutants in the livers and eggs of predatory birds. This paper describes how the PBMS works, and in particular highlights some of the key scientific and policy drivers for monitoring contaminants in predatory birds and describes the specific aims, scope, and methods of the PBMS. We also present previously unpublished data that illustrates how the PBMS has been used to demonstrate the success of mitigation measures in reversing chemical-mediated impacts; identify and evaluate chemical threats to species of high conservation value; and finally to inform and refine monitoring methodologies. In addition, we discuss how such schemes can also address wider conservation needs.

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.

On the construction and application of implicit factored schemes for conservation laws. [in computational fluid dynamics

NASA Technical Reports Server (NTRS)

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

1978-01-01

Efficient, noniterative, implicit finite difference algorithms are systematically developed for nonlinear conservation laws including purely hyperbolic systems and mixed hyperbolic parabolic systems. Utilization of a rational fraction or Pade time differencing formulas, yields a direct and natural derivation of an implicit scheme in a delta form. Attention is given to advantages of the delta formation and to various properties of one- and two-dimensional algorithms.

Momentum conserving Brownian dynamics propagator for complex soft matter fluids

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

Padding, J. T.; Briels, W. J.

2014-12-28

We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution.more » We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics.« less

2005 22nd International Symposium on Ballistics. Volume 3 Thursday - Friday

DTIC Science & Technology

2005-11-18

QinetiQ; Vladimir Titarev, Eleuterio Toro , Umeritek Limited The Mechanism Analysis of Interior Ballistics of Serial Chamber Gun, Dr. Sanjiu Ying, Charge...Elements and Meshless Particles, Gordon R. Johnson and Robert A. Stryk, Network Computing Services, Inc. Experimental and Numerical Study of the...Internal Ballistics Clive R. Woodley, David Finbow, QinetiQ; Vladimir Titarev, Eleuterio Toro , Numeritek Limited 22nd International Symposium on

Simbol-X Mirror Module Thermal Shields: I-Design and X-Ray Transmission

NASA Astrophysics Data System (ADS)

Collura, A.; Barbera, M.; Varisco, S.; Basso, S.; Pareschi, G.; Tagliaferri, G.; Ayers, T.

2009-05-01

The Simbol-X mission is designed to fly in formation flight configuration. As a consequence, the telescope has both ends open to space, and thermal shielding at telescope entrance and exit is required to maintain temperature uniformity throughout the mirrors. Both mesh and meshless solutions are presently under study for the shields. We discuss the design and the X-ray transmission.

Simulation of the hot rolling of steel with direct iteration

NASA Astrophysics Data System (ADS)

Hanoglu, Umut; Šarler, Božidar

2017-10-01

In this study a simulation system based on the meshless Local Radial Basis Function Collocation Method (LRBFCM) is applied for the hot rolling of steel. Rolling is a complex, 3D, thermo-mechanical problem; however, 2D cross-sectional slices are used as computational domains that are aligned with the rolling direction and no heat flow or strain is considered in the direction that is orthogonal to the slices. For each predefined position with respect to the rolling direction, the solution procedure is repeated until the slice reaches the final rolling position. Collocation nodes are initially distributed over the domain and boundaries of the initial slice. A local solution is achieved by considering the overlapping influence domains with either 5 or 7 nodes. Radial Basis Functions (RBFs) are used for the temperature discretization in the thermal model and displacement discretization in the mechanical model. The meshless solution procedure does not require a mesh-generation algorithm in the classic sense. Strong-form mechanical and thermal models are run for each slice regarding the contact with the roll's surface. Ideal plastic material behavior is considered for the mechanical results, where the nonlinear stress-strain relation is solved with a direct iteration. The majority of the Finite Element Model (FEM) simulations, including commercial software, use a conventional Newton-Raphson algorithm. However, direct iteration is chosen here due to its better compatibility with meshless methods. In order to overcome any unforeseen stability issues, the redistribution of the nodes by Elliptic Node Generation (ENG) is applied to one or more slices throughout the simulation. The rolling simulation presented here helps the user to design, test and optimize different rolling schedules. The results can be seen minutes after the simulation's start in terms of temperature, displacement, stress and strain fields as well as important technological parameters, like the roll-separating forces, roll toque, etc. An example of a rolling simulation, in which an initial size of 110x110 mm steel is rolled to a round bar with 80 mm diameter, is shown in Fig. 3. A user-friendly computer application for industrial use is created by using the C# and .NET frameworks.

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.

Structure-preserving operators for thermal-nonequilibrium hydrodynamics

NASA Astrophysics Data System (ADS)

Shiroto, Takashi; Kawai, Soshi; Ohnishi, Naofumi

2018-07-01

Radiation hydrodynamics simulations based on a single fluid two-temperature model may violate the law of energy conservation, because the governing equations are expressed in a nonconservative formulation. In this study, we maintain the important physical requirements by employing a strategy based on the key concept that mathematical structures associated with conservative and nonconservative equations are preserved, even at the discrete level. To this end, we discretize the conservation laws and transform them using exact algebraic operations. The proposed scheme maintains global conservation errors within the round-off level. In addition, a numerical experiment concerning the shock tube problem suggests that the proposed scheme agrees well with the jump conditions at the discontinuities regulated by the Rankine-Hugoniot relationship. The generalized derivation allows us to employ arbitrary central difference, artificial dissipation, and Runge-Kutta methods.

A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows

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

Owkes, Mark, E-mail: mfc86@cornell.edu; Desjardins, Olivier

2013-09-15

The accurate conservative level set (ACLS) method of Desjardins et al. [O. Desjardins, V. Moureau, H. Pitsch, An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys. 227 (18) (2008) 8395–8416] is extended by using a discontinuous Galerkin (DG) discretization. DG allows for the scheme to have an arbitrarily high order of accuracy with the smallest possible computational stencil resulting in an accurate method with good parallel scaling. This work includes a DG implementation of the level set transport equation, which moves the level set with the flow field velocity, and a DG implementation of themore » reinitialization equation, which is used to maintain the shape of the level set profile to promote good mass conservation. A near second order converging interface curvature is obtained by following a height function methodology (common amongst volume of fluid schemes) in the context of the conservative level set. Various numerical experiments are conducted to test the properties of the method and show excellent results, even on coarse meshes. The tests include Zalesak’s disk, two-dimensional deformation of a circle, time evolution of a standing wave, and a study of the Kelvin–Helmholtz instability. Finally, this novel methodology is employed to simulate the break-up of a turbulent liquid jet.« less

2005 22nd International Symposium on Ballistics Volume 2 Wednesday

DTIC Science & Technology

2005-11-18

Information 1 Experimental and Numerical Study of the Penetration of Tungsten Carbide Into Steel Targets During High Rates of Strain John F . Moxnes...QinetiQ; Vladimir Titarev, Eleuterio Toro , Umeritek Limited The Mechanism Analysis of Interior Ballistics of Serial Chamber Gun, Dr. Sanjiu Ying, Charge...Elements and Meshless Particles, Gordon R. Johnson and Robert A. Stryk, Network Computing Services, Inc. Experimental and Numerical Study of the

Modeling RF Fields in Hot Plasmas with Parallel Full Wave Code

NASA Astrophysics Data System (ADS)

Spencer, Andrew; Svidzinski, Vladimir; Zhao, Liangji; Galkin, Sergei; Kim, Jin-Soo

2016-10-01

FAR-TECH, Inc. is developing a suite of full wave RF plasma codes. It is based on a meshless formulation in configuration space with adapted cloud of computational points (CCP) capability and using the hot plasma conductivity kernel to model the nonlocal plasma dielectric response. The conductivity kernel is calculated by numerically integrating the linearized Vlasov equation along unperturbed particle trajectories. Work has been done on the following calculations: 1) the conductivity kernel in hot plasmas, 2) a monitor function based on analytic solutions of the cold-plasma dispersion relation, 3) an adaptive CCP based on the monitor function, 4) stencils to approximate the wave equations on the CCP, 5) the solution to the full wave equations in the cold-plasma model in tokamak geometry for ECRH and ICRH range of frequencies, and 6) the solution to the wave equations using the calculated hot plasma conductivity kernel. We will present results on using a meshless formulation on adaptive CCP to solve the wave equations and on implementing the non-local hot plasma dielectric response to the wave equations. The presentation will include numerical results of wave propagation and absorption in the cold and hot tokamak plasma RF models, using DIII-D geometry and plasma parameters. Work is supported by the U.S. DOE SBIR program.

Boson expansion theory in the seniority scheme

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

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

1985-12-01

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

Linear and nonlinear properties of numerical methods for the rotating shallow water equations

NASA Astrophysics Data System (ADS)

Eldred, Chris

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. It is desirable that numerical models posses similar properties, and the prototypical example of such a scheme is the 1981 Arakawa and Lamb (AL81) staggered (C-grid) total energy and potential enstrophy conserving scheme, based on the vector invariant form of the continuous equations. However, this scheme is restricted to a subset of logically square, orthogonal grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos and others) and Discrete Exterior Calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp and others). It is also possible to obtain these properties (along with arguably superior wave dispersion properties) through the use of a collocated (Z-grid) scheme based on the vorticity-divergence form of the continuous equations. Unfortunately, existing examples of these schemes in the literature for general, spherical grids either contain computational modes; or do not conserve total energy and potential enstrophy. This dissertation extends an existing scheme for planar grids to spherical grids, through the use of Nambu brackets (as pioneered by Rick Salmon). To compare these two schemes, the linear modes (balanced states, stationary modes and propagating modes; with and without dissipation) are examined on both uniform planar grids (square, hexagonal) and quasi-uniform spherical grids (geodesic, cubed-sphere). In addition to evaluating the linear modes, the results of the two schemes applied to a set of standard shallow water test cases and a recently developed forced-dissipative turbulence test case from John Thuburn (intended to evaluate the ability the suitability of schemes as the basis for a climate model) on both hexagonal-pentagonal icosahedral grids and cubed-sphere grids are presented. Finally, some remarks and thoughts about the suitability of these two schemes as the basis for atmospheric dynamical development are given.

Energy Conservation in Optical Fibers With Distributed Brick-Walls Filters

NASA Astrophysics Data System (ADS)

Garcia, Javier; Ghozlan, Hassan; Kramer, Gerhard

2018-05-01

A band-pass filtering scheme is proposed to mitigate spectral broadening and channel coupling in the Nonlinear Schr\\"odinger (NLS) fiber optic channel. The scheme is modeled by modifying the NLS Equation to include an attenuation profile with multiple brick-wall filters centered at different frequencies. It is shown that this brick-walls profile conserves the total in-band energy of the launch signal. Furthermore, energy fluctuations between the filtered channels are characterized, and conditions on the channel spacings are derived that ensure energy conservation in each channel. The maximum spectral efficiency of such a system is derived, and a constructive rule for achieving it using Sidon sequences is provided.

Evaluating recreational hunting as an incentive for habitat conservation on private land in California

Treesearch

Luke T. Macaulay

2015-01-01

Private land plays a crucial role in the conservation of biodiversity in California, yet these lands are the least protected and most prone to environmental degradation. In 1930, Aldo Leopold recognized the potential to better conserve private land by an incentive scheme where recreational users would pay landowners for access to conserved wildlife habitat. While...

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

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.

Modular and configurable optimal sequence alignment software: Cola.

PubMed

Zamani, Neda; Sundström, Görel; Höppner, Marc P; Grabherr, Manfred G

2014-01-01

The fundamental challenge in optimally aligning homologous sequences is to define a scoring scheme that best reflects the underlying biological processes. Maximising the overall number of matches in the alignment does not always reflect the patterns by which nucleotides mutate. Efficiently implemented algorithms that can be parameterised to accommodate more complex non-linear scoring schemes are thus desirable. We present Cola, alignment software that implements different optimal alignment algorithms, also allowing for scoring contiguous matches of nucleotides in a nonlinear manner. The latter places more emphasis on short, highly conserved motifs, and less on the surrounding nucleotides, which can be more diverged. To illustrate the differences, we report results from aligning 14,100 sequences from 3' untranslated regions of human genes to 25 of their mammalian counterparts, where we found that a nonlinear scoring scheme is more consistent than a linear scheme in detecting short, conserved motifs. Cola is freely available under LPGL from https://github.com/nedaz/cola.

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.

Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme

DOE PAGES

Burton, Donald E.; Morgan, Nathaniel Ray; Charest, Marc Robert Joseph; ...

2017-11-22

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense thatmore » it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. Particularly, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. Our paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.« less

Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme

NASA Astrophysics Data System (ADS)

Burton, D. E.; Morgan, N. R.; Charest, M. R. J.; Kenamond, M. A.; Fung, J.

2018-02-01

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian-Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. In particular, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. The paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.

Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme

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

Burton, Donald E.; Morgan, Nathaniel Ray; Charest, Marc Robert Joseph

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense thatmore » it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. Particularly, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. Our paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.« less

Ecological restoration of farmland: progress and prospects.

PubMed

Wade, Mark R; Gurr, Geoff M; Wratten, Steve D

2008-02-27

Sustainable agricultural practices in conjunction with ecological restoration methods can reduce the detrimental effects of agriculture. The Society for Ecological Restoration International has produced generic guidelines for conceiving, organizing, conducting and assessing ecological restoration projects. Additionally, there are now good conceptual frameworks, guidelines and practical methods for developing ecological restoration programmes that are based on sound ecological principles and supported by empirical evidence and modelling approaches. Restoration methods must also be technically achievable and socially acceptable and spread over a range of locations. It is important to reconcile differences between methods that favour conservation and those that favour economic returns, to ensure that conservation efforts are beneficial for both landowners and biodiversity. One option for this type of mutual benefit is the use of agri-environmental schemes to provide financial incentives to landholders in exchange for providing conservation services and other benefits. However, further work is required to define and measure the effectiveness of agri-environmental schemes. The broader potential for ecological restoration to improve the sustainability of agricultural production while conserving biodiversity in farmscapes and reducing external costs is high, but there is still much to learn, particularly for the most efficient use of agri-environmental schemes to change land use practice.

Effects of weighting schemes on the identification of wildlife corridors generated with least-cost methods.

PubMed

Parks, Sean A; McKelvey, Kevin S; Schwartz, Michael K

2013-02-01

The importance of movement corridors for maintaining connectivity within metapopulations of wild animals is a cornerstone of conservation. One common approach for determining corridor locations is least-cost corridor (LCC) modeling, which uses algorithms within a geographic information system to search for routes with the lowest cumulative resistance between target locations on a landscape. However, the presentation of multiple LCCs that connect multiple locations generally assumes all corridors contribute equally to connectivity, regardless of the likelihood that animals will use them. Thus, LCCs may overemphasize seldom-used longer routes and underemphasize more frequently used shorter routes. We hypothesize that, depending on conservation objectives and available biological information, weighting individual corridors on the basis of species-specific movement, dispersal, or gene flow data may better identify effective corridors. We tested whether locations of key connectivity areas, defined as the highest 75th and 90th percentile cumulative weighted value of approximately 155,000 corridors, shift under different weighting scenarios. In addition, we quantified the amount and location of private land that intersect key connectivity areas under each weighting scheme. Some areas that appeared well connected when analyzed with unweighted corridors exhibited much less connectivity compared with weighting schemes that discount corridors with large effective distances. Furthermore, the amount and location of key connectivity areas that intersected private land varied among weighting schemes. We believe biological assumptions and conservation objectives should be explicitly incorporated to weight corridors when assessing landscape connectivity. These results are highly relevant to conservation planning because on the basis of recent interest by government agencies and nongovernmental organizations in maintaining and enhancing wildlife corridors, connectivity will likely be an important criterion for prioritization of land purchases and swaps. ©2012 Society for Conservation Biology.

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 Hermite WENO reconstruction for fourth order temporal accurate schemes based on the GRP solver for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Du, Zhifang; Li, Jiequan

2018-02-01

This paper develops a new fifth order accurate Hermite WENO (HWENO) reconstruction method for hyperbolic conservation schemes in the framework of the two-stage fourth order accurate temporal discretization in Li and Du (2016) [13]. Instead of computing the first moment of the solution additionally in the conventional HWENO or DG approach, we can directly take the interface values, which are already available in the numerical flux construction using the generalized Riemann problem (GRP) solver, to approximate the first moment. The resulting scheme is fourth order temporal accurate by only invoking the HWENO reconstruction twice so that it becomes more compact. Numerical experiments show that such compactness makes significant impact on the resolution of nonlinear waves.

Effects of preference heterogeneity among landowners on spatial conservation prioritization.

PubMed

Nielsen, Anne Sofie Elberg; Strange, Niels; Bruun, Hans Henrik; Jacobsen, Jette Bredahl

2017-06-01

The participation of private landowners in conservation is crucial to efficient biodiversity conservation. This is especially the case in settings where the share of private ownership is large and the economic costs associated with land acquisition are high. We used probit regression analysis and historical participation data to examine the likelihood of participation of Danish forest owners in a voluntary conservation program. We used the results to spatially predict the likelihood of participation of all forest owners in Denmark. We merged spatial data on the presence of forest, cadastral information on participation contracts, and individual-level socioeconomic information about the forest owners and their households. We included predicted participation in a probability model for species survival. Uninformed and informed (included land owner characteristics) models were then incorporated into a spatial prioritization for conservation of unmanaged forests. The choice models are based on sociodemographic data on the entire population of Danish forest owners and historical data on their participation in conservation schemes. Inclusion in the model of information on private landowners' willingness to supply land for conservation yielded at intermediate budget levels up to 30% more expected species coverage than the uninformed prioritization scheme. Our landowner-choice model provides an example of moving toward more implementable conservation planning. © 2016 Society for Conservation Biology.

Normalized Implicit Radial Models for Scattered Point Cloud Data without Normal Vectors

DTIC Science & Technology

2009-03-23

points by shrinking a discrete membrane, Computer Graphics Forum, Vol. 24-4, 2005, pp. 791-808 [8] Floater , M. S., Reimers, M.: Meshless...Parameterization and Surface Reconstruction, Computer Aided Geometric Design 18, 2001, pp 77-92 [9] Floater , M. S.: Parameterization of Triangulations and...Unorganized Points, In: Tutorials on Multiresolution in Geometric Modelling, A. Iske, E. Quak and M. S. Floater (eds.), Springer , 2002, pp. 287-316 [10

Smoothed Particle Hydrodynamics and its applications for multiphase flow and reactive transport in porous media

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

Tartakovsky, Alexandre M.; Trask, Nathaniel; Pan, K.

2016-03-11

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and Advection-Diffusion-Reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.

A Target Coverage Scheduling Scheme Based on Genetic Algorithms in Directional Sensor Networks

PubMed Central

Gil, Joon-Min; Han, Youn-Hee

2011-01-01

As a promising tool for monitoring the physical world, directional sensor networks (DSNs) consisting of a large number of directional sensors are attracting increasing attention. As directional sensors in DSNs have limited battery power and restricted angles of sensing range, maximizing the network lifetime while monitoring all the targets in a given area remains a challenge. A major technique to conserve the energy of directional sensors is to use a node wake-up scheduling protocol by which some sensors remain active to provide sensing services, while the others are inactive to conserve their energy. In this paper, we first address a Maximum Set Covers for DSNs (MSCD) problem, which is known to be NP-complete, and present a greedy algorithm-based target coverage scheduling scheme that can solve this problem by heuristics. This scheme is used as a baseline for comparison. We then propose a target coverage scheduling scheme based on a genetic algorithm that can find the optimal cover sets to extend the network lifetime while monitoring all targets by the evolutionary global search technique. To verify and evaluate these schemes, we conducted simulations and showed that the schemes can contribute to extending the network lifetime. Simulation results indicated that the genetic algorithm-based scheduling scheme had better performance than the greedy algorithm-based scheme in terms of maximizing network lifetime. PMID:22319387

Numerical Methods for Nonlinear Fokker-Planck Collision Operator in TEMPEST

NASA Astrophysics Data System (ADS)

Kerbel, G.; Xiong, Z.

2006-10-01

Early implementations of Fokker-Planck collision operator and moment computations in TEMPEST used low order polynomial interpolation schemes to reuse conservative operators developed for speed/pitch-angle (v, θ) coordinates. When this approach proved to be too inaccurate we developed an alternative higher order interpolation scheme for the Rosenbluth potentials and a high order finite volume method in TEMPEST (,) coordinates. The collision operator is thus generated by using the expansion technique in (v, θ) coordinates for the diffusion coefficients only, and then the fluxes for the conservative differencing are computed directly in the TEMPEST (,) coordinates. Combined with a cut-cell treatment at the turning-point boundary, this new approach is shown to have much better accuracy and conservation properties.

Conservative and bounded volume-of-fluid advection on unstructured grids

NASA Astrophysics Data System (ADS)

Ivey, Christopher B.; Moin, Parviz

2017-12-01

This paper presents a novel Eulerian-Lagrangian piecewise-linear interface calculation (PLIC) volume-of-fluid (VOF) advection method, which is three-dimensional, unsplit, and discretely conservative and bounded. The approach is developed with reference to a collocated node-based finite-volume two-phase flow solver that utilizes the median-dual mesh constructed from non-convex polyhedra. The proposed advection algorithm satisfies conservation and boundedness of the liquid volume fraction irrespective of the underlying flux polyhedron geometry, which differs from contemporary unsplit VOF schemes that prescribe topologically complicated flux polyhedron geometries in efforts to satisfy conservation. Instead of prescribing complicated flux-polyhedron geometries, which are prone to topological failures, our VOF advection scheme, the non-intersecting flux polyhedron advection (NIFPA) method, builds the flux polyhedron iteratively such that its intersection with neighboring flux polyhedra, and any other unavailable volume, is empty and its total volume matches the calculated flux volume. During each iteration, a candidate nominal flux polyhedron is extruded using an iteration dependent scalar. The candidate is subsequently intersected with the volume guaranteed available to it at the time of the flux calculation to generate the candidate flux polyhedron. The difference in the volume of the candidate flux polyhedron and the actual flux volume is used to calculate extrusion during the next iteration. The choice in nominal flux polyhedron impacts the cost and accuracy of the scheme; however, it does not impact the methods underlying conservation and boundedness. As such, various robust nominal flux polyhedron are proposed and tested using canonical periodic kinematic test cases: Zalesak's disk and two- and three-dimensional deformation. The tests are conducted on the median duals of a quadrilateral and triangular primal mesh, in two-dimensions, and on the median duals of a hexahedral, wedge and tetrahedral primal mesh, in three-dimensions. Comparisons are made with the adaptation of a conventional unsplit VOF advection scheme to our collocated node-based flow solver. Depending on the choice in the nominal flux polyhedron, the NIFPA scheme presented accuracies ranging from zeroth to second order and calculation times that differed by orders of magnitude. For the nominal flux polyhedra which demonstrate second-order accuracy on all tests and meshes, the NIFPA method's cost was comparable to the traditional topologically complex second-order accurate VOF advection scheme.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics.

PubMed

Aguayo-Ortiz, A; Mendoza, S; Olvera, D

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics

PubMed Central

Mendoza, S.; Olvera, D.

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and “Rankine-Hugoniot” jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges. PMID:29659602

Development of a discrete gas-kinetic scheme for simulation of two-dimensional viscous incompressible and compressible flows.

PubMed

Yang, L M; Shu, C; Wang, Y

2016-03-01

In this work, a discrete gas-kinetic scheme (DGKS) is presented for simulation of two-dimensional viscous incompressible and compressible flows. This scheme is developed from the circular function-based GKS, which was recently proposed by Shu and his co-workers [L. M. Yang, C. Shu, and J. Wu, J. Comput. Phys. 274, 611 (2014)]. For the circular function-based GKS, the integrals for conservation forms of moments in the infinity domain for the Maxwellian function-based GKS are simplified to those integrals along the circle. As a result, the explicit formulations of conservative variables and fluxes are derived. However, these explicit formulations of circular function-based GKS for viscous flows are still complicated, which may not be easy for the application by new users. By using certain discrete points to represent the circle in the phase velocity space, the complicated formulations can be replaced by a simple solution process. The basic requirement is that the conservation forms of moments for the circular function-based GKS can be accurately satisfied by weighted summation of distribution functions at discrete points. In this work, it is shown that integral quadrature by four discrete points on the circle, which forms the D2Q4 discrete velocity model, can exactly match the integrals. Numerical results showed that the present scheme can provide accurate numerical results for incompressible and compressible viscous flows with roughly the same computational cost as that needed by the Roe scheme.

The alpha(3) Scheme - A Fourth-Order Neutrally Stable CESE Solver

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

2007-01-01

The conservation element and solution element (CESE) development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a non-dissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new 4th-order neutrally stable CESE solver of the advection equation Theta u/Theta + alpha Theta u/Theta x = 0. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and three points at the lower time level. Because it is associated with three independent mesh variables u(sup n) (sub j), (u(sub x))(sup n) (sub j) , and (uxz)(sup n) (sub j) (the numerical analogues of u, Theta u/Theta x, and Theta(exp 2)u/Theta x(exp 2), respectively) and four equations per mesh point, the new scheme is referred to as the alpha(3) scheme. As in the case of other similar CESE neutrally stable solvers, the alpha(3) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. These forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove that the alpha(3) scheme must be neutrally stable when it is stable. Moreover it is proved rigorously that all three amplification factors of the alpha(3) scheme are of unit magnitude for all phase angles if |v| <= 1/2 (v = alpha delta t/delta x). This theoretical result is consistent with the numerical stability condition |v| <= 1/2. Through numerical experiments, it is established that the alpha(3) scheme generally is (i) 4th-order accurate for the mesh variables u(sup n) (sub j) and (ux)(sup n) (sub j); and 2nd-order accurate for (uxx)(sup n) (sub j). However, in some exceptional cases, the scheme can achieve perfect accuracy aside from round-off errors.

Reconsidering Conceptualisations of Farm Conservation Activity: The Case of Conserving Hay Meadows

ERIC Educational Resources Information Center

Riley, Mark

2006-01-01

Changes to agri-environmental policy, with an emphasis on encouraging more environmentally friendly farming practices, have been paralleled in the last two decades by a body of research into agri-environment scheme adoption. To date much of this research has considered conservation behaviour as a static issue across whole farms, and viewed…

Non-oscillatory central differencing for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Nessyahu, Haim; Tadmor, Eitan

1988-01-01

Many of the recently developed high resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block for these schemes is the averaging of an appropriate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the direction of the wind. Instead, the use of the more robust Lax-Friedrichs (LxF) solver is proposed. The main advantage is simplicity: no Riemann problems are solved and hence field-by-field decompositions are avoided. The main disadvantage is the excessive numerical viscosity typical to the LxF solver. This is compensated for by using high-resolution MUSCL-type interpolants. Numerical experiments show that the quality of results obtained by such convenient central differencing is comparable with those of the upwind schemes.

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.

Multidimensional, fully implicit, exactly conserving electromagnetic particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Chacon, Luis

2015-09-01

We discuss a new, conservative, fully implicit 2D-3V particle-in-cell algorithm for non-radiative, electromagnetic kinetic plasma simulations, based on the Vlasov-Darwin model. Unlike earlier linearly implicit PIC schemes and standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. This has been demonstrated in 1D electrostatic and electromagnetic contexts. In this study, we build on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the Darwin field and particle orbit equations for multiple species in multiple dimensions. The Vlasov-Darwin model is very attractive for PIC simulations because it avoids radiative noise issues in non-radiative electromagnetic regimes. The algorithm conserves global energy, local charge, and particle canonical-momentum exactly, even with grid packing. The nonlinear iteration is effectively accelerated with a fluid preconditioner, which allows efficient use of large timesteps, O(√{mi/me}c/veT) larger than the explicit CFL. In this presentation, we will introduce the main algorithmic components of the approach, and demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 1D and 2D. Support from the LANL LDRD program and the DOE-SC ASCR office.

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

NASA Astrophysics Data System (ADS)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

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

Computational Aeroacoustics by the Space-time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2001-01-01

In recent years, a new numerical methodology for conservation laws-the Space-Time Conservation Element and Solution Element Method (CE/SE), was developed by Dr. Chang of NASA Glenn Research Center and collaborators. In nature, the new 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 rigorous treatment of the fluxes and geometry, it is different from the existing schemes. The CE/SE scheme features: (1) space and time treated on the same footing, the integral equations of conservation laws are solve( for with second order accuracy, (2) high resolution, low dispersion and low dissipation, (3) novel, truly multi-dimensional, simple but effective non-reflecting boundary condition, (4) effortless implementation of computation, no numerical fix or parameter choice is needed, an( (5) robust enough to cover a wide spectrum of compressible flow: from weak linear acoustic waves to strong, discontinuous waves (shocks) appropriate for linear and nonlinear aeroacoustics. Currently, the CE/SE scheme has been developed to such a stage that a 3-13 unstructured CE/SE Navier-Stokes solver is already available. However, in the present paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen as a prototype and is sketched in Section 2. Then applications of the CE/SE scheme to linear, nonlinear aeroacoustics and airframe noise are depicted in Sections 3, 4, and 5 respectively to demonstrate its robustness and capability.

Mechanics of cantilever beam: Implementation and comparison of FEM and MLPG approach

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

Trobec, Roman

2016-06-08

Two weak form solution approaches for partial differential equations, the well known meshbased finite element method and the newer meshless local Petrov Galerkin method are described and compared on a standard test case - mechanics of cantilever beam. The implementation, solution accuracy and calculation complexity are addressed for both approaches. We found out that FEM is superior in most standard criteria, but MLPG has some advantages because of its flexibility that results from its general formulation.

Computational Study of Colloidal Droplet Interactions with Three Dimensional Structures

DTIC Science & Technology

2015-05-18

on the meshless SPH method for droplet impact on and sorption into a powder bed considering free surface flow above the powder bed surface ...considering free surface flow above the powder bed surface , infiltration of the liquid in the porous matrix, and the interfacial forces on the free moving...infiltration of the liquid in the porous matrix, and the interfacial forces on the free moving surface . The model has been used to study the effect of impact

MUFASA: galaxy formation simulations with meshless hydrodynamics

NASA Astrophysics Data System (ADS)

Davé, Romeel; Thompson, Robert; Hopkins, Philip F.

2016-11-01

We present the MUFASA suite of cosmological hydrodynamic simulations, which employs the GIZMO meshless finite mass (MFM) code including H2-based star formation, nine-element chemical evolution, two-phase kinetic outflows following scalings from the Feedback in Realistic Environments zoom simulations, and evolving halo mass-based quenching. Our fiducial (50 h-1 Mpc)3 volume is evolved to z = 0 with a quarter billion elements. The predicted galaxy stellar mass functions (GSMFs) reproduces observations from z = 4 → 0 to ≲ 1.2σ in cosmic variance, providing an unprecedented match to this key diagnostic. The cosmic star formation history and stellar mass growth show general agreement with data, with a strong archaeological downsizing trend such that dwarf galaxies form the majority of their stars after z ˜ 1. We run 25 and 12.5 h-1 Mpc volumes to z = 2 with identical feedback prescriptions, the latter resolving all hydrogen-cooling haloes, and the three runs display fair resolution convergence. The specific star formation rates broadly agree with data at z = 0, but are underpredicted at z ˜ 2 by a factor of 3, re-emphasizing a longstanding puzzle in galaxy evolution models. We compare runs using MFM and two flavours of smoothed particle hydrodynamics, and show that the GSMF is sensitive to hydrodynamics methodology at the ˜×2 level, which is sub-dominant to choices for parametrizing feedback.

A multiphysics and multiscale model for low frequency electromagnetic direct-chill casting

NASA Astrophysics Data System (ADS)

Košnik, N.; Guštin, A. Z.; Mavrič, B.; Šarler, B.

2016-03-01

Simulation and control of macrosegregation, deformation and grain size in low frequency electromagnetic (EM) direct-chill casting (LFEMC) is important for downstream processing. Respectively, a multiphysics and multiscale model is developed for solution of Lorentz force, temperature, velocity, concentration, deformation and grain structure of LFEMC processed aluminum alloys, with focus on axisymmetric billets. The mixture equations with lever rule, linearized phase diagram, and stationary thermoelastic solid phase are assumed, together with EM induction equation for the field imposed by the coil. Explicit diffuse approximate meshless solution procedure [1] is used for solving the EM field, and the explicit local radial basis function collocation method [2] is used for solving the coupled transport phenomena and thermomechanics fields. Pressure-velocity coupling is performed by the fractional step method [3]. The point automata method with modified KGT model is used to estimate the grain structure [4] in a post-processing mode. Thermal, mechanical, EM and grain structure outcomes of the model are demonstrated. A systematic study of the complicated influences of the process parameters can be investigated by the model, including intensity and frequency of the electromagnetic field. The meshless solution framework, with the implemented simplest physical models, will be further extended by including more sophisticated microsegregation and grain structure models, as well as a more realistic solid and solid-liquid phase rheology.

A cut-cell immersed boundary technique for fire dynamics simulation

NASA Astrophysics Data System (ADS)

Vanella, Marcos; McDermott, Randall; Forney, Glenn

2015-11-01

Fire simulation around complex geometry is gaining increasing attention in performance based design of fire protection systems, fire-structure interaction and pollutant transport in complex terrains, among others. This presentation will focus on our present effort in improving the capability of FDS (Fire Dynamics Simulator, developed at the Fire Research Division, NIST. https://github.com/firemodels/fds-smv) to represent fire scenarios around complex bodies. Velocities in the vicinity of the bodies are reconstructed using a classical immersed boundary scheme (Fadlun and co-workers, J. Comput. Phys., 161:35-60, 2000). Also, a conservative treatment of scalar transport equations (i.e. for chemical species) will be presented. In our method, discrete conservation and no penetration of species across solid boundaries are enforced using a cut-cell finite volume scheme. The small cell problem inherent to the method is tackled using explicit-implicit domain decomposition for scalar, within the FDS time integration scheme. Some details on the derivation, implementation and numerical tests of this numerical scheme will be discussed.

Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers

NASA Technical Reports Server (NTRS)

Mueller, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)

2001-01-01

A method of minimizing numerical errors, and improving nonlinear stability and accuracy associated with low Mach number computational aeroacoustics (CAA) is proposed. The method consists of two levels. From the governing equation level, we condition the Euler equations in two steps. The first step is to split the inviscid flux derivatives into a conservative and a non-conservative portion that satisfies a so called generalized energy estimate. This involves the symmetrization of the Euler equations via a transformation of variables that are functions of the physical entropy. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the second step is to reformulate the split Euler equations in perturbation form with the new unknowns as the small changes of the conservative variables with respect to their large stagnation values. From the numerical scheme level, a stable sixth-order central interior scheme with a third-order boundary schemes that satisfies the discrete analogue of the integration-by-parts procedure used in the continuous energy estimate (summation-by-parts property) is employed.

A conservative scheme of drift kinetic electrons for gyrokinetic simulation of kinetic-MHD processes in toroidal plasmas

NASA Astrophysics Data System (ADS)

Bao, J.; Liu, D.; Lin, Z.

2017-10-01

A conservative scheme of drift kinetic electrons for gyrokinetic simulations of kinetic-magnetohydrodynamic processes in toroidal plasmas has been formulated and verified. Both vector potential and electron perturbed distribution function are decomposed into adiabatic part with analytic solution and non-adiabatic part solved numerically. The adiabatic parallel electric field is solved directly from the electron adiabatic response, resulting in a high degree of accuracy. The consistency between electrostatic potential and parallel vector potential is enforced by using the electron continuity equation. Since particles are only used to calculate the non-adiabatic response, which is used to calculate the non-adiabatic vector potential through Ohm's law, the conservative scheme minimizes the electron particle noise and mitigates the cancellation problem. Linear dispersion relations of the kinetic Alfvén wave and the collisionless tearing mode in cylindrical geometry have been verified in gyrokinetic toroidal code simulations, which show that the perpendicular grid size can be larger than the electron collisionless skin depth when the mode wavelength is longer than the electron skin depth.

Comparative Analysis Of River Conservation In The United States And South Africa

EPA Science Inventory

Both the United States and South Africa are recognized for their strong and innovative approaches to the conservation of river ecosystems. These national programs possess similar driving legislation and ecoregional classification schemes supported by comprehensive monitoring prog...

Unconditionally energy stable numerical schemes for phase-field vesicle membrane model

NASA Astrophysics Data System (ADS)

Guillén-González, F.; Tierra, G.

2018-02-01

Numerical schemes to simulate the deformation of vesicles membranes via minimizing the bending energy have been widely studied in recent times due to its connection with many biological motivated problems. In this work we propose a new unconditionally energy stable numerical scheme for a vesicle membrane model that satisfies exactly the conservation of volume constraint and penalizes the surface area constraint. Moreover, we extend these ideas to present an unconditionally energy stable splitting scheme decoupling the interaction of the vesicle with a surrounding fluid. Finally, the well behavior of the proposed schemes are illustrated through several computational experiments.

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.

Computational design of the basic dynamical processes of the UCLA general circulation model

NASA Technical Reports Server (NTRS)

Arakawa, A.; Lamb, V. R.

1977-01-01

The 12-layer UCLA general circulation model encompassing troposphere and stratosphere (and superjacent 'sponge layer') is described. Prognostic variables are: surface pressure, horizontal velocity, temperature, water vapor and ozone in each layer, planetary boundary layer (PBL) depth, temperature, moisture and momentum discontinuities at PBL top, ground temperature and water storage, and mass of snow on ground. Selection of space finite-difference schemes for homogeneous incompressible flow, with/without a free surface, nonlinear two-dimensional nondivergent flow, enstrophy conserving schemes, momentum advection schemes, vertical and horizontal difference schemes, and time differencing schemes are discussed.

High-order central ENO finite-volume scheme for hyperbolic conservation laws on three-dimensional cubed-sphere grids

NASA Astrophysics Data System (ADS)

Ivan, L.; De Sterck, H.; Susanto, A.; Groth, C. P. T.

2015-02-01

A fourth-order accurate finite-volume scheme for hyperbolic conservation laws on three-dimensional (3D) cubed-sphere grids is described. The approach is based on a central essentially non-oscillatory (CENO) finite-volume method that was recently introduced for two-dimensional compressible flows and is extended to 3D geometries with structured hexahedral grids. Cubed-sphere grids feature hexahedral cells with nonplanar cell surfaces, which are handled with high-order accuracy using trilinear geometry representations in the proposed approach. Varying stencil sizes and slope discontinuities in grid lines occur at the boundaries and corners of the six sectors of the cubed-sphere grid where the grid topology is unstructured, and these difficulties are handled naturally with high-order accuracy by the multidimensional least-squares based 3D CENO reconstruction with overdetermined stencils. A rotation-based mechanism is introduced to automatically select appropriate smaller stencils at degenerate block boundaries, where fewer ghost cells are available and the grid topology changes, requiring stencils to be modified. Combining these building blocks results in a finite-volume discretization for conservation laws on 3D cubed-sphere grids that is uniformly high-order accurate in all three grid directions. While solution-adaptivity is natural in the multi-block setting of our code, high-order accurate adaptive refinement on cubed-sphere grids is not pursued in this paper. The 3D CENO scheme is an accurate and robust solution method for hyperbolic conservation laws on general hexahedral grids that is attractive because it is inherently multidimensional by employing a K-exact overdetermined reconstruction scheme, and it avoids the complexity of considering multiple non-central stencil configurations that characterizes traditional ENO schemes. Extensive numerical tests demonstrate fourth-order convergence for stationary and time-dependent Euler and magnetohydrodynamic flows on cubed-sphere grids, and robustness against spurious oscillations at 3D shocks. Performance tests illustrate efficiency gains that can be potentially achieved using fourth-order schemes as compared to second-order methods for the same error level. Applications on extended cubed-sphere grids incorporating a seventh root block that discretizes the interior of the inner sphere demonstrate the versatility of the spatial discretization method.

HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Gammie, Charles, F.; McKinney, Jonathan C.; Tóth, Gábor

2012-09-01

HARM uses a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van Leer scheme. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence-free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. On smooth flows HARM converges at second order.

Recycling ground water in Waushara County, Wisconsin : resource management for cold-water fish hatcheries

USGS Publications Warehouse

Novitzki, R.P.

1976-01-01

Other recharge-recycling schemes can also be evaluated. Estimating the recycling efficiency (of recharge ponds, trenches, spreading areas, or irrigated fields) provides a basis for predicting water-level declines, the concentration of conservative ions (conservative in the sense that no reaction other than mixing occurs to change the character of the ion being considered) in the water supply and in the regional ground-water system, and the temperature of the water supply. Hatchery development and management schemes can be chosen to optimize hatchery productivity or minimize operation costs while protecting the ground-water system.

An analytical particle mover for the charge- and energy-conserving, nonlinearly implicit, electrostatic particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2013-08-01

We propose a 1D analytical particle mover for the recent charge- and energy-conserving electrostatic particle-in-cell (PIC) algorithm in Ref. [G. Chen, L. Chacón, D.C. Barnes, An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm, Journal of Computational Physics 230 (2011) 7018-7036]. The approach computes particle orbits exactly for a given piece-wise linear electric field. The resulting PIC algorithm maintains the exact charge and energy conservation properties of the original algorithm, but with improved performance (both in efficiency and robustness against the number of particles and timestep). We demonstrate the advantageous properties of the scheme with a challenging multiscale numerical test case, the ion acoustic wave. Using the analytical mover as a reference, we demonstrate that the choice of error estimator in the Crank-Nicolson mover has significant impact on the overall performance of the implicit PIC algorithm. The generalization of the approach to the multi-dimensional case is outlined, based on a novel and simple charge conserving interpolation scheme.

Bridging the conservation design and delivery gap for wetland bird habitat maintenance and restoration in the Midwestern United States

USGS Publications Warehouse

Thogmartin, W.E.; Potter, B.; Soulliere, G.

2011-01-01

The U.S. Fish and Wildlife Service's adoption of Strategic Habitat Conservation is intended to increase the effectiveness and efficiency of conservation delivery by targeting effort in areas where biological benefits are greatest. Conservation funding has not often been allocated in accordance with explicit biological endpoints, and the gap between conservation design (the identification of conservation priority areas) and delivery needs to be bridged to better meet conservation goals for multiple species and landscapes. We introduce a regional prioritization scheme for North American Wetlands Conservation Act funding which explicitly addresses Midwest regional goals for wetland-dependent birds. We developed decision-support maps to guide conservation of breeding and non-breeding wetland bird habitat. This exercise suggested ~55% of the Midwest consists of potential wetland bird habitat, and areas suited for maintenance (protection) were distinguished from those most suited to restoration. Areas with greater maintenance focus were identified for central Minnesota, southeastern Wisconsin, the Upper Mississippi and Illinois rivers, and the shore of western Lake Erie and Saginaw Bay. The shores of Lakes Michigan and Superior accommodated fewer waterbird species overall, but were also important for wetland bird habitat maintenance. Abundant areas suited for wetland restoration occurred in agricultural regions of central Illinois, western Iowa, and northern Indiana and Ohio. Use of this prioritization scheme can increase effectiveness, efficiency, transparency, and credibility to land and water conservation efforts for wetland birds in the Midwestern United States.

Integrating economic costs and biological traits into global conservation priorities for carnivores.

PubMed

Loyola, Rafael Dias; Oliveira-Santos, Luiz Gustavo Rodrigues; Almeida-Neto, Mário; Nogueira, Denise Martins; Kubota, Umberto; Diniz-Filho, José Alexandre Felizola; Lewinsohn, Thomas Michael

2009-08-27

Prioritization schemes usually highlight species-rich areas, where many species are at imminent risk of extinction. To be ecologically relevant these schemes should also include species biological traits into area-setting methods. Furthermore, in a world of limited funds for conservation, conservation action is constrained by land acquisition costs. Hence, including economic costs into conservation priorities can substantially improve their conservation cost-effectiveness. We examined four global conservation scenarios for carnivores based on the joint mapping of economic costs and species biological traits. These scenarios identify the most cost-effective priority sets of ecoregions, indicating best investment opportunities for safeguarding every carnivore species, and also establish priority sets that can maximize species representation in areas harboring highly vulnerable species. We compared these results with a scenario that minimizes the total number of ecoregions required for conserving all species, irrespective of other factors. We found that cost-effective conservation investments should focus on 41 ecoregions highlighted in the scenario that consider simultaneously both ecoregion vulnerability and economic costs of land acquisition. Ecoregions included in priority sets under these criteria should yield best returns of investments since they harbor species with high extinction risk and have lower mean land cost. Our study highlights ecoregions of particular importance for the conservation of the world's carnivores defining global conservation priorities in analyses that encompass socioeconomic and life-history factors. We consider the identification of a comprehensive priority-set of areas as a first step towards an in-situ biodiversity maintenance strategy.

Total Variation Diminishing (TVD) schemes of uniform accuracy

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

A Parameterization of Dry Thermals and Shallow Cumuli for Mesoscale Numerical Weather Prediction

NASA Astrophysics Data System (ADS)

Pergaud, Julien; Masson, Valéry; Malardel, Sylvie; Couvreux, Fleur

2009-07-01

For numerical weather prediction models and models resolving deep convection, shallow convective ascents are subgrid processes that are not parameterized by classical local turbulent schemes. The mass flux formulation of convective mixing is now largely accepted as an efficient approach for parameterizing the contribution of larger plumes in convective dry and cloudy boundary layers. We propose a new formulation of the EDMF scheme (for Eddy DiffusivityMass Flux) based on a single updraft that improves the representation of dry thermals and shallow convective clouds and conserves a correct representation of stratocumulus in mesoscale models. The definition of entrainment and detrainment in the dry part of the updraft is original, and is specified as proportional to the ratio of buoyancy to vertical velocity. In the cloudy part of the updraft, the classical buoyancy sorting approach is chosen. The main closure of the scheme is based on the mass flux near the surface, which is proportional to the sub-cloud layer convective velocity scale w *. The link with the prognostic grid-scale cloud content and cloud cover and the projection on the non- conservative variables is processed by the cloud scheme. The validation of this new formulation using large-eddy simulations focused on showing the robustness of the scheme to represent three different boundary layer regimes. For dry convective cases, this parameterization enables a correct representation of the countergradient zone where the mass flux part represents the top entrainment (IHOP case). It can also handle the diurnal cycle of boundary-layer cumulus clouds (EUROCSARM) and conserve a realistic evolution of stratocumulus (EUROCSFIRE).

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

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 ??.

Reconciling Mining with the Conservation of Cave Biodiversity: A Quantitative Baseline to Help Establish Conservation Priorities.

PubMed

Jaffé, Rodolfo; Prous, Xavier; Zampaulo, Robson; Giannini, Tereza C; Imperatriz-Fonseca, Vera L; Maurity, Clóvis; Oliveira, Guilherme; Brandi, Iuri V; Siqueira, José O

2016-01-01

Caves pose significant challenges for mining projects, since they harbor many endemic and threatened species, and must therefore be protected. Recent discussions between academia, environmental protection agencies, and industry partners, have highlighted problems with the current Brazilian legislation for the protection of caves. While the licensing process is long, complex and cumbersome, the criteria used to assign caves into conservation relevance categories are often subjective, with relevance being mainly determined by the presence of obligate cave dwellers (troglobites) and their presumed rarity. However, the rarity of these troglobitic species is questionable, as most remain unidentified to the species level and their habitats and distribution ranges are poorly known. Using data from 844 iron caves retrieved from different speleology reports for the Carajás region (South-Eastern Amazon, Brazil), one of the world's largest deposits of high-grade iron ore, we assess the influence of different cave characteristics on four biodiversity proxies (species richness, presence of troglobites, presence of rare troglobites, and presence of resident bat populations). We then examine how the current relevance classification scheme ranks caves with different biodiversity indicators. Large caves were found to be important reservoirs of biodiversity, so they should be prioritized in conservation programs. Our results also reveal spatial autocorrelation in all the biodiversity proxies assessed, indicating that iron caves should be treated as components of a cave network immersed in the karst landscape. Finally, we show that by prioritizing the conservation of rare troglobites, the current relevance classification scheme is undermining overall cave biodiversity and leaving ecologically important caves unprotected. We argue that conservation efforts should target subterranean habitats as a whole and propose an alternative relevance ranking scheme, which could help simplify the assessment process and channel more resources to the effective protection of overall cave biodiversity.

A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2014-10-01

In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with stiff relaxation source terms.

A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal-icosahedral and cubed sphere grids

NASA Astrophysics Data System (ADS)

Thuburn, J.; Cotter, C. J.; Dubos, T.

2013-12-01

A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal-icosahedral and cubed-sphere grids

NASA Astrophysics Data System (ADS)

Thuburn, J.; Cotter, C. J.; Dubos, T.

2014-05-01

A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

Free vibrations and buckling analysis of laminated plates by oscillatory radial basis functions

NASA Astrophysics Data System (ADS)

Neves, A. M. A.; Ferreira, A. J. M.

2015-12-01

In this paper the free vibrations and buckling analysis of laminated plates is performed using a global meshless method. A refined version of Kant's theorie which accounts for transverse normal stress and through-the-thickness deformation is used. The innovation is the use of oscillatory radial basis functions. Numerical examples are performed and results are presented and compared to available references. Such functions proved to be an alternative to the tradicional nonoscillatory radial basis functions.

Mingus Discontinuous Multiphysics

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

Pat Notz, Dan Turner

Mingus provides hybrid coupled local/non-local mechanics analysis capabilities that extend several traditional methods to applications with inherent discontinuities. Its primary features include adaptations of solid mechanics, fluid dynamics and digital image correlation that naturally accommodate dijointed data or irregular solution fields by assimilating a variety of discretizations (such as control volume finite elements, peridynamics and meshless control point clouds). The goal of this software is to provide an analysis framework form multiphysics engineering problems with an integrated image correlation capability that can be used for experimental validation and model

Meshless Local Petrov-Galerkin Method for Solving Contact, Impact and Penetration Problems

DTIC Science & Technology

2006-11-30

Crack Growth 3 point of view, this approach makes the full use of the ex- isting FE models to avoid any model regeneration , which is extremely high in...process, at point C, the pressure reduces to zero, but the volumet- ric strain does not go to zero due to the collapsed void volume. 2.2 Damage...lease rate to go beyond the critical strain energy release rate. Thus, the micro-cracks begin to growth inside these areas. At 10 micro-seconds, these

Accurate Monotonicity - Preserving Schemes With Runge-Kutta Time Stepping

NASA Technical Reports Server (NTRS)

Suresh, A.; Huynh, H. T.

1997-01-01

A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented. The interface value in these schemes is obtained by limiting a higher-order polynominal reconstruction. The limiting is designed to preserve accuracy near extrema and to work well with Runge-Kutta time stepping. Computational efficiency is enhanced by a simple test that determines whether the limiting procedure is needed. For linear advection in one dimension, these schemes are shown as well as the Euler equations also confirm their high accuracy, good shock resolution, and computational efficiency.

High-resolution two dimensional advective transport

USGS Publications Warehouse

Smith, P.E.; Larock, B.E.

1989-01-01

The paper describes a two-dimensional high-resolution scheme for advective transport that is based on a Eulerian-Lagrangian method with a flux limiter. The scheme is applied to the problem of pure-advection of a rotated Gaussian hill and shown to preserve the monotonicity property of the governing conservation law.

A mass and momentum conserving unsplit semi-Lagrangian framework for simulating multiphase flows

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

Owkes, Mark, E-mail: mark.owkes@montana.edu; Desjardins, Olivier

In this work, we present a computational methodology for convection and advection that handles discontinuities with second order accuracy and maintains conservation to machine precision. This method can transport a variety of discontinuous quantities and is used in the context of an incompressible gas–liquid flow to transport the phase interface, momentum, and scalars. The proposed method provides a modification to the three-dimensional, unsplit, second-order semi-Lagrangian flux method of Owkes & Desjardins (JCP, 2014). The modification adds a refined grid that provides consistent fluxes of mass and momentum defined on a staggered grid and discrete conservation of mass and momentum, evenmore » for flows with large density ratios. Additionally, the refined grid doubles the resolution of the interface without significantly increasing the computational cost over previous non-conservative schemes. This is possible due to a novel partitioning of the semi-Lagrangian fluxes into a small number of simplices. The proposed scheme is tested using canonical verification tests, rising bubbles, and an atomizing liquid jet.« less

An adaptive, implicit, conservative, 1D-2V multi-species Vlasov-Fokker-Planck multi-scale solver in planar geometry

NASA Astrophysics Data System (ADS)

Taitano, W. T.; Chacón, L.; Simakov, A. N.

2018-07-01

We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we extend the conservative adaptive velocity-space discretization scheme proposed in [Taitano et al., J. Comput. Phys., 318, 391-420, (2016)] to a spatially inhomogeneous system. In this approach, we normalize the velocity-space coordinate to a temporally and spatially varying local characteristic speed per species. We explicitly consider the resulting inertial terms in the Vlasov equation, and derive a discrete formulation that conserves mass, momentum, and energy up to a prescribed nonlinear tolerance upon convergence. Our conservation strategy employs nonlinear constraints to enforce these properties discretely for both the Vlasov operator and the Fokker-Planck collision operator. Numerical examples of varying degrees of complexity, including shock-wave propagation, demonstrate the favorable efficiency and accuracy properties of the scheme.

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.

Domestic water conservation potential in Saudi Arabia

NASA Astrophysics Data System (ADS)

Abdulrazzak, Mohammed J.; Khan, Muhammad Z. A.

1990-03-01

Domestic water conservation in arid climates can result in efficient utilization of existing water supplies. The impacts of conservation measures such as the installation of water-saving devices, water metering and pricing schemes, water rationing and public awareness programs, strict plumbing codes, penalties for wasting water, programs designed to reduce leakage from public water lines and within the home, water-efficient landscaping, economic and ethical incentives are addressed in detail. Cost savings in arid climates, with particular reference to Saudi Arabia, in relation to some conservation techniques, are presented. Water conservation technology and tentative demonstration and implementation of water conservation programs are discussed.

A New Time-Space Accurate Scheme for Hyperbolic Problems. 1; Quasi-Explicit Case

NASA Technical Reports Server (NTRS)

Sidilkover, David

1998-01-01

This paper presents a new discretization scheme for hyperbolic systems of conservations laws. It satisfies the TVD property and relies on the new high-resolution mechanism which is compatible with the genuinely multidimensional approach proposed recently. This work can be regarded as a first step towards extending the genuinely multidimensional approach to unsteady problems. Discontinuity capturing capabilities and accuracy of the scheme are verified by a set of numerical tests.

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.

Household adoption of energy and water-efficient appliances: An analysis of attitudes, labelling and complementary green behaviours in selected OECD countries.

PubMed

Dieu-Hang, To; Grafton, R Quentin; Martínez-Espiñeira, Roberto; Garcia-Valiñas, Maria

2017-07-15

Using a household-based data set of more than 12,000 households from 11 OECD countries, we analyse the factors underlying the decision by households to adopt energy-efficient and water-efficient equipment. We evaluate the roles of both attitudes and labelling schemes on the adoption of energy and water-efficient equipment, and also the interaction and complementarity between energy and water conservation behaviours. Our findings show: one, 'green' social norms and favourable attitudes towards the environment are associated with an increased likelihood of households' adoption of energy and water-efficient appliances; two, households' purchase decisions are positively affected by their awareness, understanding, and trust of labelling schemes; and three, there is evidence of complementarity between energy conservation and water conservation behaviours. Copyright © 2017 Elsevier Ltd. All rights reserved.

Understanding casing flow in Pelton turbines by numerical simulation

NASA Astrophysics Data System (ADS)

Rentschler, M.; Neuhauser, M.; Marongiu, J. C.; Parkinson, E.

2016-11-01

For rehabilitation projects of Pelton turbines, the flow in the casing may have an important influence on the overall performance of the machine. Water sheets returning on the jets or on the runner significantly reduce efficiency, and run-away speed depends on the flow in the casing. CFD simulations can provide a detailed insight into this type of flow, but these simulations are computationally intensive. As in general the volume of water in a Pelton turbine is small compared to the complete volume of the turbine housing, a single phase simulation greatly reduces the complexity of the simulation. In the present work a numerical tool based on the SPH-ALE meshless method is used to simulate the casing flow in a Pelton turbine. Using improved order schemes reduces the numerical viscosity. This is necessary to resolve the flow in the jet and on the casing wall, where the velocity differs by two orders of magnitude. The results are compared to flow visualizations and measurement in a hydraulic laboratory. Several rehabilitation projects proved the added value of understanding the flow in the Pelton casing. The flow simulation helps designing casing insert, not only to see their influence on the flow, but also to calculate the stress in the inserts. In some projects, the casing simulation leads to the understanding of unexpected behavior of the flow. One such example is presented where the backsplash of a deflector hit the runner, creating a reversed rotation of the runner.

A 3-dimensional mass conserving element for compressible flows

NASA Technical Reports Server (NTRS)

Fix, G.; Suri, M.

1985-01-01

A variety of finite element schemes has been used in the numerical approximation of compressible flows particularly in underwater acoustics. In many instances instabilities have been generated due to the lack of mass conservation. Two- and three-dimensional elements are developed which avoid these problems.

An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography

NASA Astrophysics Data System (ADS)

Zhou, Feng; Chen, Guoxian; Huang, Yuefei; Yang, Jerry Zhijian; Feng, Hui

2013-04-01

A new geometrical conservative interpolation on unstructured meshes is developed for preserving still water equilibrium and positivity of water depth at each iteration of mesh movement, leading to an adaptive moving finite volume (AMFV) scheme for modeling flood inundation over dry and complex topography. Unlike traditional schemes involving position-fixed meshes, the iteration process of the AFMV scheme moves a fewer number of the meshes adaptively in response to flow variables calculated in prior solutions and then simulates their posterior values on the new meshes. At each time step of the simulation, the AMFV scheme consists of three parts: an adaptive mesh movement to shift the vertices position, a geometrical conservative interpolation to remap the flow variables by summing the total mass over old meshes to avoid the generation of spurious waves, and a partial differential equations(PDEs) discretization to update the flow variables for a new time step. Five different test cases are presented to verify the computational advantages of the proposed scheme over nonadaptive methods. The results reveal three attractive features: (i) the AMFV scheme could preserve still water equilibrium and positivity of water depth within both mesh movement and PDE discretization steps; (ii) it improved the shock-capturing capability for handling topographic source terms and wet-dry interfaces by moving triangular meshes to approximate the spatial distribution of time-variant flood processes; (iii) it was able to solve the shallow water equations with a relatively higher accuracy and spatial-resolution with a lower computational cost.

The a(4) Scheme-A High Order Neutrally Stable CESE Solver

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

2009-01-01

The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a nondissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new high order (4-5th order) and neutrally stable CESE solver of a 1D advection equation with a constant advection speed a. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and two points at the lower time level. Because it is associated with four independent mesh variables (the numerical analogues of the dependent variable and its first, second, and third-order spatial derivatives) and four equations per mesh point, the new scheme is referred to as the a(4) scheme. As in the case of other similar CESE neutrally stable solvers, the a(4) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. Except for a singular case, these forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove the a(4) scheme must be neutrally stable when it is stable. Numerically, it has been established that the scheme is stable if the value of the Courant number is less than 1/3

Numerical methods for systems of conservation laws of mixed type using flux splitting

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1990-01-01

The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.

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

Mishra, Manoj K., E-mail: manoj.qit@gmail.com; Space Applications Centre, Indian Space Research Organization; Prakash, Hari

Long distance atomic teleportation (LDAT) is of prime importance in long distance quantum communication. Scheme proposed by Bose et al. (1999) in principle enables us to have LDAT using cavity decay. However it gives message state dependent fidelity and success rate. Here, using interaction of entangled coherent states with atom–cavity systems and a two-step measurement, we show how, LDAT can be achieved with unit fidelity and as good success as desired under ideal conditions. The scheme is unique in that, the first measurement predicts success or failure. If success is predicted then second measurement gives perfect teleportation. If failure is predictedmore » the message-qubit remains conserved therefore a second attempt may be started. We found that even in presence of decoherence due to dissipation of energy our scheme gives message state independent success rate and almost perfect teleportation in single attempt with mean fidelity of teleportation equal to 0.9 at long distances. However if first attempt fails, unlike ideal case where message-qubit remains conserved with unit fidelity, in presence of decoherence the message-qubit remains conserved to some degree, therefore mean fidelity of teleportation can be increased beyond 0.9 by repeating the process.« less

A staggered conservative scheme for every Froude number in rapidly varied shallow water flows

NASA Astrophysics Data System (ADS)

Stelling, G. S.; Duinmeijer, S. P. A.

2003-12-01

This paper proposes a numerical technique that in essence is based upon the classical staggered grids and implicit numerical integration schemes, but that can be applied to problems that include rapidly varied flows as well. Rapidly varied flows occur, for instance, in hydraulic jumps and bores. Inundation of dry land implies sudden flow transitions due to obstacles such as road banks. Near such transitions the grid resolution is often low compared to the gradients of the bathymetry. In combination with the local invalidity of the hydrostatic pressure assumption, conservation properties become crucial. The scheme described here, combines the efficiency of staggered grids with conservation properties so as to ensure accurate results for rapidly varied flows, as well as in expansions as in contractions. In flow expansions, a numerical approximation is applied that is consistent with the momentum principle. In flow contractions, a numerical approximation is applied that is consistent with the Bernoulli equation. Both approximations are consistent with the shallow water equations, so under sufficiently smooth conditions they converge to the same solution. The resulting method is very efficient for the simulation of large-scale inundations.

Integrating Economic Costs and Biological Traits into Global Conservation Priorities for Carnivores

PubMed Central

Loyola, Rafael Dias; Oliveira-Santos, Luiz Gustavo Rodrigues; Almeida-Neto, Mário; Nogueira, Denise Martins; Kubota, Umberto; Diniz-Filho, José Alexandre Felizola; Lewinsohn, Thomas Michael

2009-01-01

Background Prioritization schemes usually highlight species-rich areas, where many species are at imminent risk of extinction. To be ecologically relevant these schemes should also include species biological traits into area-setting methods. Furthermore, in a world of limited funds for conservation, conservation action is constrained by land acquisition costs. Hence, including economic costs into conservation priorities can substantially improve their conservation cost-effectiveness. Methodology/Principal Findings We examined four global conservation scenarios for carnivores based on the joint mapping of economic costs and species biological traits. These scenarios identify the most cost-effective priority sets of ecoregions, indicating best investment opportunities for safeguarding every carnivore species, and also establish priority sets that can maximize species representation in areas harboring highly vulnerable species. We compared these results with a scenario that minimizes the total number of ecoregions required for conserving all species, irrespective of other factors. We found that cost-effective conservation investments should focus on 41 ecoregions highlighted in the scenario that consider simultaneously both ecoregion vulnerability and economic costs of land acquisition. Ecoregions included in priority sets under these criteria should yield best returns of investments since they harbor species with high extinction risk and have lower mean land cost. Conclusions/Significance Our study highlights ecoregions of particular importance for the conservation of the world's carnivores defining global conservation priorities in analyses that encompass socioeconomic and life-history factors. We consider the identification of a comprehensive priority-set of areas as a first step towards an in-situ biodiversity maintenance strategy. PMID:19710911

Sampling scheme on genetic structure of tree species in fragmented tropical dry forest: an evaluation from landscape genetic simulations

Treesearch

Yessica Rico; Marie-Stephanie Samain

2017-01-01

Investigating how genetic variation is distributed across the landscape is fundamental to inform forest conservation and restoration. Detecting spatial genetic discontinuities has value for defining management units, germplasm collection, and target sites for reforestation; however, inappropriate sampling schemes can misidentify patterns of genetic structure....

Private Education and Disadvantage: The Experiences of Assisted Place Holders

ERIC Educational Resources Information Center

Power, Sally; Curtis, Andrew; Whitty, Geoff; Edwards, Tony

2010-01-01

It is now nearly thirty years since Margaret Thatcher and her Conservative administration introduced the Assisted Places Scheme (their first education policy) and over ten years since New Labour abolished it. The Scheme, which was designed to provide a ladder of opportunity for academically able students from poor backgrounds to attend private…

The Partners in Flight species prioritization scheme

Treesearch

William C. Hunter; Michael F. Carter; David N. Pashley; Keith Barker

1993-01-01

The prioritization scheme identifies those birds at any locality on several geographic scales most in need of conservation action. Further, it suggests some of those actions that ought to be taken. Ranking criteria used to set priorities for Neotropical migratory landbirds measure characteristics of species that make them vulnerable to local and global extinction....

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

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.

Linearization of Conservative Nonlinear Oscillators

ERIC Educational Resources Information Center

Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.

2009-01-01

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

Cubication of Conservative Nonlinear Oscillators

ERIC Educational Resources Information Center

Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada

2009-01-01

A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…

Reconstruction and analysis of hybrid composite shells using meshless methods

NASA Astrophysics Data System (ADS)

Bernardo, G. M. S.; Loja, M. A. R.

2017-06-01

The importance of focusing on the research of viable models to predict the behaviour of structures which may possess in some cases complex geometries is an issue that is growing in different scientific areas, ranging from the civil and mechanical engineering to the architecture or biomedical devices fields. In these cases, the research effort to find an efficient approach to fit laser scanning point clouds, to the desired surface, has been increasing, leading to the possibility of modelling as-built/as-is structures and components' features. However, combining the task of surface reconstruction and the implementation of a structural analysis model is not a trivial task. Although there are works focusing those different phases in separate, there is still an effective need to find approaches able to interconnect them in an efficient way. Therefore, achieving a representative geometric model able to be subsequently submitted to a structural analysis in a similar based platform is a fundamental step to establish an effective expeditious processing workflow. With the present work, one presents an integrated methodology based on the use of meshless approaches, to reconstruct shells described by points' clouds, and to subsequently predict their static behaviour. These methods are highly appropriate on dealing with unstructured points clouds, as they do not need to have any specific spatial or geometric requirement when implemented, depending only on the distance between the points. Details on the formulation, and a set of illustrative examples focusing the reconstruction of cylindrical and double-curvature shells, and its further analysis, are presented.

Spatiotemporal groundwater level modeling using hybrid artificial intelligence-meshless method

NASA Astrophysics Data System (ADS)

Nourani, Vahid; Mousavi, Shahram

2016-05-01

Uncertainties of the field parameters, noise of the observed data and unknown boundary conditions are the main factors involved in the groundwater level (GL) time series which limit the modeling and simulation of GL. This paper presents a hybrid artificial intelligence-meshless model for spatiotemporal GL modeling. In this way firstly time series of GL observed in different piezometers were de-noised using threshold-based wavelet method and the impact of de-noised and noisy data was compared in temporal GL modeling by artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS). In the second step, both ANN and ANFIS models were calibrated and verified using GL data of each piezometer, rainfall and runoff considering various input scenarios to predict the GL at one month ahead. In the final step, the simulated GLs in the second step of modeling were considered as interior conditions for the multiquadric radial basis function (RBF) based solve of governing partial differential equation of groundwater flow to estimate GL at any desired point within the plain where there is not any observation. In order to evaluate and compare the GL pattern at different time scales, the cross-wavelet coherence was also applied to GL time series of piezometers. The results showed that the threshold-based wavelet de-noising approach can enhance the performance of the modeling up to 13.4%. Also it was found that the accuracy of ANFIS-RBF model is more reliable than ANN-RBF model in both calibration and validation steps.

A nearest-neighbour discretisation of the regularized stokeslet boundary integral equation

NASA Astrophysics Data System (ADS)

Smith, David J.

2018-04-01

The method of regularized stokeslets is extensively used in biological fluid dynamics due to its conceptual simplicity and meshlessness. This simplicity carries a degree of cost in computational expense and accuracy because the number of degrees of freedom used to discretise the unknown surface traction is generally significantly higher than that required by boundary element methods. We describe a meshless method based on nearest-neighbour interpolation that significantly reduces the number of degrees of freedom required to discretise the unknown traction, increasing the range of problems that can be practically solved, without excessively complicating the task of the modeller. The nearest-neighbour technique is tested against the classical problem of rigid body motion of a sphere immersed in very viscous fluid, then applied to the more complex biophysical problem of calculating the rotational diffusion timescales of a macromolecular structure modelled by three closely-spaced non-slender rods. A heuristic for finding the required density of force and quadrature points by numerical refinement is suggested. Matlab/GNU Octave code for the key steps of the algorithm is provided, which predominantly use basic linear algebra operations, with a full implementation being provided on github. Compared with the standard Nyström discretisation, more accurate and substantially more efficient results can be obtained by de-refining the force discretisation relative to the quadrature discretisation: a cost reduction of over 10 times with improved accuracy is observed. This improvement comes at minimal additional technical complexity. Future avenues to develop the algorithm are then discussed.

The global distribution of tetrapods reveals a need for targeted reptile conservation.

PubMed

Roll, Uri; Feldman, Anat; Novosolov, Maria; Allison, Allen; Bauer, Aaron M; Bernard, Rodolphe; Böhm, Monika; Castro-Herrera, Fernando; Chirio, Laurent; Collen, Ben; Colli, Guarino R; Dabool, Lital; Das, Indraneil; Doan, Tiffany M; Grismer, Lee L; Hoogmoed, Marinus; Itescu, Yuval; Kraus, Fred; LeBreton, Matthew; Lewin, Amir; Martins, Marcio; Maza, Erez; Meirte, Danny; Nagy, Zoltán T; de C Nogueira, Cristiano; Pauwels, Olivier S G; Pincheira-Donoso, Daniel; Powney, Gary D; Sindaco, Roberto; Tallowin, Oliver J S; Torres-Carvajal, Omar; Trape, Jean-François; Vidan, Enav; Uetz, Peter; Wagner, Philipp; Wang, Yuezhao; Orme, C David L; Grenyer, Richard; Meiri, Shai

2017-11-01

The distributions of amphibians, birds and mammals have underpinned global and local conservation priorities, and have been fundamental to our understanding of the determinants of global biodiversity. In contrast, the global distributions of reptiles, representing a third of terrestrial vertebrate diversity, have been unavailable. This prevented the incorporation of reptiles into conservation planning and biased our understanding of the underlying processes governing global vertebrate biodiversity. Here, we present and analyse the global distribution of 10,064 reptile species (99% of extant terrestrial species). We show that richness patterns of the other three tetrapod classes are good spatial surrogates for species richness of all reptiles combined and of snakes, but characterize diversity patterns of lizards and turtles poorly. Hotspots of total and endemic lizard richness overlap very little with those of other taxa. Moreover, existing protected areas, sites of biodiversity significance and global conservation schemes represent birds and mammals better than reptiles. We show that additional conservation actions are needed to effectively protect reptiles, particularly lizards and turtles. Adding reptile knowledge to a global complementarity conservation priority scheme identifies many locations that consequently become important. Notably, investing resources in some of the world's arid, grassland and savannah habitats might be necessary to represent all terrestrial vertebrates efficiently.

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.

A diagonal implicit scheme for computing flows with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Eberhardt, Scott; Imlay, Scott

1990-01-01

A new algorithm for solving steady, finite-rate chemistry, flow problems is presented. The new scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The source Jacobian matrix is replaced by a diagonal matrix which is tailored to account for the fastest reactions in the chemical system. A point-implicit procedure is discussed and then the algorithm is included into the LU-SGS scheme. Solutions are presented for hypervelocity reentry and Hydrogen-Oxygen combustion. For the LU-SGS scheme a CFL number in excess of 10,000 has been achieved.

Conservative supra-characteristics method for splitting the hyperbolic systems of gasdynamics for real and perfect gases

NASA Technical Reports Server (NTRS)

Lombard, C. K.

1982-01-01

A conservative flux difference splitting is presented for the hyperbolic systems of gasdynamics. The stable robust method is suitable for wide application in a variety of schemes, explicit or implicit, iterative or direct, for marching in either time or space. The splitting is modeled on the local quasi one dimensional characteristics system for multi-dimensional flow similar to Chakravarthy's nonconservative split coefficient matrix method; but, as the result of maintaining global conservation, the method is able to capture sharp shocks correctly. The embedded characteristics formulation is cast in a primitive variable the volumetric internal energy (rather than the pressure) that is effective for treating real as well as perfect gases. Finally the relationship of the splitting to characteristics boundary conditions is discussed and the associated conservative matrix formulation for a computed blown wall boundary condition is developed as an example. The theoretical development employs and extends the notion of Roe of constructing stable upwind difference formulae by sending split simple one sided flux difference pieces to appropriate mesh sites. The developments are also believed to have the potential for aiding in the analysis of both existing and new conservative difference schemes.

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.

Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows

NASA Astrophysics Data System (ADS)

Yang, L. M.; Shu, C.; Wang, Y.; Sun, Y.

2016-08-01

The sphere function-based gas kinetic scheme (GKS), which was presented by Shu and his coworkers [23] for simulation of inviscid compressible flows, is extended to simulate 3D viscous incompressible and compressible flows in this work. Firstly, we use certain discrete points to represent the spherical surface in the phase velocity space. Then, integrals along the spherical surface for conservation forms of moments, which are needed to recover 3D Navier-Stokes equations, are approximated by integral quadrature. The basic requirement is that these conservation forms of moments can be exactly satisfied by weighted summation of distribution functions at discrete points. It was found that the integral quadrature by eight discrete points on the spherical surface, which forms the D3Q8 discrete velocity model, can exactly match the integral. In this way, the conservative variables and numerical fluxes can be computed by weighted summation of distribution functions at eight discrete points. That is, the application of complicated formulations resultant from integrals can be replaced by a simple solution process. Several numerical examples including laminar flat plate boundary layer, 3D lid-driven cavity flow, steady flow through a 90° bending square duct, transonic flow around DPW-W1 wing and supersonic flow around NACA0012 airfoil are chosen to validate the proposed scheme. Numerical results demonstrate that the present scheme can provide reasonable numerical results for 3D viscous flows.

An online-coupled NWP/ACT model with conserved Lagrangian levels

NASA Astrophysics Data System (ADS)

Sørensen, B.; Kaas, E.; Lauritzen, P. H.

2012-04-01

Numerical weather and climate modelling is under constant development. Semi-implicit semi-Lagrangian (SISL) models have proven to be numerically efficient in both short-range weather forecasts and climate models, due to the ability to use long time steps. Chemical/aerosol feedback mechanism are becoming more and more relevant in NWP as well as climate models, since the biogenic and anthropogenic emissions can have a direct effect on the dynamics and radiative properties of the atmosphere. To include chemical feedback mechanisms in the NWP models, on-line coupling is crucial. In 3D semi-Lagrangian schemes with quasi-Lagrangian vertical coordinates the Lagrangian levels are remapped to Eulerian model levels each time step. This remapping introduces an undesirable tendency to smooth sharp gradients and creates unphysical numerical diffusion in the vertical distribution. A semi-Lagrangian advection method is introduced, it combines an inherently mass conserving 2D semi-Lagrangian scheme, with a SISL scheme employing both hybrid vertical coordinates and a fully Lagrangian vertical coordinate. This minimizes the vertical diffusion and thus potentially improves the simulation of the vertical profiles of moisture, clouds, and chemical constituents. Since the Lagrangian levels suffer from traditional Lagrangian limitations caused by the convergence and divergence of the flow, remappings to the Eulerian model levels are generally still required - but this need only be applied after a number of time steps - unless dynamic remapping methods are used. For this several different remapping methods has been implemented. The combined scheme is mass conserving, consistent, and multi-tracer efficient.

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

NASA Astrophysics Data System (ADS)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

The Space-Time Conservative Schemes for Large-Scale, Time-Accurate Flow Simulations with Tetrahedral Meshes

NASA Technical Reports Server (NTRS)

Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung

2016-01-01

Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.

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.

Factorizable Schemes for the Equations of Fluid Flow

NASA Technical Reports Server (NTRS)

Sidilkover, David

1999-01-01

We present an upwind high-resolution factorizable (UHF) discrete scheme for the compressible Euler equations that allows to distinguish between full-potential and advection factors at the discrete level. The scheme approximates equations in their general conservative form and is related to the family of genuinely multidimensional upwind schemes developed previously and demonstrated to have good shock-capturing capabilities. A unique property of this scheme is that in addition to the aforementioned features it is also factorizable, i.e., it allows to distinguish between full-potential and advection factors at the discrete level. The latter property facilitates the construction of optimally efficient multigrid solvers. This is done through a relaxation procedure that utilizes the factorizability property.

Consistent Temperature Coupling with Thermal Fluctuations of Smooth Particle Hydrodynamics and Molecular Dynamics

PubMed Central

Ganzenmüller, Georg C.; Hiermaier, Stefan; Steinhauser, Martin O.

2012-01-01

We propose a thermodynamically consistent and energy-conserving temperature coupling scheme between the atomistic and the continuum domain. The coupling scheme links the two domains using the DPDE (Dissipative Particle Dynamics at constant Energy) thermostat and is designed to handle strong temperature gradients across the atomistic/continuum domain interface. The fundamentally different definitions of temperature in the continuum and atomistic domain – internal energy and heat capacity versus particle velocity – are accounted for in a straightforward and conceptually intuitive way by the DPDE thermostat. We verify the here-proposed scheme using a fluid, which is simultaneously represented as a continuum using Smooth Particle Hydrodynamics, and as an atomistically resolved liquid using Molecular Dynamics. In the case of equilibrium contact between both domains, we show that the correct microscopic equilibrium properties of the atomistic fluid are obtained. As an example of a strong non-equilibrium situation, we consider the propagation of a steady shock-wave from the continuum domain into the atomistic domain, and show that the coupling scheme conserves both energy and shock-wave dynamics. To demonstrate the applicability of our scheme to real systems, we consider shock loading of a phospholipid bilayer immersed in water in a multi-scale simulation, an interesting topic of biological relevance. PMID:23300586

A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons

NASA Astrophysics Data System (ADS)

Bao, J.; Lin, Z.; Lu, Z. X.

2018-02-01

A conservative scheme has been formulated and verified for gyrokinetic particle simulations of electromagnetic waves and instabilities in magnetized plasmas. An electron continuity equation derived from the drift kinetic equation is used to time advance the electron density perturbation by using the perturbed mechanical flow calculated from the parallel vector potential, and the parallel vector potential is solved by using the perturbed canonical flow from the perturbed distribution function. In gyrokinetic particle simulations using this new scheme, the shear Alfvén wave dispersion relation in the shearless slab and continuum damping in the sheared cylinder have been recovered. The new scheme overcomes the stringent requirement in the conventional perturbative simulation method that perpendicular grid size needs to be as small as electron collisionless skin depth even for the long wavelength Alfvén waves. The new scheme also avoids the problem in the conventional method that an unphysically large parallel electric field arises due to the inconsistency between electrostatic potential calculated from the perturbed density and vector potential calculated from the perturbed canonical flow. Finally, the gyrokinetic particle simulations of the Alfvén waves in sheared cylinder have superior numerical properties compared with the fluid simulations, which suffer from numerical difficulties associated with singular mode structures.

Targeted ENO schemes with tailored resolution property for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-11-01

In this paper, we extend the range of targeted ENO (TENO) schemes (Fu et al. (2016) [18]) by proposing an eighth-order TENO8 scheme. A general formulation to construct the high-order undivided difference τK within the weighting strategy is proposed. With the underlying scale-separation strategy, sixth-order accuracy for τK in the smooth solution regions is designed for good performance and robustness. Furthermore, a unified framework to optimize independently the dispersion and dissipation properties of high-order finite-difference schemes is proposed. The new framework enables tailoring of dispersion and dissipation as function of wavenumber. The optimal linear scheme has minimum dispersion error and a dissipation error that satisfies a dispersion-dissipation relation. Employing the optimal linear scheme, a sixth-order TENO8-opt scheme is constructed. A set of benchmark cases involving strong discontinuities and broadband fluctuations is computed to demonstrate the high-resolution properties of the new schemes.

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

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Sethian, James A.

1997-01-01

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

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.

Interpretation of ES, CS, and IOS approximations within a translational--internal coupling scheme. I. Atom--diatom collisions

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

Coombe, D.A.; Snider, R.F.

1979-12-01

Rotational invariance is applied to the description of atom--diatom collisions in a translational--internal coupling scheme, to obtain energy sudden (ES), centrifugal sudden (CS), and infinite order sudden (IOS) approximations to the reduced scattering S matrix S (j-barlambda-bar;L;jlambda). The method of presentation emphasizes that the translational--internal coupling scheme is actually the more natural description of collision processes in which one or more directions are assumed to be conserved.

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

NASA Technical Reports Server (NTRS)

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

1983-01-01

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Does environmental certification in coffee promote "business as usual"? A case study from the Western Ghats, India.

PubMed

Bose, Arshiya; Vira, Bhaskar; Garcia, Claude

2016-12-01

Conservation initiatives are designed to address threats to forests and biodiversity, often through partnerships with natural-resource users who are incentivized to change their land-use and livelihood practices to avoid further biodiversity loss. In particular, direct incentives programmes that provide monetary benefits are commended for being effective in achieving conservation across short timescales. In biodiversity-rich areas, outside protected areas, such as coffee agroforestry systems, direct incentives, such as certification schemes, are used to motivate coffee producers to maintain native tree species, natural vegetation, restrict wildlife hunting, and conserve soil and water, in addition to encouraging welfare of workers. However, despite these claims, there is a lack of strong evidence of the on-ground impact of such schemes. To assess the conservation importance of certification, we describe a case study in the Western Ghats biodiversity hotspot of India, in which coffee growers are provided price incentives to adopt Rainforest Alliance certification standards. We analyse the conservation and social outcomes of this programme by studying peoples' experiences of participating in certification. Despite high compliance and effective implementation, we find a strong case for the endorsement of 'business as usual' with no changes in farm management as a result of certification. We find that such 'business as usual' participation in certification creates grounds for diminishing credibility and local support for conservation efforts. Working towards locally relevant conservation interventions, rather than implementing global blueprints, may lead to more meaningful biodiversity conservation and increased community support for conservation initiatives in coffee landscapes.

Entropy Splitting and Numerical Dissipation

NASA Technical Reports Server (NTRS)

Yee, H. C.; Vinokur, M.; Djomehri, M. J.

1999-01-01

A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock-turbulence interactions. The fourth is to determine if this method can be extended to other physical equations of state and other evolutionary equation sets. If numerical dissipation is needed, the Yee, Sandham, and Djomehri (1999) numerical dissipation is employed. The Yee et al. schemes fit in the Olsson and Oliger framework.

Lasting Benefits: The Long-Term Legacy of the Assisted Places Scheme for Assisted Place Holders

ERIC Educational Resources Information Center

Power, Sally; Sims, Stuart; Whitty, Geoff

2013-01-01

The "Assisted Places Scheme" was introduced in 1980 by the Conservative Government to provide a "ladder of opportunity" for academically able students from poor homes. Over the next 17 years, more than 75,000 pupils received means-tested assistance from public funds to attend the most selective and prestigious private schools…

Action versus Result-Oriented Schemes in a Grassland Agroecosystem: A Dynamic Modelling Approach

PubMed Central

Sabatier, Rodolphe; Doyen, Luc; Tichit, Muriel

2012-01-01

Effects of agri-environment schemes (AES) on biodiversity remain controversial. While most AES are action-oriented, result-oriented and habitat-oriented schemes have recently been proposed as a solution to improve AES efficiency. The objective of this study was to compare action-oriented, habitat-oriented and result-oriented schemes in terms of ecological and productive performance as well as in terms of management flexibility. We developed a dynamic modelling approach based on the viable control framework to carry out a long term assessment of the three schemes in a grassland agroecosystem. The model explicitly links grazed grassland dynamics to bird population dynamics. It is applied to lapwing conservation in wet grasslands in France. We ran the model to assess the three AES scenarios. The model revealed the grazing strategies respecting ecological and productive constraints specific to each scheme. Grazing strategies were assessed by both their ecological and productive performance. The viable control approach made it possible to obtain the whole set of viable grazing strategies and therefore to quantify the management flexibility of the grassland agroecosystem. Our results showed that habitat and result-oriented scenarios led to much higher ecological performance than the action-oriented one. Differences in both ecological and productive performance between the habitat and result-oriented scenarios were limited. Flexibility of the grassland agroecosystem in the result-oriented scenario was much higher than in that of habitat-oriented scenario. Our model confirms the higher flexibility as well as the better ecological and productive performance of result-oriented schemes. A larger use of result-oriented schemes in conservation may also allow farmers to adapt their management to local conditions and to climatic variations. PMID:22496746

Cover Crops and Fertilization Alter Nitrogen Loss in Organic and Conventional Conservation Agriculture Systems

PubMed Central

Shelton, Rebecca E.; Jacobsen, Krista L.; McCulley, Rebecca L.

2018-01-01

Agroecosystem nitrogen (N) loss produces greenhouse gases, induces eutrophication, and is costly for farmers; therefore, conservation agricultural management practices aimed at reducing N loss are increasingly adopted. However, the ecosystem consequences of these practices have not been well-studied. We quantified N loss via leaching, NH3 volatilization, N2O emissions, and N retention in plant and soil pools of corn conservation agroecosystems in Kentucky, USA. Three systems were evaluated: (1) an unfertilized, organic system with cover crops hairy vetch (Vicia villosa), winter wheat (Triticum aestivum), or a mix of the two (bi-culture); (2) an organic system with a hairy vetch cover crop employing three fertilization schemes (0 N, organic N, or a fertilizer N-credit approach); and (3) a conventional system with a winter wheat cover crop and three fertilization schemes (0 N, urea N, or organic N). In the unfertilized organic system, cover crop species affected NO3-N leaching (vetch > bi-culture > wheat) and N2O-N emissions and yield during corn growth (vetch, bi-culture > wheat). Fertilization increased soil inorganic N, gaseous N loss, N leaching, and yield in the organic vetch and conventional wheat systems. Fertilizer scheme affected the magnitude of growing season N2O-N loss in the organic vetch system (organic N > fertilizer N-credit) and the timing of loss (organic N delayed N2O-N loss vs. urea) and NO3-N leaching (urea >> organic N) in the conventional wheat system, but had no effect on yield. Cover crop selection and N fertilization techniques can reduce N leaching and greenhouse gas emissions without sacrificing yield, thereby enhancing N conservation in both organic and conventional conservation agriculture systems. PMID:29403512

An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes

DOE PAGES

Taitano, William; Chacon, Luis; Simakov, Andrei Nikolaevich

2016-04-25

In this paper, we propose an adaptive velocity-space discretization scheme for the multi-species, multidimensional Rosenbluth–Fokker–Planck (RFP) equation, which is exactly mass-, momentum-, and energy-conserving. Unlike most earlier studies, our approach normalizes the velocity-space coordinate to the temporally varying individual plasma species' local thermal velocity, v th (t), and explicitly considers the resulting inertial terms in the Fokker–Planck equation. Our conservation strategy employs nonlinear constraints to enforce discretely the conservation properties of these inertial terms and the Fokker–Planck collision operator. To deal with situations of extreme thermal velocity disparities among different species, we employ an asymptotic v th -ratio-based expansion ofmore » the Rosenbluth potentials that only requires the computation of several velocity-space integrals. Numerical examples demonstrate the favorable efficiency and accuracy properties of the scheme. Specifically, we show that the combined use of the velocity-grid adaptivity and asymptotic expansions delivers many orders-of-magnitude savings in mesh resolution requirements compared to a single, static uniform mesh.« less

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes

NASA Astrophysics Data System (ADS)

Don, Wai-Sun; Borges, Rafael

2013-10-01

In the reconstruction step of (2r-1) order weighted essentially non-oscillatory conservative finite difference schemes (WENO) for solving hyperbolic conservation laws, nonlinear weights αk and ωk, such as the WENO-JS weights by Jiang et al. and the WENO-Z weights by Borges et al., are designed to recover the formal (2r-1) order (optimal order) of the upwinded central finite difference scheme when the solution is sufficiently smooth. The smoothness of the solution is determined by the lower order local smoothness indicators βk in each substencil. These nonlinear weight formulations share two important free parameters in common: the power p, which controls the amount of numerical dissipation, and the sensitivity ε, which is added to βk to avoid a division by zero in the denominator of αk. However, ε also plays a role affecting the order of accuracy of WENO schemes, especially in the presence of critical points. It was recently shown that, for any design order (2r-1), ε should be of Ω(Δx2) (Ω(Δxm) means that ε⩾CΔxm for some C independent of Δx, as Δx→0) for the WENO-JS scheme to achieve the optimal order, regardless of critical points. In this paper, we derive an alternative proof of the sufficient condition using special properties of βk. Moreover, it is unknown if the WENO-Z scheme should obey the same condition on ε. Here, using same special properties of βk, we prove that in fact the optimal order of the WENO-Z scheme can be guaranteed with a much weaker condition ε=Ω(Δxm), where m(r,p)⩾2 is the optimal sensitivity order, regardless of critical points. Both theoretical results are confirmed numerically on smooth functions with arbitrary order of critical points. This is a highly desirable feature, as illustrated with the Lax problem and the Mach 3 shock-density wave interaction of one dimensional Euler equations, for a smaller ε allows a better essentially non-oscillatory shock capturing as it does not over-dominate over the size of βk. We also show that numerical oscillations can be further attenuated by increasing the power parameter 2⩽p⩽r-1, at the cost of increased numerical dissipation. Compact formulas of βk for WENO schemes are also presented.

Particle-based and meshless methods with Aboria

NASA Astrophysics Data System (ADS)

Robinson, Martin; Bruna, Maria

Aboria is a powerful and flexible C++ library for the implementation of particle-based numerical methods. The particles in such methods can represent actual particles (e.g. Molecular Dynamics) or abstract particles used to discretise a continuous function over a domain (e.g. Radial Basis Functions). Aboria provides a particle container, compatible with the Standard Template Library, spatial search data structures, and a Domain Specific Language to specify non-linear operators on the particle set. This paper gives an overview of Aboria's design, an example of use, and a performance benchmark.

Comparison of Response Surface Construction Methods for Derivative Estimation Using Moving Least Squares, Kriging and Radial Basis Functions

NASA Technical Reports Server (NTRS)

Krishnamurthy, Thiagarajan

2005-01-01

Response construction methods using Moving Least Squares (MLS), Kriging and Radial Basis Functions (RBF) are compared with the Global Least Squares (GLS) method in three numerical examples for derivative generation capability. Also, a new Interpolating Moving Least Squares (IMLS) method adopted from the meshless method is presented. It is found that the response surface construction methods using the Kriging and RBF interpolation yields more accurate results compared with MLS and GLS methods. Several computational aspects of the response surface construction methods also discussed.

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

NASA Technical Reports Server (NTRS)

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

2015-01-01

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

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1993-01-01

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Reconciling Mining with the Conservation of Cave Biodiversity: A Quantitative Baseline to Help Establish Conservation Priorities

PubMed Central

Prous, Xavier; Zampaulo, Robson; Giannini, Tereza C.; Imperatriz-Fonseca, Vera L.; Maurity, Clóvis; Oliveira, Guilherme; Brandi, Iuri V.; Siqueira, José O.

2016-01-01

Caves pose significant challenges for mining projects, since they harbor many endemic and threatened species, and must therefore be protected. Recent discussions between academia, environmental protection agencies, and industry partners, have highlighted problems with the current Brazilian legislation for the protection of caves. While the licensing process is long, complex and cumbersome, the criteria used to assign caves into conservation relevance categories are often subjective, with relevance being mainly determined by the presence of obligate cave dwellers (troglobites) and their presumed rarity. However, the rarity of these troglobitic species is questionable, as most remain unidentified to the species level and their habitats and distribution ranges are poorly known. Using data from 844 iron caves retrieved from different speleology reports for the Carajás region (South-Eastern Amazon, Brazil), one of the world's largest deposits of high-grade iron ore, we assess the influence of different cave characteristics on four biodiversity proxies (species richness, presence of troglobites, presence of rare troglobites, and presence of resident bat populations). We then examine how the current relevance classification scheme ranks caves with different biodiversity indicators. Large caves were found to be important reservoirs of biodiversity, so they should be prioritized in conservation programs. Our results also reveal spatial autocorrelation in all the biodiversity proxies assessed, indicating that iron caves should be treated as components of a cave network immersed in the karst landscape. Finally, we show that by prioritizing the conservation of rare troglobites, the current relevance classification scheme is undermining overall cave biodiversity and leaving ecologically important caves unprotected. We argue that conservation efforts should target subterranean habitats as a whole and propose an alternative relevance ranking scheme, which could help simplify the assessment process and channel more resources to the effective protection of overall cave biodiversity. PMID:27997576

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.

Mixed biodiversity benefits of agri-environment schemes in five European countries.

PubMed

Kleijn, D; Baquero, R A; Clough, Y; Díaz, M; De Esteban, J; Fernández, F; Gabriel, D; Herzog, F; Holzschuh, A; Jöhl, R; Knop, E; Kruess, A; Marshall, E J P; Steffan-Dewenter, I; Tscharntke, T; Verhulst, J; West, T M; Yela, J L

2006-03-01

Agri-environment schemes are an increasingly important tool for the maintenance and restoration of farmland biodiversity in Europe but their ecological effects are poorly known. Scheme design is partly based on non-ecological considerations and poses important restrictions on evaluation studies. We describe a robust approach to evaluate agri-environment schemes and use it to evaluate the biodiversity effects of agri-environment schemes in five European countries. We compared species density of vascular plants, birds, bees, grasshoppers and crickets, and spiders on 202 paired fields, one with an agri-environment scheme, the other conventionally managed. In all countries, agri-environment schemes had marginal to moderately positive effects on biodiversity. However, uncommon species benefited in only two of five countries and species listed in Red Data Books rarely benefited from agri-environment schemes. Scheme objectives may need to differentiate between biodiversity of common species that can be enhanced with relatively simple modifications in farming practices and diversity or abundance of endangered species which require more elaborate conservation measures.

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

NASA Astrophysics Data System (ADS)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures

NASA Astrophysics Data System (ADS)

Pötz, Walter

2017-11-01

A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

An Energy Efficient Cooperative Hierarchical MIMO Clustering Scheme for Wireless Sensor Networks

PubMed Central

Nasim, Mehwish; Qaisar, Saad; Lee, Sungyoung

2012-01-01

In this work, we present an energy efficient hierarchical cooperative clustering scheme for wireless sensor networks. Communication cost is a crucial factor in depleting the energy of sensor nodes. In the proposed scheme, nodes cooperate to form clusters at each level of network hierarchy ensuring maximal coverage and minimal energy expenditure with relatively uniform distribution of load within the network. Performance is enhanced by cooperative multiple-input multiple-output (MIMO) communication ensuring energy efficiency for WSN deployments over large geographical areas. We test our scheme using TOSSIM and compare the proposed scheme with cooperative multiple-input multiple-output (CMIMO) clustering scheme and traditional multihop Single-Input-Single-Output (SISO) routing approach. Performance is evaluated on the basis of number of clusters, number of hops, energy consumption and network lifetime. Experimental results show significant energy conservation and increase in network lifetime as compared to existing schemes. PMID:22368459

High-Resolution Genuinely Multidimensional Solution of Conservation Laws by the Space-Time Conservation Element and Solution Element Method

NASA Technical Reports Server (NTRS)

Himansu, Ananda; Chang, Sin-Chung; Yu, Sheng-Tao; Wang, Xiao-Yen; Loh, Ching-Yuen; Jorgenson, Philip C. E.

1999-01-01

In this overview paper, we review the basic principles of the method of space-time conservation element and solution element for solving the conservation laws in one and two spatial dimensions. The present method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. In contrast to the modern upwind schemes, the approach here does not use the Riemann solver and the reconstruction procedure as the building blocks. The drawbacks of the upwind approach, such as the difficulty of rationally extending the 1D scalar approach to systems of equations and particularly to multiple dimensions is here contrasted with the uniformity and ease of generalization of the Conservation Element and Solution Element (CE/SE) 1D scalar schemes to systems of equations and to multiple spatial dimensions. The assured compatibility with the simplest type of unstructured meshes, and the uniquely simple nonreflecting boundary conditions of the present method are also discussed. The present approach has yielded high-resolution shocks, rarefaction waves, acoustic waves, vortices, ZND detonation waves, and shock/acoustic waves/vortices interactions. Moreover, since no directional splitting is employed, numerical resolution of two-dimensional calculations is comparable to that of the one-dimensional calculations. Some sample applications displaying the strengths and broad applicability of the CE/SE method are reviewed.

Comparison of different interpolation operators including nonlinear subdivision schemes in the simulation of particle trajectories

NASA Astrophysics Data System (ADS)

Bensiali, Bouchra; Bodi, Kowsik; Ciraolo, Guido; Ghendrih, Philippe; Liandrat, Jacques

2013-03-01

In this work, we compare different interpolation operators in the context of particle tracking with an emphasis on situations involving velocity field with steep gradients. Since, in this case, most classical methods give rise to the Gibbs phenomenon (generation of oscillations near discontinuities), we present new methods for particle tracking based on subdivision schemes and especially on the Piecewise Parabolic Harmonic (PPH) scheme which has shown its advantage in image processing in presence of strong contrasts. First an analytic univariate case with a discontinuous velocity field is considered in order to highlight the effect of the Gibbs phenomenon on trajectory calculation. Theoretical results are provided. Then, we show, regardless of the interpolation method, the need to use a conservative approach when integrating a conservative problem with a velocity field deriving from a potential. Finally, the PPH scheme is applied in a more realistic case of a time-dependent potential encountered in the edge turbulence of magnetically confined plasmas, to compare the propagation of density structures (turbulence bursts) with the dynamics of test particles. This study highlights the difference between particle transport and density transport in turbulent fields.

Calculation of steady and unsteady transonic flow using a Cartesian mesh and gridless boundary conditions with application to aeroelasticity

NASA Astrophysics Data System (ADS)

Kirshman, David

A numerical method for the solution of inviscid compressible flow using an array of embedded Cartesian meshes in conjunction with gridless surface boundary conditions is developed. The gridless boundary treatment is implemented by means of a least squares fitting of the conserved flux variables using a cloud of nodes in the vicinity of the surface geometry. The method allows for accurate treatment of the surface boundary conditions using a grid resolution an order of magnitude coarser than required of typical Cartesian approaches. Additionally, the method does not suffer from issues associated with thin body geometry or extremely fine cut cells near the body. Unlike some methods that consider a gridless (or "meshless") treatment throughout the entire domain, multi-grid acceleration can be effectively incorporated and issues associated with global conservation are alleviated. The "gridless" surface boundary condition provides for efficient and simple problem set up since definition of the body geometry is generated independently from the field mesh, and automatically incorporated into the field discretization of the domain. The applicability of the method is first demonstrated for steady flow of single and multi-element airfoil configurations. Using this method, comparisons with traditional body-fitted grid simulations reveal that steady flow solutions can be obtained accurately with minimal effort associated with grid generation. The method is then extended to unsteady flow predictions. In this application, flow field simulations for the prescribed oscillation of an airfoil indicate excellent agreement with experimental data. Furthermore, it is shown that the phase lag associated with shock oscillation is accurately predicted without the need for a deformable mesh. Lastly, the method is applied to the prediction of transonic flutter using a two-dimensional wing model, in which comparisons with moving mesh simulations yield nearly identical results. As a result, applicability of the method to transient and vibrating fluid-structure interaction problems is established in which the requirement for a deformable mesh is eliminated.

Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

NASA Astrophysics Data System (ADS)

Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael

2018-06-01

In this work, we present a novel second-order accurate well-balanced arbitrary Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

A 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.

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.

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.

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1994-01-01

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Coexistence and survival in conservative Lotka-Volterra networks.

PubMed

Knebel, Johannes; Krüger, Torben; Weber, Markus F; Frey, Erwin

2013-04-19

Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network's interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time.

Coexistence and Survival in Conservative Lotka-Volterra Networks

NASA Astrophysics Data System (ADS)

Knebel, Johannes; Krüger, Torben; Weber, Markus F.; Frey, Erwin

2013-04-01

Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network’s interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time.

Stable schemes for dissipative particle dynamics with conserved energy

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

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

2017-07-01

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

Convergence of the Critical Cooling Rate for Protoplanetary Disk Fragmentation Achieved: The Key Role of Numerical Dissipation of Angular Momentum

NASA Astrophysics Data System (ADS)

Deng, Hongping; Mayer, Lucio; Meru, Farzana

2017-09-01

We carry out simulations of gravitationally unstable disks using smoothed particle hydrodynamics (SPH) and the novel Lagrangian meshless finite mass (MFM) scheme in the GIZMO code. Our aim is to understand the cause of the nonconvergence of the cooling boundary for fragmentation reported in the literature. We run SPH simulations with two different artificial viscosity implementations and compare them with MFM, which does not employ any artificial viscosity. With MFM we demonstrate convergence of the critical cooling timescale for fragmentation at {β }{crit}≈ 3. Nonconvergence persists in SPH codes. We show how the nonconvergence problem is caused by artificial fragmentation triggered by excessive dissipation of angular momentum in domains with large velocity derivatives. With increased resolution, such domains become more prominent. Vorticity lags behind density, due to numerical viscous dissipation in these regions, promoting collapse with longer cooling times. Such effect is shown to be dominant over the competing tendency of artificial viscosity to diminish with increasing resolution. When the initial conditions are first relaxed for several orbits, the flow is more regular, with lower shear and vorticity in nonaxisymmetric regions, aiding convergence. Yet MFM is the only method that converges exactly. Our findings are of general interest, as numerical dissipation via artificial viscosity or advection errors can also occur in grid-based codes. Indeed, for the FARGO code values of {β }{crit} significantly higher than our converged estimate have been reported in the literature. Finally, we discuss implications for giant planet formation via disk instability.

The Formation of a Milky Way-sized Disk Galaxy. I. A Comparison of Numerical Methods

NASA Astrophysics Data System (ADS)

Zhu, Qirong; Li, Yuexing

2016-11-01

The long-standing challenge of creating a Milky Way- (MW-) like disk galaxy from cosmological simulations has motivated significant developments in both numerical methods and physical models. We investigate these two fundamental aspects in a new comparison project using a set of cosmological hydrodynamic simulations of an MW-sized galaxy. In this study, we focus on the comparison of two particle-based hydrodynamics methods: an improved smoothed particle hydrodynamics (SPH) code Gadget, and a Lagrangian Meshless Finite-Mass (MFM) code Gizmo. All the simulations in this paper use the same initial conditions and physical models, which include star formation, “energy-driven” outflows, metal-dependent cooling, stellar evolution, and metal enrichment. We find that both numerical schemes produce a late-type galaxy with extended gaseous and stellar disks. However, notable differences are present in a wide range of galaxy properties and their evolution, including star-formation history, gas content, disk structure, and kinematics. Compared to Gizmo, the Gadget simulation produced a larger fraction of cold, dense gas at high redshift which fuels rapid star formation and results in a higher stellar mass by 20% and a lower gas fraction by 10% at z = 0, and the resulting gas disk is smoother and more coherent in rotation due to damping of turbulent motion by the numerical viscosity in SPH, in contrast to the Gizmo simulation, which shows a more prominent spiral structure. Given its better convergence properties and lower computational cost, we argue that the MFM method is a promising alternative to SPH in cosmological hydrodynamic simulations.

THE FORMATION OF A MILKY WAY-SIZED DISK GALAXY. I. A COMPARISON OF NUMERICAL METHODS

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

Zhu, Qirong; Li, Yuexing, E-mail: qxz125@psu.edu

The long-standing challenge of creating a Milky Way- (MW-) like disk galaxy from cosmological simulations has motivated significant developments in both numerical methods and physical models. We investigate these two fundamental aspects in a new comparison project using a set of cosmological hydrodynamic simulations of an MW-sized galaxy. In this study, we focus on the comparison of two particle-based hydrodynamics methods: an improved smoothed particle hydrodynamics (SPH) code Gadget, and a Lagrangian Meshless Finite-Mass (MFM) code Gizmo. All the simulations in this paper use the same initial conditions and physical models, which include star formation, “energy-driven” outflows, metal-dependent cooling, stellarmore » evolution, and metal enrichment. We find that both numerical schemes produce a late-type galaxy with extended gaseous and stellar disks. However, notable differences are present in a wide range of galaxy properties and their evolution, including star-formation history, gas content, disk structure, and kinematics. Compared to Gizmo, the Gadget simulation produced a larger fraction of cold, dense gas at high redshift which fuels rapid star formation and results in a higher stellar mass by 20% and a lower gas fraction by 10% at z = 0, and the resulting gas disk is smoother and more coherent in rotation due to damping of turbulent motion by the numerical viscosity in SPH, in contrast to the Gizmo simulation, which shows a more prominent spiral structure. Given its better convergence properties and lower computational cost, we argue that the MFM method is a promising alternative to SPH in cosmological hydrodynamic simulations.« less

Numerical investigation of sixth order Boussinesq equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.; Vucheva, V.

2017-10-01

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

Numerical Simulation of a Solar Domestic Hot Water System

NASA Astrophysics Data System (ADS)

Mongibello, L.; Bianco, N.; Di Somma, M.; Graditi, G.; Naso, V.

2014-11-01

An innovative transient numerical model is presented for the simulation of a solar Domestic Hot Water (DHW) system. The solar collectors have been simulated by using a zerodimensional analytical model. The temperature distributions in the heat transfer fluid and in the water inside the tank have been evaluated by one-dimensional models. The reversion elimination algorithm has been used to include the effects of natural convection among the water layers at different heights in the tank on the thermal stratification. A finite difference implicit scheme has been implemented to solve the energy conservation equation in the coil heat exchanger, and the energy conservation equation in the tank has been solved by using the finite difference Euler implicit scheme. Energy conservation equations for the solar DHW components models have been coupled by means of a home-made implicit algorithm. Results of the simulation performed using as input data the experimental values of the ambient temperature and the solar irradiance in a summer day are presented and discussed.

Uniformly high-order accurate non-oscillatory schemes, 1

NASA Technical Reports Server (NTRS)

Harten, A.; Osher, S.

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Canonical-ensemble extended Lagrangian Born-Oppenheimer molecular dynamics for the linear scaling density functional theory.

PubMed

Hirakawa, Teruo; Suzuki, Teppei; Bowler, David R; Miyazaki, Tsuyoshi

2017-10-11

We discuss the development and implementation of a constant temperature (NVT) molecular dynamics scheme that combines the Nosé-Hoover chain thermostat with the extended Lagrangian Born-Oppenheimer molecular dynamics (BOMD) scheme, using a linear scaling density functional theory (DFT) approach. An integration scheme for this canonical-ensemble extended Lagrangian BOMD is developed and discussed in the context of the Liouville operator formulation. Linear scaling DFT canonical-ensemble extended Lagrangian BOMD simulations are tested on bulk silicon and silicon carbide systems to evaluate our integration scheme. The results show that the conserved quantity remains stable with no systematic drift even in the presence of the thermostat.

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

Land-use protection for climate change mitigation

NASA Astrophysics Data System (ADS)

Popp, Alexander; Humpenöder, Florian; Weindl, Isabelle; Bodirsky, Benjamin Leon; Bonsch, Markus; Lotze-Campen, Hermann; Müller, Christoph; Biewald, Anne; Rolinski, Susanne; Stevanovic, Miodrag; Dietrich, Jan Philipp

2014-12-01

Land-use change, mainly the conversion of tropical forests to agricultural land, is a massive source of carbon emissions and contributes substantially to global warming. Therefore, mechanisms that aim to reduce carbon emissions from deforestation are widely discussed. A central challenge is the avoidance of international carbon leakage if forest conservation is not implemented globally. Here, we show that forest conservation schemes, even if implemented globally, could lead to another type of carbon leakage by driving cropland expansion in non-forested areas that are not subject to forest conservation schemes (non-forest leakage). These areas have a smaller, but still considerable potential to store carbon. We show that a global forest policy could reduce carbon emissions by 77 Gt CO2, but would still allow for decreases in carbon stocks of non-forest land by 96 Gt CO2 until 2100 due to non-forest leakage effects. Furthermore, abandonment of agricultural land and associated carbon uptake through vegetation regrowth is hampered. Effective mitigation measures thus require financing structures and conservation investments that cover the full range of carbon-rich ecosystems. However, our analysis indicates that greater agricultural productivity increases would be needed to compensate for such restrictions on agricultural expansion.

Mass-corrections for the conservative coupling of flow and transport on collocated meshes

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

Waluga, Christian, E-mail: waluga@ma.tum.de; Wohlmuth, Barbara; Rüde, Ulrich

2016-01-15

Buoyancy-driven flow models demand a careful treatment of the mass-balance equation to avoid spurious source and sink terms in the non-linear coupling between flow and transport. In the context of finite-elements, it is therefore commonly proposed to employ sufficiently rich pressure spaces, containing piecewise constant shape functions to obtain local or even strong mass-conservation. In three-dimensional computations, this usually requires nonconforming approaches, special meshes or higher order velocities, which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code. In this paper, we therefore propose a lean and conservatively coupled scheme based on standard stabilizedmore » linear equal-order finite elements for the Stokes part and vertex-centered finite volumes for the energy equation. We show that in a weak mass-balance it is possible to recover exact conservation properties by a local flux-correction which can be computed efficiently on the control volume boundaries of the transport mesh. We discuss implementation aspects and demonstrate the effectiveness of the flux-correction by different two- and three-dimensional examples which are motivated by geophysical applications.« less

On large time step TVD scheme for hyperbolic conservation laws and its efficiency evaluation

NASA Astrophysics Data System (ADS)

Qian, ZhanSen; Lee, Chun-Hian

2012-08-01

A large time step (LTS) TVD scheme originally proposed by Harten is modified and further developed in the present paper and applied to Euler equations in multidimensional problems. By firstly revealing the drawbacks of Harten's original LTS TVD scheme, and reasoning the occurrence of the spurious oscillations, a modified formulation of its characteristic transformation is proposed and a high resolution, strongly robust LTS TVD scheme is formulated. The modified scheme is proven to be capable of taking larger number of time steps than the original one. Following the modified strategy, the LTS TVD schemes for Yee's upwind TVD scheme and Yee-Roe-Davis's symmetric TVD scheme are constructed. The family of the LTS schemes is then extended to multidimensional by time splitting procedure, and the associated boundary condition treatment suitable for the LTS scheme is also imposed. The numerical experiments on Sod's shock tube problem, inviscid flows over NACA0012 airfoil and ONERA M6 wing are performed to validate the developed schemes. Computational efficiencies for the respective schemes under different CFL numbers are also evaluated and compared. The results reveal that the improvement is sizable as compared to the respective single time step schemes, especially for the CFL number ranging from 1.0 to 4.0.

Preparing CAM-SE for Multi-Tracer Applications: CAM-SE-Cslam

NASA Astrophysics Data System (ADS)

Lauritzen, P. H.; Taylor, M.; Goldhaber, S.

2014-12-01

The NCAR-DOE spectral element (SE) dynamical core comes from the HOMME (High-Order Modeling Environment; Dennis et al., 2012) and it is available in CAM. The CAM-SE dynamical core is designed with intrinsic mimetic properties guaranteeing total energy conservation (to time-truncation errors) and mass-conservation, and has demonstrated excellent scalability on massively parallel compute platforms (Taylor, 2011). For applications involving many tracers such as chemistry and biochemistry modeling, CAM-SE has been found to be significantly more computationally costly than the current "workhorse" model CAM-FV (Finite-Volume; Lin 2004). Hence a multi-tracer efficient scheme, called the CSLAM (Conservative Semi-Lagrangian Multi-tracer; Lauritzen et al., 2011) scheme, has been implemented in the HOMME (Erath et al., 2012). The CSLAM scheme has recently been cast in flux-form in HOMME so that it can be coupled to the SE dynamical core through conventional flux-coupling methods where the SE dynamical core provides background air mass fluxes to CSLAM. Since the CSLAM scheme makes use of a finite-volume gnomonic cubed-sphere grid and hence does not operate on the SE quadrature grid, the capability of running tracer advection, the physical parameterization suite and dynamics on separate grids has been implemented in CAM-SE. The default CAM-SE-CSLAM setup is to run physics on the quasi-equal area CSLAM grid. The capability of running physics on a different grid than the SE dynamical core may provide a more consistent coupling since the physics grid option operates with quasi-equal-area cell average values rather than non-equi-distant grid-point (SE quadrature point) values. Preliminary results on the performance of CAM-SE-CSLAM will be presented.

Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows.

PubMed

Sanjeevi, Sathish K P; Zarghami, Ahad; Padding, Johan T

2018-04-01

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows

NASA Astrophysics Data System (ADS)

Sanjeevi, Sathish K. P.; Zarghami, Ahad; Padding, Johan T.

2018-04-01

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

Energy conserving schemes for the simulation of musical instrument contact dynamics

NASA Astrophysics Data System (ADS)

Chatziioannou, Vasileios; van Walstijn, Maarten

2015-03-01

Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are non-analytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton's equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton's method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument.

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1990-01-01

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

Development of high-accuracy convection schemes for sequential solvers

NASA Technical Reports Server (NTRS)

Thakur, Siddharth; Shyy, Wei

1993-01-01

An exploration is conducted of the applicability of such high resolution schemes as TVD to the resolving of sharp flow gradients using a sequential solution approach borrowed from pressure-based algorithms. It is shown that by extending these high-resolution shock-capturing schemes to a sequential solver that treats the equations as a collection of scalar conservation equations, the speed of signal propagation in the solution has to be coordinated by assigning the local convection speed as the characteristic speed for the entire system. A higher amount of dissipation is therefore needed to eliminate oscillations near discontinuities.

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

NASA Astrophysics Data System (ADS)

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

2018-05-01

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.

Electric load management and energy conservation

NASA Technical Reports Server (NTRS)

Kheir, N. A.

1976-01-01

Electric load management and energy conservation relate heavily to the major problems facing power industry at present. The three basic modes of energy conservation are identified as demand reduction, increased efficiency and substitution for scarce fuels. Direct and indirect load management objectives are to reduce peak loads and have future growth in electricity requirements in such a manner to cause more of it to fall off the system's peak. In this paper, an overview of proposed and implemented load management options is presented. Research opportunities exist for the evaluation of socio-economic impacts of energy conservation and load management schemes specially on the electric power industry itself.

Conservative zonal schemes for patched grids in 2 and 3 dimensions

NASA Technical Reports Server (NTRS)

Hessenius, Kristin A.

1987-01-01

The computation of flow over complex geometries, such as realistic aircraft configurations, poses difficult grid generation problems for computational aerodynamicists. The creation of a traditional, single-module grid of acceptable quality about an entire configuration may be impossible even with the most sophisticated of grid generation techniques. A zonal approach, wherein the flow field is partitioned into several regions within which grids are independently generated, is a practical alternative for treating complicated geometries. This technique not only alleviates the problems of discretizing a complex region, but also facilitates a block processing approach to computation thereby circumventing computer memory limitations. The use of such a zonal scheme, however, requires the development of an interfacing procedure that ensures a stable, accurate, and conservative calculation for the transfer of information across the zonal borders.

Numerical investigation of shock induced bubble collapse in water

NASA Astrophysics Data System (ADS)

Apazidis, N.

2016-04-01

A semi-conservative, stable, interphase-capturing numerical scheme for shock propagation in heterogeneous systems is applied to the problem of shock propagation in liquid-gas systems. The scheme is based on the volume-fraction formulation of the equations of motion for liquid and gas phases with separate equations of state. The semi-conservative formulation of the governing equations ensures the absence of spurious pressure oscillations at the material interphases between liquid and gas. Interaction of a planar shock in water with a single spherical bubble as well as twin adjacent bubbles is investigated. Several stages of the interaction process are considered, including focusing of the transmitted shock within the deformed bubble, creation of a water-hammer shock as well as generation of high-speed liquid jet in the later stages of the process.

A non-oscillatory energy-splitting method for the computation of compressible multi-fluid flows

NASA Astrophysics Data System (ADS)

Lei, Xin; Li, Jiequan

2018-04-01

This paper proposes a new non-oscillatory energy-splitting conservative algorithm for computing multi-fluid flows in the Eulerian framework. In comparison with existing multi-fluid algorithms in the literature, it is shown that the mass fraction model with isobaric hypothesis is a plausible choice for designing numerical methods for multi-fluid flows. Then we construct a conservative Godunov-based scheme with the high order accurate extension by using the generalized Riemann problem solver, through the detailed analysis of kinetic energy exchange when fluids are mixed under the hypothesis of isobaric equilibrium. Numerical experiments are carried out for the shock-interface interaction and shock-bubble interaction problems, which display the excellent performance of this type of schemes and demonstrate that nonphysical oscillations are suppressed around material interfaces substantially.

Some observations on boundary conditions for numerical conservation laws

NASA Technical Reports Server (NTRS)

Kamowitz, David

1988-01-01

Four choices of outflow boundary conditions are considered for numerical conservation laws. All four methods are stable for linear problems, for which examples are presented where either a boundary layer forms or the numerical scheme, together with the boundary condition, is unstable due to the formation of a reflected shock. A simple heuristic argument is presented for determining the suitability of the boundary condition.

Secure Wake-Up Scheme for WBANs

NASA Astrophysics Data System (ADS)

Liu, Jing-Wei; Ameen, Moshaddique Al; Kwak, Kyung-Sup

Network life time and hence device life time is one of the fundamental metrics in wireless body area networks (WBAN). To prolong it, especially those of implanted sensors, each node must conserve its energy as much as possible. While a variety of wake-up/sleep mechanisms have been proposed, the wake-up radio potentially serves as a vehicle to introduce vulnerabilities and attacks to WBAN, eventually resulting in its malfunctions. In this paper, we propose a novel secure wake-up scheme, in which a wake-up authentication code (WAC) is employed to ensure that a BAN Node (BN) is woken up by the correct BAN Network Controller (BNC) rather than unintended users or malicious attackers. The scheme is thus particularly implemented by a two-radio architecture. We show that our scheme provides higher security while consuming less energy than the existing schemes.

Studies of Inviscid Flux Schemes for Acoustics and Turbulence Problems

NASA Technical Reports Server (NTRS)

Morris, Chris

2013-01-01

Five different central difference schemes, based on a conservative differencing form of the Kennedy and Gruber skew-symmetric scheme, were compared with six different upwind schemes based on primitive variable reconstruction and the Roe flux. These eleven schemes were tested on a one-dimensional acoustic standing wave problem, the Taylor-Green vortex problem and a turbulent channel flow problem. The central schemes were generally very accurate and stable, provided the grid stretching rate was kept below 10%. As near-DNS grid resolutions, the results were comparable to reference DNS calculations. At coarser grid resolutions, the need for an LES SGS model became apparent. There was a noticeable improvement moving from CD-2 to CD-4, and higher-order schemes appear to yield clear benefits on coarser grids. The UB-7 and CU-5 upwind schemes also performed very well at near-DNS grid resolutions. The UB-5 upwind scheme does not do as well, but does appear to be suitable for well-resolved DNS. The UF-2 and UB-3 upwind schemes, which have significant dissipation over a wide spectral range, appear to be poorly suited for DNS or LES.

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.

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.

Discrete and continuum modelling of soil cutting

NASA Astrophysics Data System (ADS)

Coetzee, C. J.

2014-12-01

Both continuum and discrete methods are used to investigate the soil cutting process. The Discrete Element Method ( dem) is used for the discrete modelling and the Material-Point Method ( mpm) is used for continuum modelling. M pmis a so-called particle method or meshless finite element method. Standard finite element methods have difficulty in modelling the entire cutting process due to large displacements and deformation of the mesh. The use of meshless methods overcomes this problem. M pm can model large deformations, frictional contact at the soil-tool interface, and dynamic effects (inertia forces). In granular materials the discreteness of the system is often important and rotational degrees of freedom are active, which might require enhanced theoretical approaches like polar continua. In polar continuum theories, the material points are considered to possess orientations. A material point has three degrees-of-freedom for rigid rotations, in addition to the three classic translational degrees-of-freedom. The Cosserat continuum is the most transparent and straightforward extension of the nonpolar (classic) continuum. Two-dimensional dem and mpm (polar and nonpolar) simulations of the cutting problem are compared to experiments. The drag force and flow patterns are compared using cohesionless corn grains as material. The corn macro (continuum) and micro ( dem) properties were obtained from shear and oedometer tests. Results show that the dilatancy angle plays a significant role in the flow of material but has less of an influence on the draft force. Nonpolar mpm is the most accurate in predicting blade forces, blade-soil interface stresses and the position and orientation of shear bands. Polar mpm fails in predicting the orientation of the shear band, but is less sensitive to mesh size and mesh orientation compared to nonpolar mpm. dem simulations show less material dilation than observed during experiments.

Modeling Pulse Transmission in the Monterey Bay Using Parabolic Equation Methods

DTIC Science & Technology

1991-12-01

Collins 9-13 was chosen for this purpose due its energy conservation scheme , and its ability to efficiently incorporate higher order terms in its...pressure field generated by the PE model into normal modes. Additionally, this process provides increased physical understanding of mode coupling and...separation of variables (i.e. normal modes or fast field), as well as pure numerical schemes such as the parabolic equation methods, can be used. However, as

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.

Conservative DEC Discretization of Incompressible Navier-Stokes Equations on Arbitrary Surface Simplicial Meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh; Hirani, Anil; Samtaney, Ravi

2017-11-01

A conservative discretization of incompressible Navier-Stokes equations over surfaces is developed using discrete exterior calculus (DEC). The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of signed diagonal Hodge star operators, while using the circumcentric dual defined on arbitrary meshes, is shown to produce correct solutions even when many non-Delaunay triangles pairs exist. This allows the DEC discretization to admit arbitrary surface simplicial meshes, in contrast to the previously held notion that DEC was limited only to Delaunay meshes. The discretization scheme is presented along with several numerical test cases demonstrating its numerical convergence and conservation properties. Recent developments regarding the extension to conservative higher order methods are also presented. KAUST Baseline Research Funds of R. Samtaney.

Research on the supercapacitor support schemes for LVRT of variable-frequency drive in the thermal power plant

NASA Astrophysics Data System (ADS)

Han, Qiguo; Zhu, Kai; Shi, Wenming; Wu, Kuayu; Chen, Kai

2018-02-01

In order to solve the problem of low voltage ride through(LVRT) of the major auxiliary equipment’s variable-frequency drive (VFD) in thermal power plant, the scheme of supercapacitor paralleled in the DC link of VFD is put forward, furthermore, two solutions of direct parallel support and voltage boost parallel support of supercapacitor are proposed. The capacitor values for the relevant motor loads are calculated according to the law of energy conservation, and they are verified by Matlab simulation. At last, a set of test prototype is set up, and the test results prove the feasibility of the proposed schemes.

HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Gammie, Charles F.; McKinney, Jonathan C.; Tóth, Gábor

2003-05-01

We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van Leer scheme. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence-free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.

Recent applications of the transonic wing analysis computer code, TWING

NASA Technical Reports Server (NTRS)

Subramanian, N. R.; Holst, T. L.; Thomas, S. D.

1982-01-01

An evaluation of the transonic-wing-analysis computer code TWING is given. TWING utilizes a fully implicit approximate factorization iteration scheme to solve the full potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations were analyzed, and the limits of applicability of this code was evaluated. Comparisons of computed results were made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative full potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

A conservative MHD scheme on unstructured Lagrangian grids for Z-pinch hydrodynamic simulations

NASA Astrophysics Data System (ADS)

Wu, Fuyuan; Ramis, Rafael; Li, Zhenghong

2018-03-01

A new algorithm to model resistive magnetohydrodynamics (MHD) in Z-pinches has been developed. Two-dimensional axisymmetric geometry with azimuthal magnetic field Bθ is considered. Discretization is carried out using unstructured meshes made up of arbitrarily connected polygons. The algorithm is fully conservative for mass, momentum, and energy. Matter energy and magnetic energy are managed separately. The diffusion of magnetic field is solved using a derivative of the Symmetric-Semi-Implicit scheme, Livne et al. (1985) [23], where unconditional stability is obtained without needing to solve large sparse systems of equations. This MHD package has been integrated into the radiation-hydrodynamics code MULTI-2D, Ramis et al. (2009) [20], that includes hydrodynamics, laser energy deposition, heat conduction, and radiation transport. This setup allows to simulate Z-pinch configurations relevant for Inertial Confinement Fusion.

Geometric integration in Born-Oppenheimer molecular dynamics.

PubMed

Odell, Anders; Delin, Anna; Johansson, Börje; Cawkwell, Marc J; Niklasson, Anders M N

2011-12-14

Geometric integration schemes for extended Lagrangian self-consistent Born-Oppenheimer molecular dynamics, including a weak dissipation to remove numerical noise, are developed and analyzed. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. We investigate three different geometric integration schemes: (1) regular time reversible Verlet, (2) second order optimal symplectic, and (3) third order optimal symplectic. We look at energy conservation, accuracy, and stability as a function of dissipation, integration time step, and SCF convergence. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. © 2011 American Institute of Physics

Ecologically-friendly operation scheme for the Jinping cascaded reservoirs in the Yalongjiang River, China

NASA Astrophysics Data System (ADS)

Chen, Duan; Chen, Qiuwen; Li, Ruonan; Blanckaert, Koen; Cai, Desuo

2014-06-01

Ecologically-friendly reservoir operation procedures aim to conserve key ecosystem properties in the rivers, while minimizing the sacrifice of socioeconomic interests. This study focused on the Jinping cascaded reservoirs as a case study. An optimization model was developed to explore a balance between the ecological flow requirement (EFR) of a target fish species ( Schizothorax chongi) in the dewatered natural channel section, and annual power production. The EFR for the channel was determined by the Tennant method and a fish habitat model, respectively. The optimization model was solved by using an adaptive real-coded genetic algorithm. Several operation scenarios corresponding to the ecological flow series were evaluated using the optimization model. Through comparisons, an optimal operational scheme, which combines relatively low power production loss with a preferred ecological flow regime in the dewatered channel, is proposed for the cascaded reservoirs. Under the recommended scheme, the discharge into the Dahewan river reach in the dry season ranges from 36 to 50 m3/s. This will enable at least 50% of the target fish habitats in the channel to be conserved, at a cost of only 2.5% annual power production loss. The study demonstrates that the use of EFRs is an efficient approach to the optimization of reservoir operation in an ecologically friendly way. Similar modeling, for other important fish species and ecosystem functions, supplemented by field validation of results, is needed in order to secure the long-term conservation of the affected river ecosystem.

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.

Implicit approximate-factorization schemes for the low-frequency transonic equation

NASA Technical Reports Server (NTRS)

Ballhaus, W. F.; Steger, J. L.

1975-01-01

Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

A self-consistent density based embedding scheme applied to the adsorption of CO on Pd(111)

NASA Astrophysics Data System (ADS)

Lahav, D.; Klüner, T.

2007-06-01

We derive a variant of a density based embedded cluster approach as an improvement to a recently proposed embedding theory for metallic substrates (Govind et al 1999 J. Chem. Phys. 110 7677; Klüner et al 2001 Phys. Rev. Lett. 86 5954). In this scheme, a local region in space is represented by a small cluster which is treated by accurate quantum chemical methodology. The interaction of the cluster with the infinite solid is taken into account by an effective one-electron embedding operator representing the surrounding region. We propose a self-consistent embedding scheme which resolves intrinsic problems of the former theory, in particular a violation of strict density conservation. The proposed scheme is applied to the well-known benchmark system CO/Pd(111).

A Shock-Adaptive Godunov Scheme Based on the Generalised Lagrangian Formulation

NASA Astrophysics Data System (ADS)

Lepage, C. Y.; Hui, W. H.

1995-12-01

Application of the Godunov scheme to the Euler equations of gas dynamics based on the Eulerian formulation of flow smears discontinuities, sliplines especially, over several computational cells, while the accuracy in the smooth flow region is of the order O( h), where h is the cell width. Based on the generalised Lagrangian formulation (GLF) of Hui et al., the Godunov scheme yields superior accuracy. By the use of coordinate streamlines in the GLF, the slipline—itself a streamline—is resolved crisply. Infinite shock resolution is achieved through the splitting of shock-cells. An improved entropy-conservation formulation of the governing equations is also proposed for computations in smooth flow regions. Finally, the use of the GLF substantially simplifies the programming logic resulting in a very robust, accurate, and efficient scheme.

Towards information-optimal simulation of partial differential equations.

PubMed

Leike, Reimar H; Enßlin, Torsten A

2018-03-01

Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation. The result is an action that can be minimized to obtain an information-optimal simulation scheme. It can be brought into a closed form using field operators to calculate the appearing Gaussian integrals. The resulting simulation schemes are tested numerically in two instances for the Burgers equation. Their accuracy surpasses finite-difference schemes on the same resolution. The IFD scheme, however, has to be correctly informed on the subgrid correlation structure. In certain limiting cases we recover well-known simulation schemes like spectral Fourier-Galerkin methods. We discuss implications of the approximations made.

Three-dimensional simulation of vortex breakdown

NASA Technical Reports Server (NTRS)

Kuruvila, G.; Salas, M. D.

1990-01-01

The integral form of the complete, unsteady, compressible, three-dimensional Navier-Stokes equations in the conservation form, cast in generalized coordinate system, are solved, numerically, to simulate the vortex breakdown phenomenon. The inviscid fluxes are discretized using Roe's upwind-biased flux-difference splitting scheme and the viscous fluxes are discretized using central differencing. Time integration is performed using a backward Euler ADI (alternating direction implicit) scheme. A full approximation multigrid is used to accelerate the convergence to steady state.

Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs

NASA Astrophysics Data System (ADS)

Tang, Wensheng; Sun, Yajuan; Cai, Wenjun

2017-02-01

In this article, we present a unified framework of discontinuous Galerkin (DG) discretizations for Hamiltonian ODEs and PDEs. We show that with appropriate numerical fluxes the numerical algorithms deduced from DG discretizations can be combined with the symplectic methods in time to derive the multi-symplectic PRK schemes. The resulting numerical discretizations are applied to the linear and nonlinear Schrödinger equations. Some conservative properties of the numerical schemes are investigated and confirmed in the numerical experiments.

Constructing space difference schemes which satisfy a cell entropy inequality

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1989-01-01

A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2014-10-01

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen et al., 2011). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation to Maxwell's equations, which avoids radiative noise issues by ordering out the light wave. An implicit, orbit-averaged, time-space-centered finite difference scheme is employed in both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. We have developed a simple preconditioner that targets electrostatic waves and skin currents, and allows us to employ time steps O(√{mi /me } c /veT) larger than the explicit CFL. Several 1D numerical experiments demonstrate the accuracy, performance, and conservation properties of the algorithm. In particular, the scheme is shown to be second-order accurate, and CPU speedups of more than three orders of magnitude vs. an explicit Vlasov-Maxwell solver are demonstrated in the "cold" plasma regime (where kλD ≪ 1).

Novel two-way artificial boundary condition for 2D vertical water wave propagation modelled with Radial-Basis-Function Collocation Method

NASA Astrophysics Data System (ADS)

Mueller, A.

2018-04-01

A new transparent artificial boundary condition for the two-dimensional (vertical) (2DV) free surface water wave propagation modelled using the meshless Radial-Basis-Function Collocation Method (RBFCM) as boundary-only solution is derived. The two-way artificial boundary condition (2wABC) works as pure incidence, pure radiation and as combined incidence/radiation BC. In this work the 2wABC is applied to harmonic linear water waves; its performance is tested against the analytical solution for wave propagation over horizontal sea bottom, standing and partially standing wave as well as wave interference of waves with different periods.

A semi-Lagrangian approach to the shallow water equation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Mccormick, Stephen F.; Ruge, John; Sholl, David S.; Yavneh, Irad

1993-01-01

We present a formulation of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-Lagrangian time-stepping scheme is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.

On the conservation of adiabatic invariants for a system of coupled rotators

NASA Astrophysics Data System (ADS)

Benettin, G.; Carati, A.; Fassò, F.

1997-02-01

We study the accuracy of the conservation of adiabatic invariants in a model of n weakly coupled rotators. Most attention is devoted to n = 2 and frequency ω = ( ω1, ω2), with {ω 2}/{ω 1} quadratic irrational. We apply a heuristic approximation scheme, going back to Jeans and to Landau and Teller, and perform a very accurate numerical check of the result, observing a quite remarkable agreement.

Spatial relationship between climatic diversity and biodiversity conservation value.

PubMed

Wang, Junjun; Wu, Ruidong; He, Daming; Yang, Feiling; Hu, Peijun; Lin, Shiwei; Wu, Wei; Diao, Yixin; Guo, Yang

2018-06-04

Capturing the full range of climatic diversity in a reserve network is expected to improve the resilience of biodiversity to climate change. Therefore, a study on systematic conservation planning for climatic diversity that explicitly or implicitly hypothesizes that regions with higher climatic diversity will support greater biodiversity is needed. However, little is known about the extent and generality of this hypothesis. This study utilized the case of Yunnan, southwest China, to quantitatively classify climatic units and modeled 4 climatic diversity indicators, including the variety of climatic units (VCU), rarity of climatic units (RCU), endemism of climatic units (ECU) and a composite index of climatic units (CICD). We used 5 reliable priority conservation area (PCA) schemes to represent the areas with high biodiversity conservation value. We then investigated the spatial relationships between the 4 climatic diversity indicators and the 5 PCA schemes and assessed the representation of climatic diversity within the existing nature reserves. The CICD exhibited the best performance for indicating high conservation value areas, followed by the ECU and RCU. However, contrary to conventional knowledge, VCU did not show a positive association with biodiversity conservation value. The rarer or more endemic climatic units tended to have higher reserve coverage than the more common units. However, only 28 units covering 10.5% of the land in Yunnan had more than 17% of their areas protected. In addition to climatic factors, topography and human disturbances also significantly affected the relationship between climatic diversity and biodiversity conservation value. This analysis suggests that climatic diversity can be an effective surrogate for establishing a more robust reserve network under climate change in Yunnan. Our study improves the understanding of the relationship between climatic diversity and biodiversity and helps build an evidence-based foundation for systematic conservation planning that targets climatic diversity in response to climate change. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

Assessing conservation opportunity on private land: socio-economic, behavioral, and spatial dimensions.

PubMed

Raymond, Christopher M; Brown, Gregory

2011-10-01

This study presents a method for assessing conservation opportunity on private land based on landholders' socio-economic, behavioral, and farm characteristics. These characteristics include age, gender, education, level of off-farm income, farm size, proportion of remnant native vegetation on-farm, and ecological value of native vegetation on-farm. A sample of landholders who own greater than 2 ha of land in the South Australian Murray-Darling Basin region were sent a mail-based survey about their values and preferences for environmental management (N = 659, 52% response). Cross-tabulations and ANOVA statistical analysis techniques were used to compare the socio-economic attributes across three landholder classes: disengaged, moderately engaged, and highly engaged in native vegetation planting. Results indicate that highly engaged landholders were more likely to be female, formally educated, hobby farmers who managed small parcels of land and have high off-farm incomes, whereas disengaged landholders held significantly stronger farming connections (more farming experience, family have lived on the farm for more generations). Spatial analysis revealed area-specific differences in conservation opportunity and conservation priority. In some areas, properties of high ecological value were managed by highly engaged landholders, but nearby properties of high value were managed by moderately engaged or disengaged landholders. Environmental managers therefore cannot assume areas of high conservation priority will be areas of high conservation opportunity. At the regional scale, the potential for revegetation seems most promising within the moderately engaged landholder group considering the vast amount of land managed by this group in areas of high ecological value, particularly within the less represented Mallee and Coorong and Rangelands sub-regions. We suggest that incentive schemes which purchase conservation need to be targeted at disengaged landholders; mentoring schemes led by commercial farmers highly engaged in native vegetation planting should be directed at moderately engaged landholders, and; awards programs which acknowledge conservation successes should be targeted at highly engaged landholders. Copyright © 2011 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Nonequilibrium thermo-chemical calculations using a diagonal implicit scheme

NASA Technical Reports Server (NTRS)

Imlay, Scott T.; Roberts, Donald W.; Soetrisno, Moeljo; Eberhardt, Scott

1991-01-01

A recently developed computer program for hypersonic vehicle flow analysis is described. The program uses a diagonal implicit algorithm to solve the equations of viscous flow for a gas in thermochemical nonequilibrium. The diagonal scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The program uses multiple zones of grids patched together and includes radiation wall and rarefied gas boundary conditions. Solutions are presented for hypersonic flows of air and hydrogen air mixtures.

CFD in Support of Wind Tunnel Testing for Aircraft/Weapons Integration

DTIC Science & Technology

2004-06-01

Warming flux vector splitting scheme. Viscous rate t mies s to the oDentati ote t fluxes (computed using spatial central differencing) in erotate try...computations factors to eliminate them from the current computation. performed. The grid system consisted of 18 x 106 points These newly i-blanked grid...273-295. 130 14. van Leer, B., "Towards the Ultimate Conservative 18 . Suhs, N.E., and R.W. Tramel, "PEGSUS 4.0 Users Manual." Difference Scheme V. A

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.

Efficient Conservative Reformulation Schemes for Lithium Intercalation

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

Urisanga, PC; Rife, D; De, S

Porous electrode theory coupled with transport and reaction mechanisms is a widely used technique to model Li-ion batteries employing an appropriate discretization or approximation for solid phase diffusion with electrode particles. One of the major difficulties in simulating Li-ion battery models is the need to account for solid phase diffusion in a second radial dimension r, which increases the computation time/cost to a great extent. Various methods that reduce the computational cost have been introduced to treat this phenomenon, but most of them do not guarantee mass conservation. The aim of this paper is to introduce an inherently mass conservingmore » yet computationally efficient method for solid phase diffusion based on Lobatto III A quadrature. This paper also presents coupling of the new solid phase reformulation scheme with a macro-homogeneous porous electrode theory based pseudo 20 model for Li-ion battery. (C) The Author(s) 2015. Published by ECS. All rights reserved.« less

Extension of a streamwise upwind algorithm to a moving grid system

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru; Goorjian, Peter M.; Guruswamy, Guru P.

1990-01-01

A new streamwise upwind algorithm was derived to compute unsteady flow fields with the use of a moving-grid system. The temporally nonconservative LU-ADI (lower-upper-factored, alternating-direction-implicit) method was applied for time marching computations. A comparison of the temporally nonconservative method with a time-conservative implicit upwind method indicates that the solutions are insensitive to the conservative properties of the implicit solvers when practical time steps are used. Using this new method, computations were made for an oscillating wing at a transonic Mach number. The computed results confirm that the present upwind scheme captures the shock motion better than the central-difference scheme based on the beam-warming algorithm. The new upwind option of the code allows larger time-steps and thus is more efficient, even though it requires slightly more computational time per time step than the central-difference option.

A multi-dimensional nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell (PIC) algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; CoCoMans Team

2014-10-01

For decades, the Vlasov-Darwin model has been recognized to be attractive for PIC simulations (to avoid radiative noise issues) in non-radiative electromagnetic regimes. However, the Darwin model results in elliptic field equations that renders explicit time integration unconditionally unstable. Improving on linearly implicit schemes, fully implicit PIC algorithms for both electrostatic and electromagnetic regimes, with exact discrete energy and charge conservation properties, have been recently developed in 1D. This study builds on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the particle-field equations in multiple dimensions. The algorithm conserves energy, charge, and canonical-momentum exactly, even with grid packing. A simple fluid preconditioner allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. We demonstrate the accuracy and efficiency properties of the of the algorithm with various numerical experiments in 2D3V.

A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1994-01-01

The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts 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 waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic 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 flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.

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.

Numerical solution of the unsteady Navier-Stokes equation

NASA Technical Reports Server (NTRS)

Osher, Stanley J.; Engquist, Bjoern

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Patched-grid calculations with the Euler and Navier-Stokes equations: Theory and applications

NASA Technical Reports Server (NTRS)

Rai, M. M.

1986-01-01

A patched-grid approach is one in which the flow region of interest is divided into subregions which are then discretized independently using existing grid generator. The equations of motion are integrated in each subregion in conjunction with patch-boundary schemes which allow proper information transfer across interfaces that separate subregions. The patched-grid approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. A conservative patch-boundary condition that can be used with explicit, implicit factored and implicit relaxation schemes is described. Several example calculations that demonstrate the capabilities of the patched-grid scheme are also included.

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

NASA Astrophysics Data System (ADS)

Toth, G.; Keppens, R.; Botchev, M. A.

1998-04-01

We describe and evaluate various implicit and semi-implicit time integration schemes applied to the numerical simulation of hydrodynamical and magnetohydrodynamical problems. The schemes were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing methods to solve systems of conservation laws with optional source terms. The main advantage of implicit solution strategies over explicit time integration is that the restrictive constraint on the allowed time step can be (partially) eliminated, thus the computational cost is reduced. The test problems cover one and two dimensional, steady state and time accurate computations, and the solutions contain discontinuities. For each test, we confront explicit with implicit solution strategies.

A structure-preserving split finite element discretization of the split 1D linear shallow-water equations

NASA Astrophysics Data System (ADS)

Bauer, Werner; Behrens, Jörn

2017-04-01

We present a locally conservative, low-order finite element (FE) discretization of the covariant 1D linear shallow-water equations written in split form (cf. tet{[1]}). The introduction of additional differential forms (DF) that build pairs with the original ones permits a splitting of these equations into topological momentum and continuity equations and metric-dependent closure equations that apply the Hodge-star. Our novel discretization framework conserves this geometrical structure, in particular it provides for all DFs proper FE spaces such that the differential operators (here gradient and divergence) hold in strong form. The discrete topological equations simply follow by trivial projections onto piecewise constant FE spaces without need to partially integrate. The discrete Hodge-stars operators, representing the discretized metric equations, are realized by nontrivial Galerkin projections (GP). Here they follow by projections onto either a piecewise constant (GP0) or a piecewise linear (GP1) space. Our framework thus provides essentially three different schemes with significantly different behavior. The split scheme using twice GP1 is unstable and shares the same discrete dispersion relation and similar second-order convergence rates as the conventional P1-P1 FE scheme that approximates both velocity and height variables by piecewise linear spaces. The split scheme that applies both GP1 and GP0 is stable and shares the dispersion relation of the conventional P1-P0 FE scheme that approximates the velocity by a piecewise linear and the height by a piecewise constant space with corresponding second- and first-order convergence rates. Exhibiting for both velocity and height fields second-order convergence rates, we might consider the split GP1-GP0 scheme though as stable versions of the conventional P1-P1 FE scheme. For the split scheme applying twice GP0, we are not aware of a corresponding conventional formulation to compare with. Though exhibiting larger absolute error values, it shows similar convergence rates as the other split schemes, but does not provide a satisfactory approximation of the dispersion relation as short waves are propagated much to fast. Despite this, the finding of this new scheme illustrates the potential of our discretization framework as a toolbox to find and to study new FE schemes based on new combinations of FE spaces. [1] Bauer, W. [2016], A new hierarchically-structured n-dimensional covariant form of rotating equations of geophysical fluid dynamics, GEM - International Journal on Geomathematics, 7(1), 31-101.

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

NASA Technical Reports Server (NTRS)

Weinan, E.; Shu, Chi-Wang

1994-01-01

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

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

NASA Technical Reports Server (NTRS)

Weinan, E.; Shu, Chi-Wang

1992-01-01

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

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.

Effective grid-dependent dispersion coefficient for conservative and reactive transport simulations in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Cortinez, J. M.; Valocchi, A. J.; Herrera, P. A.

2013-12-01

Because of the finite size of numerical grids, it is very difficult to correctly account for processes that occur at different spatial scales to accurately simulate the migration of conservative and reactive compounds dissolved in groundwater. In one hand, transport processes in heterogeneous porous media are controlled by local-scale dispersion associated to transport processes at the pore-scale. On the other hand, variations of velocity at the continuum- or Darcy-scale produce spreading of the contaminant plume, which is referred to as macro-dispersion. Furthermore, under some conditions both effects interact, so that spreading may enhance the action of local-scale dispersion resulting in higher mixing, dilution and reaction rates. Traditionally, transport processes at different spatial scales have been included in numerical simulations by using a single dispersion coefficient. This approach implicitly assumes that the separate effects of local-dispersion and macro-dispersion can be added and represented by a unique effective dispersion coefficient. Moreover, the selection of the effective dispersion coefficient for numerical simulations usually do not consider the filtering effect of the grid size over the small-scale flow features. We have developed a multi-scale Lagragian numerical method that allows using two different dispersion coefficients to represent local- and macro-scale dispersion. This technique considers fluid particles that carry solute mass and whose locations evolve according to a deterministic component given by the grid-scale velocity and a stochastic component that corresponds to a block-effective macro-dispersion coefficient. Mass transfer between particles due to local-scale dispersion is approximated by a meshless method. We use our model to test under which transport conditions the combined effect of local- and macro-dispersion are additive and can be represented by a single effective dispersion coefficient. We also demonstrate that for the situations where both processes are additive, an effective grid-dependent dispersion coefficient can be derived based on the concept of block-effective dispersion. We show that the proposed effective dispersion coefficient is able to reproduce dilution, mixing and reaction rates for a wide range of transport conditions similar to the ones found in many practical applications.

A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes

DOE PAGES

Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...

2015-02-24

We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved atmore » the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.« less

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

NASA Astrophysics Data System (ADS)

Ersoy, Mehmet; Lakkis, Omar; Townsend, Philip

2016-04-01

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

Multi-objective optimization of radiotherapy: distributed Q-learning and agent-based simulation

NASA Astrophysics Data System (ADS)

Jalalimanesh, Ammar; Haghighi, Hamidreza Shahabi; Ahmadi, Abbas; Hejazian, Hossein; Soltani, Madjid

2017-09-01

Radiotherapy (RT) is among the regular techniques for the treatment of cancerous tumours. Many of cancer patients are treated by this manner. Treatment planning is the most important phase in RT and it plays a key role in therapy quality achievement. As the goal of RT is to irradiate the tumour with adequately high levels of radiation while sparing neighbouring healthy tissues as much as possible, it is a multi-objective problem naturally. In this study, we propose an agent-based model of vascular tumour growth and also effects of RT. Next, we use multi-objective distributed Q-learning algorithm to find Pareto-optimal solutions for calculating RT dynamic dose. We consider multiple objectives and each group of optimizer agents attempt to optimise one of them, iteratively. At the end of each iteration, agents compromise the solutions to shape the Pareto-front of multi-objective problem. We propose a new approach by defining three schemes of treatment planning created based on different combinations of our objectives namely invasive, conservative and moderate. In invasive scheme, we enforce killing cancer cells and pay less attention about irradiation effects on normal cells. In conservative scheme, we take more care of normal cells and try to destroy cancer cells in a less stressed manner. The moderate scheme stands in between. For implementation, each of these schemes is handled by one agent in MDQ-learning algorithm and the Pareto optimal solutions are discovered by the collaboration of agents. By applying this methodology, we could reach Pareto treatment plans through building different scenarios of tumour growth and RT. The proposed multi-objective optimisation algorithm generates robust solutions and finds the best treatment plan for different conditions.

Recursive estimators of mean-areal and local bias in precipitation products that account for conditional bias

NASA Astrophysics Data System (ADS)

Zhang, Yu; Seo, Dong-Jun

2017-03-01

This paper presents novel formulations of Mean field bias (MFB) and local bias (LB) correction schemes that incorporate conditional bias (CB) penalty. These schemes are based on the operational MFB and LB algorithms in the National Weather Service (NWS) Multisensor Precipitation Estimator (MPE). By incorporating CB penalty in the cost function of exponential smoothers, we are able to derive augmented versions of recursive estimators of MFB and LB. Two extended versions of MFB algorithms are presented, one incorporating spatial variation of gauge locations only (MFB-L), and the second integrating both gauge locations and CB penalty (MFB-X). These two MFB schemes and the extended LB scheme (LB-X) are assessed relative to the original MFB and LB algorithms (referred to as MFB-O and LB-O, respectively) through a retrospective experiment over a radar domain in north-central Texas, and through a synthetic experiment over the Mid-Atlantic region. The outcome of the former experiment indicates that introducing the CB penalty to the MFB formulation leads to small, but consistent improvements in bias and CB, while its impacts on hourly correlation and Root Mean Square Error (RMSE) are mixed. Incorporating CB penalty in LB formulation tends to improve the RMSE at high rainfall thresholds, but its impacts on bias are also mixed. The synthetic experiment suggests that beneficial impacts are more conspicuous at low gauge density (9 per 58,000 km2), and tend to diminish at higher gauge density. The improvement at high rainfall intensity is partly an outcome of the conservativeness of the extended LB scheme. This conservativeness arises in part from the more frequent presence of negative eigenvalues in the extended covariance matrix which leads to no, or smaller incremental changes to the smoothed rainfall amounts.

A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows

DOE PAGES

Charest, Marc R.J.; Canfield, Thomas R.; Morgan, Nathaniel R.; ...

2015-03-11

High-order discretization methods offer the potential to reduce the computational cost associated with modeling compressible flows. However, it is difficult to obtain accurate high-order discretizations of conservation laws that do not produce spurious oscillations near discontinuities, especially on multi-dimensional unstructured meshes. A novel, high-order, central essentially non-oscillatory (CENO) finite-volume method that does not have these difficulties is proposed for tetrahedral meshes. The proposed unstructured method is vertex-based, which differs from existing cell-based CENO formulations, and uses a hybrid reconstruction procedure that switches between two different solution representations. It applies a high-order k-exact reconstruction in smooth regions and a limited linearmore » reconstruction when discontinuities are encountered. Both reconstructions use a single, central stencil for all variables, making the application of CENO to arbitrary unstructured meshes relatively straightforward. The new approach was applied to the conservation equations governing compressible flows and assessed in terms of accuracy and computational cost. For all problems considered, which included various function reconstructions and idealized flows, CENO demonstrated excellent reliability and robustness. Up to fifth-order accuracy was achieved in smooth regions and essentially non-oscillatory solutions were obtained near discontinuities. The high-order schemes were also more computationally efficient for high-accuracy solutions, i.e., they took less wall time than the lower-order schemes to achieve a desired level of error. In one particular case, it took a factor of 24 less wall-time to obtain a given level of error with the fourth-order CENO scheme than to obtain the same error with the second-order scheme.« less

Standardized terminology and nomenclature for pancreatobiliary cytology: The Papanicolaou Society of Cytopathology Guidelines.

PubMed

Pitman, Martha B; Centeno, Barbara A; Ali, Syed Z; Genevay, Muriel; Stelow, Ed; Mino-Kenudson, Mari; Castillo, Carlos Fernandez-Del; Schmidt, C Max; Brugge, William R; Layfield, Lester J

2014-01-01

The Papanicolaou Society of Cytopathology has developed a set of guidelines for pancreatobiliary cytology including indications for endoscopic ultrasound (EUS) guided fine-needle aspiration (FNA) biopsy, techniques of EUS-FNA, terminology and nomenclature of pancreatobiliary disease, ancillary testing and post-biopsy treatment and management. All documents are based on the expertise of the authors, a review of the literature, discussion of the draft document at several national and international meetings over an 18 month period and synthesis of online comments of the draft document on the Papanicolaou Society of Cytopathology web site [www.papsociety.org]. This document selectively presents the results of these discussions and focuses on a proposed standardized terminology scheme for pancreatobiliary specimens that correlate cytological diagnosis with biological behavior and increasingly conservative patient management of surveillance only. The proposed terminology scheme recommends a six-tiered system: Non-diagnostic, negative, atypical, neoplastic [benign or other], suspicious and positive. Unique to this scheme is the "neoplastic" category separated into "benign" (serous cystadenoma) or "other" (premalignant mucinous cysts, neuroendocrine tumors and solid-pseudopapillary neoplasms (SPNs)). The positive or malignant category is reserved for high-grade, aggressive malignancies including ductal adenocarcinoma, acinar cell carcinoma, poorly differentiated neuroendocrine carcinomas, pancreatoblastoma, lymphoma and metastases. Interpretation categories do not have to be used. Some pathology laboratory information systems require an interpretation category, which places the cytological diagnosis into a general category. This proposed scheme provides terminology that standardizes the category of the various diseases of the pancreas, some of which are difficult to diagnose specifically by cytology. In addition, this terminology scheme attempts to provide maximum flexibility for patient management, which has become increasingly conservative for some neoplasms.

Standardized terminology and nomenclature for pancreatobiliary cytology: the Papanicolaou Society of Cytopathology guidelines.

PubMed

Pitman, Martha B; Centeno, Barbara A; Ali, Syed Z; Genevay, Muriel; Stelow, Ed; Mino-Kenudson, Mari; Fernandez-del Castillo, Carlos; Max Schmidt, C; Brugge, William; Layfield, Lester

2014-04-01

The Papanicolaou Society of Cytopathology has developed a set of guidelines for pancreatobiliary cytology including indications for endoscopic ultrasound (EUS)-guided fine needle aspiration (FNA) biopsy, techniques of EUS-FNA, terminology and nomenclature of pancreatobiliary disease, ancillary testing, and postbiopsy treatment and management. All documents are based on the expertise of the authors, a review of the literature, discussions of the draft document at several national and international meetings over an 18-month period and synthesis of online comments of the draft document on the Papanicolaou Society of Cytopathology web site (www.papsociety.org). This document selectively presents the results of these discussions and focuses on a proposed standardized terminology scheme for pancreatobiliary specimens that correlate cytological diagnosis with biological behavior and increasingly conservative patient management of surveillance only. The proposed terminology scheme recommends a six-tiered system: Nondiagnostic, Negative, Atypical, Neoplastic (benign or other), Suspicious and Positive. Unique to this scheme is the "Neoplastic" category separated into "benign" (serous cystadenoma), or "Other" (premalignant mucinous cysts, neuroendocrine tumors, and solid-pseudopapillary neoplasms). The positive or malignant category is reserved for high-grade, aggressive malignancies including ductal adenocarcinoma, acinar cell carcinoma, poorly differentiated neuroendocrine carcinomas, pancreatoblastoma, lymphoma, and metastases. Interpretation categories do not have to be used. Some pathology laboratory information systems require an interpretation category, which places the cytological diagnosis into a general category. This proposed scheme provides terminology that standardizes the category of the various diseases of the pancreas, some of which are difficult to diagnose specifically by cytology. In addition, this terminology scheme attempts to provide maximum flexibility for patient management, which has become increasingly conservative for some neoplasms. Copyright © 2014 Wiley Periodicals, Inc.

Advection of Microphysical Scalars in Terminal Area Simulation System (TASS)

NASA Technical Reports Server (NTRS)

Ahmad, Nashat N.; Proctor, Fred H.

2011-01-01

The Terminal Area Simulation System (TASS) is a large eddy scale atmospheric flow model with extensive turbulence and microphysics packages. It has been applied successfully in the past to a diverse set of problems ranging from prediction of severe convective events (Proctor et al. 2002), tracking storms and for simulating weapons effects such as the dispersion and fallout of fission debris (Bacon and Sarma 1991), etc. More recently, TASS has been used for predicting the transport and decay of wake vortices behind aircraft (Proctor 2009). An essential part of the TASS model is its comprehensive microphysics package, which relies on the accurate computation of microphysical scalar transport. This paper describes an evaluation of the Leonard scheme implemented in the TASS model for transporting microphysical scalars. The scheme is validated against benchmark cases with exact solutions and compared with two other schemes - a Monotone Upstream-centered Scheme for Conservation Laws (MUSCL)-type scheme after van Leer and LeVeque's high-resolution wave propagation method. Finally, a comparison between the schemes is made against an incident of severe tornadic super-cell convection near Del City, Oklahoma.

Valuing investments in sustainable land management using an integrated modelling framework to support a watershed conservation scheme in the Upper Tana River, Kenya

NASA Astrophysics Data System (ADS)

Hunink, Johannes E.; Bryant, Benjamin P.; Vogl, Adrian; Droogers, Peter

2015-04-01

We analyse the multiple impacts of investments in sustainable land use practices on ecosystem services in the Upper Tana basin (Kenya) to support a watershed conservation scheme (a "water fund"). We apply an integrated modelling framework, building on previous field-based and modelling studies in the basin, and link biophysical outputs to economic benefits for the main actors in the basin. The first step in the modelling workflow is the use of a high-resolution spatial prioritization tool (Resource Investment Optimization System -- RIOS) to allocate the type and location of conservation investments in the different subbasins, subject to budget constraints and stakeholder concerns. We then run the Soil and Water Assessment Tool (SWAT) using the RIOS-identified investment scenarios to produce spatially explicit scenarios that simulate changes in water yield and suspended sediment. Finally, in close collaboration with downstream water users (urban water supply and hydropower) we link those biophysical outputs to monetary metrics, including: reduced water treatment costs, increased hydropower production, and crop yield benefits for upstream farmers in the conservation area. We explore how different budgets and different spatial targeting scenarios influence the return of the investments and the effectiveness of the water fund scheme. This study is novel in that it presents an integrated analysis targeting interventions in a decision context that takes into account local environmental and socio-economic conditions, and then relies on detailed, process-based, biophysical models to demonstrate the economic return on those investments. We conclude that the approach allows for an analysis on different spatial and temporal scales, providing conclusive evidence to stakeholders and decision makers on the contribution and benefits of the land-based investments in this basin. This is serving as foundational work to support the implementation of the Upper Tana-Nairobi Water Fund, a public-private partnership to safeguard ecosystem service provision and food security.

Nodes, networks, and MUMs: Preserving diversity at all scales

NASA Astrophysics Data System (ADS)

Noss, Reed F.; Harris, Larry D.

1986-05-01

The present focus of practical conservation efforts is limited in scope. This narrowness results in an inability to evaluate and manage phenomena that operate at large spatiotemporal scales. Whereas real ecological phenomena function in a space-time mosaic across a full hierarchy of biological entities and processes, current conservation strategies address a limited spectrum of this complexity. Conservation typically is static (time-limited), concentrates on the habitat content rather than the landscape context of protected areas, evaluates relatively homogeneous communities instead of heterogeneous landscapes, and directs attention to particular species populations and/or the aggregate statistic of species diversity. Insufficient attention has been given to broad ecological patterns and processes and to the conservation of species in natural relative abundance patterns (native diversity). The authors present a conceptual scheme that evaluates not only habitat content within protected areas, but also the landscape context in which each preserve exists. Nodes of concentrated ecological value exist in each landscape at all levels in the biological hierarchy. Integration of these high-quality nodes into a functional network is possible through the establishment of a system of interconnected multiple-use modules (MUMs). The MUM network protects and buffers important ecological entities and phenomena, while encouraging movement of individuals, species, nutrients, energy, and even habitat patches across space and time. An example is presented for the southeastern USA (south Georgia-north Florida), that uses riparian and coastal corridors to interconnect existing protected areas. This scheme will facilitate reintroduction and preservation of wide-ranging species such as the Florida panther, and help reconcile species-level and ecosystem-level conservation approaches.

OSLG: A new granting scheme in WDM Ethernet passive optical networks

NASA Astrophysics Data System (ADS)

Razmkhah, Ali; Rahbar, Akbar Ghaffarpour

2011-12-01

Several granting schemes have been proposed to grant transmission window and dynamic bandwidth allocation (DBA) in passive optical networks (PON). Generally, granting schemes suffer from bandwidth wastage of granted windows. Here, we propose a new granting scheme for WDM Ethernet PONs, called optical network unit (ONU) Side Limited Granting (OSLG) that conserves upstream bandwidth, thus resulting in decreasing queuing delay and packet drop ratio. In OSLG instead of optical line terminal (OLT), each ONU determines its transmission window. Two OSLG algorithms are proposed in this paper: the OSLG_GA algorithm that determines the size of its transmission window in such a way that the bandwidth wastage problem is relieved, and the OSLG_SC algorithm that saves unused bandwidth for more bandwidth utilization later on. The OSLG can be used as granting scheme of any DBA to provide better performance in the terms of packet drop ratio and queuing delay. Our performance evaluations show the effectiveness of OSLG in reducing packet drop ratio and queuing delay under different DBA techniques.

Efficient massively parallel simulation of dynamic channel assignment schemes for wireless cellular communications

NASA Technical Reports Server (NTRS)

Greenberg, Albert G.; Lubachevsky, Boris D.; Nicol, David M.; Wright, Paul E.

1994-01-01

Fast, efficient parallel algorithms are presented for discrete event simulations of dynamic channel assignment schemes for wireless cellular communication networks. The driving events are call arrivals and departures, in continuous time, to cells geographically distributed across the service area. A dynamic channel assignment scheme decides which call arrivals to accept, and which channels to allocate to the accepted calls, attempting to minimize call blocking while ensuring co-channel interference is tolerably low. Specifically, the scheme ensures that the same channel is used concurrently at different cells only if the pairwise distances between those cells are sufficiently large. Much of the complexity of the system comes from ensuring this separation. The network is modeled as a system of interacting continuous time automata, each corresponding to a cell. To simulate the model, conservative methods are used; i.e., methods in which no errors occur in the course of the simulation and so no rollback or relaxation is needed. Implemented on a 16K processor MasPar MP-1, an elegant and simple technique provides speedups of about 15 times over an optimized serial simulation running on a high speed workstation. A drawback of this technique, typical of conservative methods, is that processor utilization is rather low. To overcome this, new methods were developed that exploit slackness in event dependencies over short intervals of time, thereby raising the utilization to above 50 percent and the speedup over the optimized serial code to about 120 times.

Cost-effectiveness of conservation payment schemes for species with different range sizes.

PubMed

Drechsler, Martin; Smith, Henrik G; Sturm, Astrid; Wätzold, Frank

2016-08-01

Payments to compensate landowners for carrying out costly land-use measures that benefit endangered biodiversity have become an important policy instrument. When designing such payments, it is important to take into account that spatially connected habitats are more valuable for many species than isolated ones. One way to incentivize provision of connected habitats is to offer landowners an agglomeration bonus, that is, a bonus on top of payments they are receiving to conserve land if the land is spatially connected. Researchers have compared the cost-effectiveness of the agglomeration bonus with 2 alternatives: an all-or-nothing, agglomeration payment, where landowners receive a payment only if the conserved land parcels have a certain level of spatial connectivity, and a spatially homogeneous payment, where landowners receive a payment for conserved land parcels irrespective of their location. Their results show the agglomeration bonus is rarely the most cost-effective option, and when it is, it is only slightly better than one of the alternatives. This suggests that the agglomeration bonus should not be given priority as a policy design option. However, this finding is based on consideration of only 1 species. We examined whether the same applied to 2 species, one for which the homogeneous payment is best and the other for which the agglomeration payment is most cost-effective. We modified a published conceptual model so that we were able to assess the cost-effectiveness of payment schemes for 2 species and applied it to a grassland bird and a grassland butterfly in Germany that require the same habitat but have different spatial-connectivity needs. When conserving both species, the agglomeration bonus was more cost-effective than the agglomeration and the homogeneous payment; thus, we showed that as a policy the agglomeration bonus is a useful conservation-payment option. © 2016 Society for Conservation Biology.

Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations

NASA Astrophysics Data System (ADS)

Lucas-Serrano, A.; Font, J. A.; Ibáñez, J. M.; Martí, J. M.

2004-12-01

We assess the suitability of a recent high-resolution central scheme developed by \\cite{kurganov} for the solution of the relativistic hydrodynamic equations. The novelty of this approach relies on the absence of Riemann solvers in the solution procedure. The computations we present are performed in one and two spatial dimensions in Minkowski spacetime. Standard numerical experiments such as shock tubes and the relativistic flat-faced step test are performed. As an astrophysical application the article includes two-dimensional simulations of the propagation of relativistic jets using both Cartesian and cylindrical coordinates. The simulations reported clearly show the capabilities of the numerical scheme of yielding satisfactory results, with an accuracy comparable to that obtained by the so-called high-resolution shock-capturing schemes based upon Riemann solvers (Godunov-type schemes), even well inside the ultrarelativistic regime. Such a central scheme can be straightforwardly applied to hyperbolic systems of conservation laws for which the characteristic structure is not explicitly known, or in cases where a numerical computation of the exact solution of the Riemann problem is prohibitively expensive. Finally, we present comparisons with results obtained using various Godunov-type schemes as well as with those obtained using other high-resolution central schemes which have recently been reported in the literature.

Development of a nonlocal convective mixing scheme with varying upward mixing rates for use in air quality and chemical transport models.

PubMed

Mihailović, Dragutin T; Alapaty, Kiran; Sakradzija, Mirjana

2008-06-01

Asymmetrical convective non-local scheme (CON) with varying upward mixing rates is developed for simulation of vertical turbulent mixing in the convective boundary layer in air quality and chemical transport models. The upward mixing rate form the surface layer is parameterized using the sensible heat flux and the friction and convective velocities. Upward mixing rates varying with height are scaled with an amount of turbulent kinetic energy in layer, while the downward mixing rates are derived from mass conservation. This scheme provides a less rapid mass transport out of surface layer into other layers than other asymmetrical convective mixing schemes. In this paper, we studied the performance of a nonlocal convective mixing scheme with varying upward mixing in the atmospheric boundary layer and its impact on the concentration of pollutants calculated with chemical and air-quality models. This scheme was additionally compared versus a local eddy-diffusivity scheme (KSC). Simulated concentrations of NO(2) and the nitrate wet deposition by the CON scheme are closer to the observations when compared to those obtained from using the KSC scheme. Concentrations calculated with the CON scheme are in general higher and closer to the observations than those obtained by the KSC scheme (of the order of 15-20%). Nitrate wet deposition calculated with the CON scheme are in general higher and closer to the observations than those obtained by the KSC scheme. To examine the performance of the scheme, simulated and measured concentrations of a pollutant (NO(2)) and nitrate wet deposition was compared for the year 2002. The comparison was made for the whole domain used in simulations performed by the chemical European Monitoring and Evaluation Programme Unified model (version UNI-ACID, rv2.0) where schemes were incorporated.

A low-dispersion, exactly energy-charge-conserving semi-implicit relativistic particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Luis, Chacon; Bird, Robert; Stark, David; Yin, Lin; Albright, Brian

2017-10-01

Leap-frog based explicit algorithms, either ``energy-conserving'' or ``momentum-conserving'', do not conserve energy discretely. Time-centered fully implicit algorithms can conserve discrete energy exactly, but introduce large dispersion errors in the light-wave modes, regardless of timestep sizes. This can lead to intolerable simulation errors where highly accurate light propagation is needed (e.g. laser-plasma interactions, LPI). In this study, we selectively combine the leap-frog and Crank-Nicolson methods to produce a low-dispersion, exactly energy-and-charge-conserving PIC algorithm. Specifically, we employ the leap-frog method for Maxwell equations, and the Crank-Nicolson method for particle equations. Such an algorithm admits exact global energy conservation, exact local charge conservation, and preserves the dispersion properties of the leap-frog method for the light wave. The algorithm has been implemented in a code named iVPIC, based on the VPIC code developed at LANL. We will present numerical results that demonstrate the properties of the scheme with sample test problems (e.g. Weibel instability run for 107 timesteps, and LPI applications.

Positivity-preserving numerical schemes for multidimensional advection

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

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.

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.

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)

The Orthoptera of Castro Verde Special Protection Area (Southern Portugal): new data and conservation value

PubMed Central

Pina, Sílvia; Vasconcelos, Sasha; Reino, Luís; Santana, Joana; Beja, Pedro; Sánchez-Oliver, Juan S.; Catry, Inês; Moreira, Francisco; Ferreira, Sónia

2017-01-01

Abstract With the increasing awareness of the need for Orthoptera conservation, greater efforts must be gathered to implement specific monitoring schemes. Despite recent surveys, little is known about Portuguese Orthoptera populations. This study was performed in 2014 and 2015 mainly in Castro Verde Special Protection Area (SPA), southern Portugal, and is the first Orthoptera inventory conducted in the area. A total of 35 Orthoptera species was recorded, with two new species reported for Portugal. We provide species’ habitat occurrences within the protected area and use information on the conservation status and the Iberian distribution of each documented species to discuss the importance of Castro Verde SPA for Orthoptera conservation. The data presented here sheds new light on Castro Verde SPA biodiversity and emphasizes the inclusion of this area in the conservation of Orthoptera diversity, particularly in the protection of threatened endemic species. PMID:29200922

The Orthoptera of Castro Verde Special Protection Area (Southern Portugal): new data and conservation value.

PubMed

Pina, Sílvia; Vasconcelos, Sasha; Reino, Luís; Santana, Joana; Beja, Pedro; Sánchez-Oliver, Juan S; Catry, Inês; Moreira, Francisco; Ferreira, Sónia

2017-01-01

With the increasing awareness of the need for Orthoptera conservation, greater efforts must be gathered to implement specific monitoring schemes. Despite recent surveys, little is known about Portuguese Orthoptera populations. This study was performed in 2014 and 2015 mainly in Castro Verde Special Protection Area (SPA), southern Portugal, and is the first Orthoptera inventory conducted in the area. A total of 35 Orthoptera species was recorded, with two new species reported for Portugal. We provide species' habitat occurrences within the protected area and use information on the conservation status and the Iberian distribution of each documented species to discuss the importance of Castro Verde SPA for Orthoptera conservation. The data presented here sheds new light on Castro Verde SPA biodiversity and emphasizes the inclusion of this area in the conservation of Orthoptera diversity, particularly in the protection of threatened endemic species.

The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme

NASA Technical Reports Server (NTRS)

Tadmor, E.

1983-01-01

The Lax-Friedrichs scheme, approximating the scalar, genuinely nonlinear conservation law u sub t + f sub x (u) = 0 where f(u) is, say, strictly convex double dot f dot a sub asterisk 0 is studied. The divided differences of the numerical solution at time t do not exceed 2 (t dot a sub asterisk) to the -1. This one-sided Lipschitz boundedness is in complete agreement with the corresponding estimate one has in the differential case; in particular, it is independent of the initial amplitude in sharp contrast to liner problems. It guarantees the entropy compactness of the scheme in this case, as well as providing a quantitive insight into the large-time behavior of the numerical computation.

Nonlinear truncation error analysis of finite difference schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1983-01-01

It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

Relaxation approximations to second-order traffic flow models by high-resolution schemes

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

Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.

2015-03-10

A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reportedmore » demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.« less

Extended bounds limiter for high-order finite-volume schemes on unstructured meshes

NASA Astrophysics Data System (ADS)

Tsoutsanis, Panagiotis

2018-06-01

This paper explores the impact of the definition of the bounds of the limiter proposed by Michalak and Ollivier-Gooch in [56] (2009), for higher-order Monotone-Upstream Central Scheme for Conservation Laws (MUSCL) numerical schemes on unstructured meshes in the finite-volume (FV) framework. A new modification of the limiter is proposed where the bounds are redefined by utilising all the spatial information provided by all the elements in the reconstruction stencil. Numerical results obtained on smooth and discontinuous test problems of the Euler equations on unstructured meshes, highlight that the newly proposed extended bounds limiter exhibits superior performance in terms of accuracy and mesh sensitivity compared to the cell-based or vertex-based bounds implementations.

Newly-Developed 3D GRMHD Code and its Application to Jet Formation

NASA Technical Reports Server (NTRS)

Mizuno, Y.; Nishikawa, K.-I.; Koide, S.; Hardee, P.; Fishman, G. J.

2006-01-01

We have developed a new three-dimensional general relativistic magnetohydrodynamic code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-interpolated constrained transport scheme is used to maintain a divergence-free magnetic field. We have performed various 1-dimensional test problems in both special and general relativity by using several reconstruction methods and found that the new 3D GRMHD code shows substantial improvements over our previous model. The . preliminary results show the jet formations from a geometrically thin accretion disk near a non-rotating and a rotating black hole. We will discuss the jet properties depended on the rotation of a black hole and the magnetic field strength.

Generation of dark hollow beam by use of phase-only filtering

NASA Astrophysics Data System (ADS)

Liu, Zhengjun; Dai, Jingmin; Zhao, Xiaoyi; Sun, Xiaogang; Liu, Shutian; Ashfaq Ahmad, Muhammad

2009-11-01

A simple but effective scheme to generate dark hollow beams is proposed by use of phase-only filtering and optical Fourier transform. A Gaussian beam of fundamental mode is modulated by a pre-designed phase mask, which is a piecewise modification of an axicon lens, and followed by a Fourier transform to generate an ideal dark hollow beam at the focal plane. This method has an advantage that the total energy of the beam is conserved under paraxial approximation. Numerical calculations are provided to show the validity of the proposed scheme.

Digital Baseband Architecture For Transponder

NASA Technical Reports Server (NTRS)

Nguyen, Tien M.; Yeh, Hen-Geul

1995-01-01

Proposed advanced transponder for long-distance radio communication system with turnaround ranging contains carrier-signal-tracking loop including baseband digital "front end." For reduced cost, transponder includes analog intermediate-frequency (IF) section and analog automatic gain control (AGC) loop at first of two IF mixers. However, second IF mixer redesigned to ease digitization of baseband functions. To conserve power and provide for simpler and smaller transponder hardware, baseband digital signal-processing circuits designed to implement undersampling scheme. Furthermore, sampling scheme and sampling frequency chosen so redesign involves minimum modification of command-detector unit (CDU).

On the Quality of Velocity Interpolation Schemes for Marker-In-Cell Methods on 3-D Staggered Grids

NASA Astrophysics Data System (ADS)

Kaus, B.; Pusok, A. E.; Popov, A.

2015-12-01

The marker-in-cell method is generally considered to be a flexible and robust method to model advection of heterogenous non-diffusive properties (i.e. rock type or composition) in geodynamic problems or incompressible Stokes problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an immobile, Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without preserving the zero 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 (Jenny et al., 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. Solutions to this problem include: using larger mesh resolutions and/or marker densities, or repeatedly controlling the marker distribution (i.e. inject/delete), but which does not have an established physical background. To remedy this at low computational costs, Jenny et al. (2001) and Meyer and Jenny (2004) proposed a simple, conservative velocity interpolation (CVI) scheme for 2-D staggered grid, while Wang et al. (2015) extended the formulation to 3-D finite element methods. Here, we follow up with these studies and report on the quality of velocity interpolation methods for 2-D and 3-D staggered grids. We adapt the formulations from both Jenny et al. (2001) and Wang et al. (2015) for use on 3-D staggered grids, where the velocity components have different node locations as compared to finite element, where they share the same node location. We test the different interpolation schemes (CVI and non-CVI) in combination with different advection schemes (Euler, RK2 and RK4) and with/out marker control on Stokes problems with strong velocity gradients, which are discretized using a finite difference method. We show that a conservative formulation reduces the dispersion or clustering of markers and that the density of markers remains steady over time without the need of additional marker control. Jenny et al. (2001, J Comp Phys, 166, 218-252 Meyer and Jenny (2004), Proc Appl Math Mech, 4, 466-467 Wang et al. (2015), G3, Vol.16 Funding was provided by the ERC Starting Grant #258830.

New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1993-01-01

A new numerical framework 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 conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

Dynamico-FE: A Structure-Preserving Hydrostatic Dynamical Core

NASA Astrophysics Data System (ADS)

Eldred, Christopher; Dubos, Thomas; Kritsikis, Evaggelos

2017-04-01

It is well known that the inviscid, adiabatic equations of atmospheric motion constitute a non-canonical Hamiltonian system, and therefore posses many important conserved quantities such as as mass, potential vorticity and total energy. In addition, there are also key mimetic properties (such as curl grad = 0) of the underlying continuous vector calculus. Ideally, a dynamical core should have similar properties. A general approach to deriving such structure-preserving numerical schemes has been developed under the frameworks of Hamiltonian methods and mimetic discretizations, and over the past decade, there has been a great deal of work on the development of atmospheric dynamical cores using these techniques. An important example is Dynamico, which conserves mass, potential vorticity and total energy; and possesses additional mimetic properties such as a curl-free pressure gradient. Unfortunately, the underlying finite-difference discretization scheme used in Dynamico has been shown to be inconsistent on general grids. To resolve these accuracy issues, a scheme based on mimetic Galerkin discretizations has been developed that achieves higher-order accuracy while retaining the structure-preserving properties of the existing discretization. This presentation will discuss the new dynamical core, termed Dynamico-FE, and show results from a standard set of test cases on both the plane and the sphere.

Problems and pressures, management and measures in a site of marine conservation importance: Carmarthen Bay and Estuaries

NASA Astrophysics Data System (ADS)

Bullimore, Blaise

2014-10-01

Management of anthropogenic activities that cause pressure on estuarine wildlife and biodiversity is beset by a wide range of challenges. Some, such as the differing environmental and socio-economic objectives and conflicting views and priorities, are common to many estuaries; others are site specific. The Carmarthen Bay and Estuaries European Marine Site encompasses four estuaries of European wildlife and conservation importance and considerable socio-economic value. The estuaries and their wildlife are subject to a range of pressures and threats and the statutory authorities responsible for management in and adjacent to the Site have developed a management scheme to address these. Preparation of the management scheme included an assessment of human activities known to occur in and adjacent to the Site for their potential to cause a threat to the designated habitats and species features, and identified actions the management authorities need to take to minimise or eliminate pressures and threats. To deliver the scheme the partner authorities need to accept the requirement for management actions and work together to achieve them. The Welsh Government also needs to work with these authorities because it is responsible for management of many of the most important pressure-causing activities. However, the absence of statutory obligations for partnership working has proved an impediment to successful management.

Ranking Mammal Species for Conservation and the Loss of Both Phylogenetic and Trait Diversity.

PubMed

Redding, David W; Mooers, Arne O

2015-01-01

The 'edge of existence' (EDGE) prioritisation scheme is a new approach to rank species for conservation attention that aims to identify species that are both isolated on the tree of life and at imminent risk of extinction as defined by the World Conservation Union (IUCN). The self-stated benefit of the EDGE system is that it effectively captures unusual 'unique' species, and doing so will preserve the total evolutionary history of a group into the future. Given the EDGE metric was not designed to capture total evolutionary history, we tested this claim. Our analyses show that the total evolutionary history of mammals preserved is indeed much higher if EDGE species are protected than if at-risk species are chosen randomly. More of the total tree is also protected by EDGE species than if solely threat status or solely evolutionary distinctiveness were used for prioritisation. When considering how much trait diversity is captured by IUCN and EDGE prioritisation rankings, interestingly, preserving the highest-ranked EDGE species, or indeed just the most threatened species, captures more total trait diversity compared to sets of randomly-selected at-risk species. These results suggest that, as advertised, EDGE mammal species contribute evolutionary history to the evolutionary tree of mammals non-randomly, and EDGE-style rankings among endangered species can also capture important trait diversity. If this pattern holds for other groups, the EDGE prioritisation scheme has greater potential to be an efficient method to allocate scarce conservation effort.

Effectiveness of vegetation-based biodiversity offset metrics as surrogates for ants.

PubMed

Hanford, Jayne K; Crowther, Mathew S; Hochuli, Dieter F

2017-02-01

Biodiversity offset schemes are globally popular policy tools for balancing the competing demands of conservation and development. Trading currencies for losses and gains in biodiversity value at development and credit sites are usually based on several vegetation attributes combined to yield a simple score (multimetric), but the score is rarely validated prior to implementation. Inaccurate biodiversity trading currencies are likely to accelerate global biodiversity loss through unrepresentative trades of losses and gains. We tested a model vegetation multimetric (i.e., vegetation structural and compositional attributes) typical of offset trading currencies to determine whether it represented measurable components of compositional and functional biodiversity. Study sites were located in remnant patches of a critically endangered ecological community in western Sydney, Australia, an area representative of global conflicts between conservation and expanding urban development. We sampled ant fauna composition with pitfall traps and enumerated removal by ants of native plant seeds from artificial seed containers (seed depots). Ants are an excellent model taxon because they are strongly associated with habitat complexity, respond rapidly to environmental change, and are functionally important at many trophic levels. The vegetation multimetric did not predict differences in ant community composition or seed removal, despite underlying assumptions that biodiversity trading currencies used in offset schemes represent all components of a site's biodiversity value. This suggests that vegetation multimetrics are inadequate surrogates for total biodiversity value. These findings highlight the urgent need to refine existing offsetting multimetrics to ensure they meet underlying assumptions of surrogacy. Despite the best intentions, offset schemes will never achieve their goal of no net loss of biodiversity values if trades are based on metrics unrepresentative of total biodiversity. © 2016 Society for Conservation Biology.

Data-driven Modeling of the Solar Corona by a New Three-dimensional Path-conservative Osher-Solomon MHD Model

NASA Astrophysics Data System (ADS)

Feng, Xueshang; Li, Caixia; Xiang, Changqing; Zhang, Man; Li, HuiChao; Wei, Fengsi

2017-11-01

A second-order path-conservative scheme with a Godunov-type finite-volume method has been implemented to advance the equations of single-fluid solar wind plasma magnetohydrodynamics (MHD) in time. This code operates on the six-component composite grid system in three-dimensional spherical coordinates with hexahedral cells of quadrilateral frustum type. The generalized Osher-Solomon Riemann solver is employed based on a numerical integration of the path-dependent dissipation matrix. For simplicity, the straight line segment path is used, and the path integral is evaluated in a fully numerical way by a high-order numerical Gauss-Legendre quadrature. Besides its very close similarity to Godunov type, the resulting scheme retains the attractive features of the original solver: it is nonlinear, free of entropy-fix, differentiable, and complete, in that each characteristic field results in a different numerical viscosity, due to the full use of the MHD eigenstructure. By using a minmod limiter for spatial oscillation control, the path-conservative scheme is realized for the generalized Lagrange multiplier and the extended generalized Lagrange multiplier formulation of solar wind MHD systems. This new model that is second order in space and time is written in the FORTRAN language with Message Passing Interface parallelization and validated in modeling the time-dependent large-scale structure of the solar corona, driven continuously by Global Oscillation Network Group data. To demonstrate the suitability of our code for the simulation of solar wind, we present selected results from 2009 October 9 to 2009 December 29 show its capability of producing a structured solar corona in agreement with solar coronal observations.

Stable, non-dissipative, and conservative flux-reconstruction schemes in split forms

NASA Astrophysics Data System (ADS)

Abe, Yoshiaki; Morinaka, Issei; Haga, Takanori; Nonomura, Taku; Shibata, Hisaichi; Miyaji, Koji

2018-01-01

A stable, non-dissipative, and conservative flux-reconstruction (FR) scheme is constructed and demonstrated for the compressible Euler and Navier-Stokes equations. A proposed FR framework adopts a split form (also known as the skew-symmetric form) for convective terms. Sufficient conditions to satisfy both the primary conservation (PC) and kinetic energy preservation (KEP) properties are rigorously derived by polynomial-based analysis for a general FR framework. It is found that the split form needs to be expressed in the PC split form or KEP split form to satisfy each property in discrete sense. The PC split form is retrieved from existing general forms (Kennedy and Gruber [33]); in contrast, we have newly introduced the KEP split form as a comprehensive form constituting a KEP scheme in the FR framework. Furthermore, Gauss-Lobatto (GL) solution points and g2 correction function are required to satisfy the KEP property while any correction functions are available for the PC property. The split-form FR framework to satisfy the KEP property, eventually, is similar to the split-form DGSEM-GL method proposed by Gassner [23], but which, in this study, is derived solely by polynomial-based analysis without explicitly using the diagonal-norm SBP property. Based on a series of numerical tests (e.g., Sod shock tube), both the PC and KEP properties have been verified. We have also demonstrated that using a non-dissipative KEP flux, a sixteenth-order (p15) simulation of the viscous Taylor-Green vortex (Re = 1 , 600) is stable and its results are free of unphysical oscillations on relatively coarse mesh (total number of degrees of freedom (DoFs) is 1283).

Effects of using a posteriori methods for the conservation of integral invariants. [for weather forecasting

NASA Technical Reports Server (NTRS)

Takacs, Lawrence L.

1988-01-01

The nature and effect of using a posteriori adjustments to nonconservative finite-difference schemes to enforce integral invariants of the corresponding analytic system are examined. The method of a posteriori integral constraint restoration is analyzed for the case of linear advection, and the harmonic response associated with the a posteriori adjustments is examined in detail. The conservative properties of the shallow water system are reviewed, and the constraint restoration algorithm applied to the shallow water equations are described. A comparison is made between forecasts obtained using implicit and a posteriori methods for the conservation of mass, energy, and potential enstrophy in the complete nonlinear shallow-water system.

Finite area method for nonlinear supersonic conical flows

NASA Technical Reports Server (NTRS)

Sritharan, S. S.; Seebass, A. R.

1983-01-01

A fully conservative numerical method for the computation of steady inviscid supersonic flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell; a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is symmetrized by adding artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigators.

Finite area method for nonlinear conical flows

NASA Technical Reports Server (NTRS)

Sritharan, S. S.; Seebass, A. R.

1982-01-01

A fully conservative finite area method for the computation of steady inviscid flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell and a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is desymmetrized by adding appropriate artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigations.

A new third order finite volume weighted essentially non-oscillatory scheme on tetrahedral meshes

NASA Astrophysics Data System (ADS)

Zhu, Jun; Qiu, Jianxian

2017-11-01

In this paper a third order finite volume weighted essentially non-oscillatory scheme is designed for solving hyperbolic conservation laws on tetrahedral meshes. Comparing with other finite volume WENO schemes designed on tetrahedral meshes, the crucial advantages of such new WENO scheme are its simplicity and compactness with the application of only six unequal size spatial stencils for reconstructing unequal degree polynomials in the WENO type spatial procedures, and easy choice of the positive linear weights without considering the topology of the meshes. The original innovation of such scheme is to use a quadratic polynomial defined on a big central spatial stencil for obtaining third order numerical approximation at any points inside the target tetrahedral cell in smooth region and switch to at least one of five linear polynomials defined on small biased/central spatial stencils for sustaining sharp shock transitions and keeping essentially non-oscillatory property simultaneously. By performing such new procedures in spatial reconstructions and adopting a third order TVD Runge-Kutta time discretization method for solving the ordinary differential equation (ODE), the new scheme's memory occupancy is decreased and the computing efficiency is increased. So it is suitable for large scale engineering requirements on tetrahedral meshes. Some numerical results are provided to illustrate the good performance of such scheme.

An MBO Scheme for Minimizing the Graph Ohta-Kawasaki Functional

NASA Astrophysics Data System (ADS)

van Gennip, Yves

2018-06-01

We study a graph-based version of the Ohta-Kawasaki functional, which was originally introduced in a continuum setting to model pattern formation in diblock copolymer melts and has been studied extensively as a paradigmatic example of a variational model for pattern formation. Graph-based problems inspired by partial differential equations (PDEs) and variational methods have been the subject of many recent papers in the mathematical literature, because of their applications in areas such as image processing and data classification. This paper extends the area of PDE inspired graph-based problems to pattern-forming models, while continuing in the tradition of recent papers in the field. We introduce a mass conserving Merriman-Bence-Osher (MBO) scheme for minimizing the graph Ohta-Kawasaki functional with a mass constraint. We present three main results: (1) the Lyapunov functionals associated with this MBO scheme Γ -converge to the Ohta-Kawasaki functional (which includes the standard graph-based MBO scheme and total variation as a special case); (2) there is a class of graphs on which the Ohta-Kawasaki MBO scheme corresponds to a standard MBO scheme on a transformed graph and for which generalized comparison principles hold; (3) this MBO scheme allows for the numerical computation of (approximate) minimizers of the graph Ohta-Kawasaki functional with a mass constraint.

A Comprehensive Study of Data Collection Schemes Using Mobile Sinks in Wireless Sensor Networks

PubMed Central

Khan, Abdul Waheed; Abdullah, Abdul Hanan; Anisi, Mohammad Hossein; Bangash, Javed Iqbal

2014-01-01

Recently sink mobility has been exploited in numerous schemes to prolong the lifetime of wireless sensor networks (WSNs). Contrary to traditional WSNs where sensory data from sensor field is ultimately sent to a static sink, mobile sink-based approaches alleviate energy-holes issues thereby facilitating balanced energy consumption among nodes. In mobility scenarios, nodes need to keep track of the latest location of mobile sinks for data delivery. However, frequent propagation of sink topological updates undermines the energy conservation goal and therefore should be controlled. Furthermore, controlled propagation of sinks' topological updates affects the performance of routing strategies thereby increasing data delivery latency and reducing packet delivery ratios. This paper presents a taxonomy of various data collection/dissemination schemes that exploit sink mobility. Based on how sink mobility is exploited in the sensor field, we classify existing schemes into three classes, namely path constrained, path unconstrained, and controlled sink mobility-based schemes. We also organize existing schemes based on their primary goals and provide a comparative study to aid readers in selecting the appropriate scheme in accordance with their particular intended applications and network dynamics. Finally, we conclude our discussion with the identification of some unresolved issues in pursuit of data delivery to a mobile sink. PMID:24504107

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.

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.

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.

Division of Agriculture

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High Order Finite Difference Methods, Multidimensional Linear Problems and Curvilinear Coordinates

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1999-01-01

Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

Object-constrained meshless deformable algorithm for high speed 3D nonrigid registration between CT and CBCT

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

Chen Ting; Kim, Sung; Goyal, Sharad

2010-01-15

Purpose: High-speed nonrigid registration between the planning CT and the treatment CBCT data is critical for real time image guided radiotherapy (IGRT) to improve the dose distribution and to reduce the toxicity to adjacent organs. The authors propose a new fully automatic 3D registration framework that integrates object-based global and seed constraints with the grayscale-based ''demons'' algorithm. Methods: Clinical objects were segmented on the planning CT images and were utilized as meshless deformable models during the nonrigid registration process. The meshless models reinforced a global constraint in addition to the grayscale difference between CT and CBCT in order to maintainmore » the shape and the volume of geometrically complex 3D objects during the registration. To expedite the registration process, the framework was stratified into hierarchies, and the authors used a frequency domain formulation to diffuse the displacement between the reference and the target in each hierarchy. Also during the registration of pelvis images, they replaced the air region inside the rectum with estimated pixel values from the surrounding rectal wall and introduced an additional seed constraint to robustly track and match the seeds implanted into the prostate. The proposed registration framework and algorithm were evaluated on 15 real prostate cancer patients. For each patient, prostate gland, seminal vesicle, bladder, and rectum were first segmented by a radiation oncologist on planning CT images for radiotherapy planning purpose. The same radiation oncologist also manually delineated the tumor volumes and critical anatomical structures in the corresponding CBCT images acquired at treatment. These delineated structures on the CBCT were only used as the ground truth for the quantitative validation, while structures on the planning CT were used both as the input to the registration method and the ground truth in validation. By registering the planning CT to the CBCT, a displacement map was generated. Segmented volumes in the CT images deformed using the displacement field were compared against the manual segmentations in the CBCT images to quantitatively measure the convergence of the shape and the volume. Other image features were also used to evaluate the overall performance of the registration. Results: The algorithm was able to complete the segmentation and registration process within 1 min, and the superimposed clinical objects achieved a volumetric similarity measure of over 90% between the reference and the registered data. Validation results also showed that the proposed registration could accurately trace the deformation inside the target volume with average errors of less than 1 mm. The method had a solid performance in registering the simulated images with up to 20 Hounsfield unit white noise added. Also, the side by side comparison with the original demons algorithm demonstrated its improved registration performance over the local pixel-based registration approaches. Conclusions: Given the strength and efficiency of the algorithm, the proposed method has significant clinical potential to accelerate and to improve the CBCT delineation and targets tracking in online IGRT applications.« less

Bond Order Conservation Strategies in Catalysis Applied to the NH 3 Decomposition Reaction

DOE PAGES

Yu, Liang; Abild-Pedersen, Frank

2016-12-14

On the basis of an extensive set of density functional theory calculations, it is shown that a simple scheme provides a fundamental understanding of variations in the transition state energies and structures of reaction intermediates on transition metal surfaces across the periodic table. The scheme is built on the bond order conservation principle and requires a limited set of input data, still achieving transition state energies as a function of simple descriptors with an error smaller than those of approaches based on linear fits to a set of calculated transition state energies. Here, we have applied this approach together withmore » linear scaling of adsorption energies to obtain the energetics of the NH 3 decomposition reaction on a series of stepped fcc(211) transition metal surfaces. Moreover, this information is used to establish a microkinetic model for the formation of N 2 and H 2, thus providing insight into the components of the reaction that determines the activity.« less

Numerical simulation of the interaction between a flowfield and chemical reaction on premixed pulsed jet combustion

NASA Astrophysics Data System (ADS)

Hishida, Manabu; Hayashi, A. Koichi

1992-12-01

Pulsed Jet Combustion (PJC) is numerically simulated using time-dependent, axisymmetric, full Navier-Stokes equations with the mass, momentum, energy, and species conservation equations for a hydrogen-air mixture. A hydrogen-air reaction mechanism is modeled by nine species and nineteen elementary forward and backward reactions to evaluate the effect of the chemical reactions accurately. A point implicit method with the Harten and Yee's non-MUSCL (Monotone Upstream-centerd Schemes for Conservation Laws) modified-flux type TVD (Total Variation Diminishing) scheme is applied to deal with the stiff partial differential equations. Furthermore, a zonal method making use of the Fortified Solution Algorithm (FSA) is applied to simulate the phenomena in the complicated shape of the sub-chamber. The numerical result shows that flames propagating in the sub-chamber interact with pressure waves and are deformed to be wrinkled like a 'tulip' flame and a jet passed through the orifice changes its mass flux quasi-periodically.

Setting temporal baselines for biodiversity: the limits of available monitoring data for capturing the full impact of anthropogenic pressures

PubMed Central

Mihoub, Jean-Baptiste; Henle, Klaus; Titeux, Nicolas; Brotons, Lluís; Brummitt, Neil A.; Schmeller, Dirk S.

2017-01-01

Temporal baselines are needed for biodiversity, in order for the change in biodiversity to be measured over time, the targets for biodiversity conservation to be defined and conservation progress to be evaluated. Limited biodiversity information is widely recognized as a major barrier for identifying temporal baselines, although a comprehensive quantitative assessment of this is lacking. Here, we report on the temporal baselines that could be drawn from biodiversity monitoring schemes in Europe and compare those with the rise of important anthropogenic pressures. Most biodiversity monitoring schemes were initiated late in the 20th century, well after anthropogenic pressures had already reached half of their current magnitude. Setting temporal baselines from biodiversity monitoring data would therefore underestimate the full range of impacts of major anthropogenic pressures. In addition, biases among taxa and organization levels provide a truncated picture of biodiversity over time. These limitations need to be explicitly acknowledged when designing management strategies and policies as they seriously constrain our ability to identify relevant conservation targets aimed at restoring or reversing biodiversity losses. We discuss the need for additional research efforts beyond standard biodiversity monitoring to reconstruct the impacts of major anthropogenic pressures and to identify meaningful temporal baselines for biodiversity. PMID:28134310

Multi-dimensional, fully implicit, exactly conserving electromagnetic particle-in-cell simulations in curvilinear geometry

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacon, Luis

2015-11-01

We discuss a new, conservative, fully implicit 2D3V Vlasov-Darwin particle-in-cell algorithm in curvilinear geometry for non-radiative, electromagnetic kinetic plasma simulations. Unlike standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. Here, we extend these algorithms to curvilinear geometry. The algorithm retains its exact conservation properties in curvilinear grids. The nonlinear iteration is effectively accelerated with a fluid preconditioner for weakly to modestly magnetized plasmas, which allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. In this presentation, we will introduce the main algorithmic components of the approach, and demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 1D (slow shock) and 2D (island coalescense).

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.

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

MPDATA: A positive definite solver for geophysical flows

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

Smolarkiewicz, P.K.; Margolin, L.G.

1997-12-31

This paper is a review of MPDATA, a class of methods for the numerical simulation of advection based on the sign-preserving properties of upstream differencing. MPDATA was designed originally as an inexpensive alternative to flux-limited schemes for evaluating the transport of nonnegative thermodynamic variables (such as liquid water or water vapor) in atmospheric models. During the last decade, MPDATA has evolved from a simple advection scheme to a general approach for integrating the conservation laws of geophysical fluids on micro-to-planetary scales. The purpose of this paper is to summarize the basic concepts leading to a family of MPDATA schemes, reviewmore » the existing MPDATA options, as well as to demonstrate the efficacy of the approach using diverse examples of complex geophysical flows.« less

Further analytical study of hybrid rocket combustion

NASA Technical Reports Server (NTRS)

Hung, W. S. Y.; Chen, C. S.; Haviland, J. K.

1972-01-01

Analytical studies of the transient and steady-state combustion processes in a hybrid rocket system are discussed. The particular system chosen consists of a gaseous oxidizer flowing within a tube of solid fuel, resulting in a heterogeneous combustion. Finite rate chemical kinetics with appropriate reaction mechanisms were incorporated in the model. A temperature dependent Arrhenius type fuel surface regression rate equation was chosen for the current study. The governing mathematical equations employed for the reacting gas phase and for the solid phase are the general, two-dimensional, time-dependent conservation equations in a cylindrical coordinate system. Keeping the simplifying assumptions to a minimum, these basic equations were programmed for numerical computation, using two implicit finite-difference schemes, the Lax-Wendroff scheme for the gas phase, and, the Crank-Nicolson scheme for the solid phase.

Multidimensional FEM-FCT schemes for arbitrary time stepping

NASA Astrophysics Data System (ADS)

Kuzmin, D.; Möller, M.; Turek, S.

2003-05-01

The flux-corrected-transport paradigm is generalized to finite-element schemes based on arbitrary time stepping. A conservative flux decomposition procedure is proposed for both convective and diffusive terms. Mathematical properties of positivity-preserving schemes are reviewed. A nonoscillatory low-order method is constructed by elimination of negative off-diagonal entries of the discrete transport operator. The linearization of source terms and extension to hyperbolic systems are discussed. Zalesak's multidimensional limiter is employed to switch between linear discretizations of high and low order. A rigorous proof of positivity is provided. The treatment of non-linearities and iterative solution of linear systems are addressed. The performance of the new algorithm is illustrated by numerical examples for the shock tube problem in one dimension and scalar transport equations in two dimensions.

An equilibrium-conserving taxation scheme for income from capital

NASA Astrophysics Data System (ADS)

Tempere, Jacques

2018-02-01

Under conditions of market equilibrium, the distribution of capital income follows a Pareto power law, with an exponent that characterizes the given equilibrium. Here, a simple taxation scheme is proposed such that the post-tax capital income distribution remains an equilibrium distribution, albeit with a different exponent. This taxation scheme is shown to be progressive, and its parameters can be simply derived from (i) the total amount of tax that will be levied, (ii) the threshold selected above which capital income will be taxed and (iii) the total amount of capital income. The latter can be obtained either by using Piketty's estimates of the capital/labor income ratio or by fitting the initial Pareto exponent. Both ways moreover provide a check on the amount of declared income from capital.

Mass-conservative reconstruction of Galerkin velocity fields for transport simulations

NASA Astrophysics Data System (ADS)

Scudeler, C.; Putti, M.; Paniconi, C.

2016-08-01

Accurate calculation of mass-conservative velocity fields from numerical solutions of Richards' equation is central to reliable surface-subsurface flow and transport modeling, for example in long-term tracer simulations to determine catchment residence time distributions. In this study we assess the performance of a local Larson-Niklasson (LN) post-processing procedure for reconstructing mass-conservative velocities from a linear (P1) Galerkin finite element solution of Richards' equation. This approach, originally proposed for a-posteriori error estimation, modifies the standard finite element velocities by imposing local conservation on element patches. The resulting reconstructed flow field is characterized by continuous fluxes on element edges that can be efficiently used to drive a second order finite volume advective transport model. Through a series of tests of increasing complexity that compare results from the LN scheme to those using velocity fields derived directly from the P1 Galerkin solution, we show that a locally mass-conservative velocity field is necessary to obtain accurate transport results. We also show that the accuracy of the LN reconstruction procedure is comparable to that of the inherently conservative mixed finite element approach, taken as a reference solution, but that the LN scheme has much lower computational costs. The numerical tests examine steady and unsteady, saturated and variably saturated, and homogeneous and heterogeneous cases along with initial and boundary conditions that include dry soil infiltration, alternating solute and water injection, and seepage face outflow. Typical problems that arise with velocities derived from P1 Galerkin solutions include outgoing solute flux from no-flow boundaries, solute entrapment in zones of low hydraulic conductivity, and occurrences of anomalous sources and sinks. In addition to inducing significant mass balance errors, such manifestations often lead to oscillations in concentration values that can moreover cause the numerical solution to explode. These problems do not occur when using LN post-processed velocities.

Flexible risk metrics for identifying and monitoring conservation-priority species

USGS Publications Warehouse

Stanton, Jessica C.; Semmens, Brice X.; McKann, Patrick C.; Will, Tom; Thogmartin, Wayne E.

2016-01-01

Region-specific conservation programs should have objective, reliable metrics for species prioritization and progress evaluation that are customizable to the goals of a program, easy to comprehend and communicate, and standardized across time. Regional programs may have vastly different goals, spatial coverage, or management agendas, and one-size-fits-all schemes may not always be the best approach. We propose a quantitative and objective framework for generating metrics for prioritizing species that is straightforward to implement and update, customizable to different spatial resolutions, and based on readily available time-series data. This framework is also well-suited to handling missing-data and observer error. We demonstrate this approach using North American Breeding Bird Survey (NABBS) data to identify conservation priority species from a list of over 300 landbirds across 33 bird conservation regions (BCRs). To highlight the flexibility of the framework for different management goals and timeframes we calculate two different metrics. The first identifies species that may be inadequately monitored by NABBS protocols in the near future (TMT, time to monitoring threshold), and the other identifies species likely to decline significantly in the near future based on recent trends (TPD, time to percent decline). Within the individual BCRs we found up to 45% (mean 28%) of the species analyzed had overall declining population trajectories, which could result in up to 37 species declining below a minimum NABBS monitoring threshold in at least one currently occupied BCR within the next 50 years. Additionally, up to 26% (mean 8%) of the species analyzed within the individual BCRs may decline by 30% within the next decade. Conservation workers interested in conserving avian diversity and abundance within these BCRs can use these metrics to plan alternative monitoring schemes or highlight the urgency of those populations experiencing the fastest declines. However, this framework is adaptable to many taxa besides birds where abundance time-series data are available.

Conference Proceedings on Validation of Computational Fluid Dynamics. Volume 1. Symposium Papers and Round Table Discussion Held in Lisbon, Portugal on 2-5 May 1988

DTIC Science & Technology

1988-05-01

the representation of the shock, the non -conservative difference scheme in the original method being replaced by a ’ quasi - conservative’ operator 3...domain. In order to simulate the experimentally observed pressure distribution at the exit a formulation of the non -reflecting pressure condition Is used...and Experimental Aero- dynamics: Wing Surface Generator Code, Control Surface and Boundary Conditions". DFVLR IB 221-87 A 01, 1987. [11] Kordulla, W.(ed

High order filtering methods for approximating hyperbolic systems of conservation laws

NASA Technical Reports Server (NTRS)

Lafon, F.; Osher, S.

1991-01-01

The essentially nonoscillatory (ENO) schemes, while potentially useful in the computation of discontinuous solutions of hyperbolic conservation-law systems, are computationally costly relative to simple central-difference methods. A filtering technique is presented which employs central differencing of arbitrarily high-order accuracy except where a local test detects the presence of spurious oscillations and calls upon the full ENO apparatus to remove them. A factor-of-three speedup is thus obtained over the full-ENO method for a wide range of problems, with high-order accuracy in regions of smooth flow.

Hybrid upwind discretization of nonlinear two-phase flow with gravity

NASA Astrophysics Data System (ADS)

Lee, S. H.; Efendiev, Y.; Tchelepi, H. A.

2015-08-01

Multiphase flow in porous media is described by coupled nonlinear mass conservation laws. For immiscible Darcy flow of multiple fluid phases, whereby capillary effects are negligible, the transport equations in the presence of viscous and buoyancy forces are highly nonlinear and hyperbolic. Numerical simulation of multiphase flow processes in heterogeneous formations requires the development of discretization and solution schemes that are able to handle the complex nonlinear dynamics, especially of the saturation evolution, in a reliable and computationally efficient manner. In reservoir simulation practice, single-point upwinding of the flux across an interface between two control volumes (cells) is performed for each fluid phase, whereby the upstream direction is based on the gradient of the phase-potential (pressure plus gravity head). This upwinding scheme, which we refer to as Phase-Potential Upwinding (PPU), is combined with implicit (backward-Euler) time discretization to obtain a Fully Implicit Method (FIM). Even though FIM suffers from numerical dispersion effects, it is widely used in practice. This is because of its unconditional stability and because it yields conservative, monotone numerical solutions. However, FIM is not unconditionally convergent. The convergence difficulties are particularly pronounced when the different immiscible fluid phases switch between co-current and counter-current states as a function of time, or (Newton) iteration. Whether the multiphase flow across an interface (between two control-volumes) is co-current, or counter-current, depends on the local balance between the viscous and buoyancy forces, and how the balance evolves in time. The sensitivity of PPU to small changes in the (local) pressure distribution exacerbates the problem. The common strategy to deal with these difficulties is to cut the timestep and try again. Here, we propose a Hybrid-Upwinding (HU) scheme for the phase fluxes, then HU is combined with implicit time discretization to yield a fully implicit method. In the HU scheme, the phase flux is divided into two parts based on the driving force. The viscous-driven and buoyancy-driven phase fluxes are upwinded differently. Specifically, the viscous flux, which is always co-current, is upwinded based on the direction of the total-velocity. The buoyancy-driven flux across an interface is always counter-current and is upwinded such that the heavier fluid goes downward and the lighter fluid goes upward. We analyze the properties of the Implicit Hybrid Upwinding (IHU) scheme. It is shown that IHU is locally conservative and produces monotone, physically-consistent numerical solutions. The IHU solutions show numerical diffusion levels that are slightly higher than those for standard FIM (i.e., implicit PPU). The primary advantage of the IHU scheme is that the numerical overall-flux of a fluid phase remains continuous and differentiable as the flow regime changes between co-current and counter-current conditions. This is in contrast to the standard phase-potential upwinding scheme, in which the overall fractional-flow (flux) function is non-differentiable across the boundary between co-current and counter-current flows.

The EU Emissions Trading Scheme: A Challenge to U.S. Sovereignty

DTIC Science & Technology

2012-02-07

biofuels, and fuel-conserving winglets .51 The technological improvements are not insignificant. The IPCC assumed that advances in aircraft...16, 2012.) 51 Winglets are extensions added to the ends of an aircraft wings. They disrupt the wingtip vortices created during the production of lift

Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type

NASA Technical Reports Server (NTRS)

Agapov, A. V.; Kolosov, B. I.

1979-01-01

The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.

On the implementation of a class of upwind schemes for system of hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Yee, H. C.

1985-01-01

The relative computational effort among the spatially five point numerical flux functions of Harten, van Leer, and Osher and Chakravarthy is explored. These three methods typify the design principles most often used in constructing higher than first order upwind total variation diminishing (TVD) schemes. For the scalar case the difference in operation count between any two algorithms may be very small and yet the operation count for their system counterparts might be vastly different. The situation occurs even though one starts with two different yet equivalent representations for the scalar case.

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

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Sethian, James A.

2006-01-01

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

Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion

NASA Astrophysics Data System (ADS)

Lv, Yu; Ihme, Matthias

2014-08-01

This paper presents the development of a discontinuous Galerkin (DG) method for application to chemically reacting flows in subsonic and supersonic regimes under the consideration of variable thermo-viscous-diffusive transport properties, detailed and stiff reaction chemistry, and shock capturing. A hybrid-flux formulation is developed for treatment of the convective fluxes, combining a conservative Riemann-solver and an extended double-flux scheme. A computationally efficient splitting scheme is proposed, in which advection and diffusion operators are solved in the weak form, and the chemically stiff substep is advanced in the strong form using a time-implicit scheme. The discretization of the viscous-diffusive transport terms follows the second form of Bassi and Rebay, and the WENO-based limiter due to Zhong and Shu is extended to multicomponent systems. Boundary conditions are developed for subsonic and supersonic flow conditions, and the algorithm is coupled to thermochemical libraries to account for detailed reaction chemistry and complex transport. The resulting DG method is applied to a series of test cases of increasing physico-chemical complexity. Beginning with one- and two-dimensional multispecies advection and shock-fluid interaction problems, computational efficiency, convergence, and conservation properties are demonstrated. This study is followed by considering a series of detonation and supersonic combustion problems to investigate the convergence-rate and the shock-capturing capability in the presence of one- and multistep reaction chemistry. The DG algorithm is then applied to diffusion-controlled deflagration problems. By examining convergence properties for polynomial order and spatial resolution, and comparing these with second-order finite-volume solutions, it is shown that optimal convergence is achieved and that polynomial refinement provides advantages in better resolving the localized flame structure and complex flow-field features associated with multidimensional and hydrodynamic/thermo-diffusive instabilities in deflagration and detonation systems. Comparisons with standard third- and fifth-order WENO schemes are presented to illustrate the benefit of the DG scheme for application to detonation and multispecies flow/shock-interaction problems.

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

Wintermeyer, Niklas; Winters, Andrew R., E-mail: awinters@math.uni-koeln.de; Gassner, Gregor J.

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 schememore » 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.« less

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

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

High-order flux correction/finite difference schemes for strand grids

NASA Astrophysics Data System (ADS)

Katz, Aaron; Work, Dalon

2015-02-01

A novel high-order method combining unstructured flux correction along body surfaces and high-order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids. The flux correction algorithm is applied in each unstructured layer of the strand grid, and the layers are then coupled together via a source term containing derivatives in the strand direction. Strand-direction derivatives are approximated to high-order via summation-by-parts operators for first derivatives and second derivatives with variable coefficients. We show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme. The resulting scheme possesses third-order design accuracy, but often exhibits fourth-order accuracy when higher-order derivatives are employed in the strand direction, especially for highly viscous flows. We prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms. Results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second-order algorithms.

Accuracy Study of the Space-Time CE/SE Method for Computational Aeroacoustics Problems Involving Shock Waves

NASA Technical Reports Server (NTRS)

Wang, Xiao Yen; Chang, Sin-Chung; Jorgenson, Philip C. E.

1999-01-01

The space-time conservation element and solution element(CE/SE) method is used to study the sound-shock interaction problem. The order of accuracy of numerical schemes is investigated. The linear model problem.govemed by the 1-D scalar convection equation, sound-shock interaction problem governed by the 1-D Euler equations, and the 1-D shock-tube problem which involves moving shock waves and contact surfaces are solved to investigate the order of accuracy of numerical schemes. It is concluded that the accuracy of the CE/SE numerical scheme with designed 2nd-order accuracy becomes 1st order when a moving shock wave exists. However, the absolute error in the CE/SE solution downstream of the shock wave is on the same order as that obtained using a fourth-order accurate essentially nonoscillatory (ENO) scheme. No special techniques are used for either high-frequency low-amplitude waves or shock waves.

An Implicit LU/AF FDTD Method

NASA Technical Reports Server (NTRS)

Beggs, John H.; Briley, W. Roger

2001-01-01

There has been some recent work to develop two and three-dimensional alternating direction implicit (ADI) FDTD schemes. These ADI schemes are based upon the original ADI concept developed by Peaceman and Rachford and Douglas and Gunn, which is a popular solution method in Computational Fluid Dynamics (CFD). These ADI schemes work well and they require solution of a tridiagonal system of equations. A new approach proposed in this paper applies a LU/AF approximate factorization technique from CFD to Maxwell s equations in flux conservative form for one space dimension. The result is a scheme that will retain its unconditional stability in three space dimensions, but does not require the solution of tridiagonal systems. The theory for this new algorithm is outlined in a one-dimensional context for clarity. An extension to two and threedimensional cases is discussed. Results of Fourier analysis are discussed for both stability and dispersion/damping properties of the algorithm. Results are presented for a one-dimensional model problem, and the explicit FDTD algorithm is chosen as a convenient reference for comparison.

Evaluating the suitability of the Soil Vulnerability Index (SVI) classification scheme using the SWAT model

USDA-ARS?s Scientific Manuscript database

Conservation practices are effective ways to mitigate non-point source pollution, especially when implemented on critical source areas (CSAs) known to be the areas contributing disproportionately to high pollution loads. Although hydrologic models are promising tools to identify CSAs within agricul...

Field sports and conservation in the United Kingdom.

PubMed

Oldfield, T E E; Smith, R J; Harrop, S R; Leader-Williams, N

2003-05-29

Many natural habitats exist on privately owned land outside protected areas, but few governments can afford to enforce or subsidize conservation of this biodiversity. Even in some developed countries, conservation subsidy schemes have only achieved limited success. Fortunately, some landowners may be willing to accept management costs in return for other benefits, although this remains controversial when it involves the killing of charismatic species. For example, participants in British field sports, such as fox hunting and game-bird shooting, may voluntarily conserve important habitats that are required by quarry species. Here we report results from a multidisciplinary study that addressed this issue by focusing on three sites across central England. We found that landowners participating in field sports maintained the most established woodland and planted more new woodland and hedgerows than those who did not, despite the equal availability of subsidies. Therefore, voluntary habitat management appears to be important for biodiversity conservation in Britain. Current debates on the future of field sports in Britain, and similar activities globally, may benefit from considering their utility as incentives to conserve additional habitat on private land.

Discrete conservation properties for shallow water flows using mixed mimetic spectral elements

NASA Astrophysics Data System (ADS)

Lee, D.; Palha, A.; Gerritsma, M.

2018-03-01

A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in one dimension. These are used to construct tensor product solution spaces which satisfy the generalized Stokes theorem, as well as the annihilation of the gradient operator by the curl and the curl by the divergence. This allows for the exact conservation of first order moments (mass, vorticity), as well as higher moments (energy, potential enstrophy), subject to the truncation error of the time stepping scheme. The continuity equation is solved in the strong form, such that mass conservation holds point wise, while the momentum equation is solved in the weak form such that vorticity is globally conserved. While mass, vorticity and energy conservation hold for any quadrature rule, potential enstrophy conservation is dependent on exact spatial integration. The method possesses a weak form statement of geostrophic balance due to the compatible nature of the solution spaces and arbitrarily high order spatial error convergence.

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

NASA Astrophysics Data System (ADS)

Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

2018-04-01

In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1995-01-01

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Functional planning units for the management of an endangered Brazilian titi monkey.

PubMed

Gouveia, Sidney F; Souza-Alves, João Pedro; de Souza, Bruno B; Beltrão-Mendes, Raone; Jerusalinsky, Leandro; Ferrari, Stephen F

2017-05-01

Conservation practices in the tropics often rely on the data available for a few, better-known species and the adoption of an appropriate spatial scale. By defining a set of landscape units that account for critical aspects of the focal species, the information available on these conservation targets can support regional conservation policies. Here, we define and classify adjacent landscapes, termed planning units, to orientate management decisions within and among these landscapes, which are occupied by an endangered flagship primate species (Coimbra-Filho's titi monkey, Callicebus coimbrai) from eastern Brazil. We use landscape boundaries (highways and river systems), and a high-resolution map of forest remnants to identify continuous and manageable landscapes. We employed functional landscape metrics based on the species' dispersal ability and home range size to characterize and classify these landscapes. We classified planning units by scoring them according to a suite of selected metrics through a Principal Component Analysis. We propose 31 planning units, containing one to six C. coimbrai populations, most with low values of habitat availability, functional connectivity and carrying capacity, and a high degree of degradation. Due to this poor landscape configuration, basic management practices are recommendable. However, additional aspects of the landscapes and the populations they contain (e.g., matrix type and genetic variability) should improve the scheme, which will require a closer integration of research aims with socio-political strategies. Even so, our scheme should prove useful for the combination of information on conservation targets (i.e., focal species) with management strategies on an administrative scale. © 2017 Wiley Periodicals, Inc.

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Bart, Timothy J.; Kutler, Paul (Technical Monitor)

1998-01-01

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.

An interpolation-free ALE scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids

NASA Astrophysics Data System (ADS)

Re, B.; Dobrzynski, C.; Guardone, A.

2017-07-01

A novel strategy to solve the finite volume discretization of the unsteady Euler equations within the Arbitrary Lagrangian-Eulerian framework over tetrahedral adaptive grids is proposed. The volume changes due to local mesh adaptation are treated as continuous deformations of the finite volumes and they are taken into account by adding fictitious numerical fluxes to the governing equation. This peculiar interpretation enables to avoid any explicit interpolation of the solution between different grids and to compute grid velocities so that the Geometric Conservation Law is automatically fulfilled also for connectivity changes. The solution on the new grid is obtained through standard ALE techniques, thus preserving the underlying scheme properties, such as conservativeness, stability and monotonicity. The adaptation procedure includes node insertion, node deletion, edge swapping and points relocation and it is exploited both to enhance grid quality after the boundary movement and to modify the grid spacing to increase solution accuracy. The presented approach is assessed by three-dimensional simulations of steady and unsteady flow fields. The capability of dealing with large boundary displacements is demonstrated by computing the flow around the translating infinite- and finite-span NACA 0012 wing moving through the domain at the flight speed. The proposed adaptive scheme is applied also to the simulation of a pitching infinite-span wing, where the bi-dimensional character of the flow is well reproduced despite the three-dimensional unstructured grid. Finally, the scheme is exploited in a piston-induced shock-tube problem to take into account simultaneously the large deformation of the domain and the shock wave. In all tests, mesh adaptation plays a crucial role.

Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations.

PubMed

Bell, John B; Garcia, Alejandro L; Williams, Sarah A

2007-07-01

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.

Agricultural intensification escalates future conservation costs.

PubMed

Phelps, Jacob; Carrasco, Luis Roman; Webb, Edward L; Koh, Lian Pin; Pascual, Unai

2013-05-07

The supposition that agricultural intensification results in land sparing for conservation has become central to policy formulations across the tropics. However, underlying assumptions remain uncertain and have been little explored in the context of conservation incentive schemes such as policies for Reducing Emissions from Deforestation and forest Degradation, conservation, sustainable management, and enhancement of carbon stocks (REDD+). Incipient REDD+ forest carbon policies in a number of countries propose agricultural intensification measures to replace extensive "slash-and-burn" farming systems. These may result in conservation in some contexts, but will also increase future agricultural land rents as productivity increases, creating new incentives for agricultural expansion and deforestation. While robust governance can help to ensure land sparing, we propose that conservation incentives will also have to increase over time, tracking future agricultural land rents, which might lead to runaway conservation costs. We present a conceptual framework that depicts these relationships, supported by an illustrative model of the intensification of key crops in the Democratic Republic of Congo, a leading REDD+ country. A von Thünen land rent model is combined with geographic information systems mapping to demonstrate how agricultural intensification could influence future conservation costs. Once postintensification agricultural land rents are considered, the cost of reducing forest sector emissions could significantly exceed current and projected carbon credit prices. Our analysis highlights the importance of considering escalating conservation costs from agricultural intensification when designing conservation initiatives.

Agricultural intensification escalates future conservation costs

PubMed Central

Phelps, Jacob; Carrasco, Luis Roman; Webb, Edward L.; Koh, Lian Pin; Pascual, Unai

2013-01-01

The supposition that agricultural intensification results in land sparing for conservation has become central to policy formulations across the tropics. However, underlying assumptions remain uncertain and have been little explored in the context of conservation incentive schemes such as policies for Reducing Emissions from Deforestation and forest Degradation, conservation, sustainable management, and enhancement of carbon stocks (REDD+). Incipient REDD+ forest carbon policies in a number of countries propose agricultural intensification measures to replace extensive “slash-and-burn” farming systems. These may result in conservation in some contexts, but will also increase future agricultural land rents as productivity increases, creating new incentives for agricultural expansion and deforestation. While robust governance can help to ensure land sparing, we propose that conservation incentives will also have to increase over time, tracking future agricultural land rents, which might lead to runaway conservation costs. We present a conceptual framework that depicts these relationships, supported by an illustrative model of the intensification of key crops in the Democratic Republic of Congo, a leading REDD+ country. A von Thünen land rent model is combined with geographic information systems mapping to demonstrate how agricultural intensification could influence future conservation costs. Once postintensification agricultural land rents are considered, the cost of reducing forest sector emissions could significantly exceed current and projected carbon credit prices. Our analysis highlights the importance of considering escalating conservation costs from agricultural intensification when designing conservation initiatives. PMID:23589860

A conservation and biophysics guided stochastic approach to refining docked multimeric proteins.

PubMed

Akbal-Delibas, Bahar; Haspel, Nurit

2013-01-01

We introduce a protein docking refinement method that accepts complexes consisting of any number of monomeric units. The method uses a scoring function based on a tight coupling between evolutionary conservation, geometry and physico-chemical interactions. Understanding the role of protein complexes in the basic biology of organisms heavily relies on the detection of protein complexes and their structures. Different computational docking methods are developed for this purpose, however, these methods are often not accurate and their results need to be further refined to improve the geometry and the energy of the resulting complexes. Also, despite the fact that complexes in nature often have more than two monomers, most docking methods focus on dimers since the computational complexity increases exponentially due to the addition of monomeric units. Our results show that the refinement scheme can efficiently handle complexes with more than two monomers by biasing the results towards complexes with native interactions, filtering out false positive results. Our refined complexes have better IRMSDs with respect to the known complexes and lower energies than those initial docked structures. Evolutionary conservation information allows us to bias our results towards possible functional interfaces, and the probabilistic selection scheme helps us to escape local energy minima. We aim to incorporate our refinement method in a larger framework which also enables docking of multimeric complexes given only monomeric structures.

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.

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.

The Urban Environment. A Teacher's Guide, Grades K-3.

ERIC Educational Resources Information Center

Busch, Phyllis S.

Sixty-three learning activities comprise this curriculum guide to conservation education designed for elementary students. The activities enable the teacher to relate the urban child's immediate environment to the ecological problems which confront our world. Four conceptual schemes are used for each of the four grades, K-3: Living things (plants,…

Ecological Values amid Local Interests: Natural Resource Conservation, Social Differentiation, and Human Survival in Honduras

ERIC Educational Resources Information Center

Gareau, Brian J.

2007-01-01

Local peoples living in protected areas often have a different understanding about their natural space than do non-local groups that promote and declare such areas "protected." By designing protected areas without local involvement, or understandings of local social differentiation and power, natural resources management schemes will…

An Entropy-Based Approach to Nonlinear Stability

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1989-01-01

Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.

Experimental tests of coherence and entanglement conservation under unitary evolutions

NASA Astrophysics Data System (ADS)

Černoch, Antonín; Bartkiewicz, Karol; Lemr, Karel; Soubusta, Jan

2018-04-01

We experimentally demonstrate the migration of coherence between composite quantum systems and their subsystems. The quantum systems are implemented using polarization states of photons in two experimental setups. The first setup is based on a linear optical controlled-phase quantum gate and the second scheme utilizes effects of nonlinear optics. Our experiment allows one to verify the relation between correlations of the subsystems and the coherence of the composite system, which was given in terms of a conservation law for maximal accessible coherence by Svozilík et al. [J. Svozilík et al., Phys. Rev. Lett. 115, 220501 (2015), 10.1103/PhysRevLett.115.220501]. We observe that the maximal accessible coherence is conserved for the implemented class of global evolutions of the composite system.

Modified unified kinetic scheme for all flow regimes.

PubMed

Liu, Sha; Zhong, Chengwen

2012-06-01

A modified unified kinetic scheme for the prediction of fluid flow behaviors in all flow regimes is described. The time evolution of macrovariables at the cell interface is calculated with the idea that both free transport and collision mechanisms should be considered. The time evolution of macrovariables is obtained through the conservation constraints. The time evolution of local Maxwellian distribution is obtained directly through the one-to-one mapping from the evolution of macrovariables. These improvements provide more physical realities in flow behaviors and more accurate numerical results in all flow regimes especially in the complex transition flow regime. In addition, the improvement steps introduce no extra computational complexity.

Numerical Hydrodynamics in General Relativity.

PubMed

Font, José A

2000-01-01

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented. Supplementary material is available for this article at 10.12942/lrr-2000-2.

Saving the superstar: a review of the social factors affecting tiger conservation in India.

PubMed

Rastogi, Archi; Hickey, Gordon M; Badola, Ruchi; Hussain, Syed Ainul

2012-12-30

Tiger conservation in India represents an excellent case study of the many challenges facing conservation programs internationally. It is well understood that tigers are sensitive to human disturbances and large areas of habitat need to be protected for their conservation. Such protected areas in India are managed by the governments using an exclusionary approach. However, this approach is known to create several issues with local communities, including historical, legal, livelihood and management issues; with a volume of literature suggesting the inclusion of local communities in management. Yet, other evidence suggests that inclusion of communities in tiger conservation may lead to anthropogenic disturbances that can jeopardize tigers. The gravity of the situation is reflected in the recent disappearance of tigers from two key protected areas in India, the Sariska and Panna Tiger Reserves. This review paper connects the key literature from conservation biology, environmental history, management sciences, policy and political sciences to underline the gridlock of tiger conservation: it needs exclusive protected areas that antagonize communities, and it depends on the support of the same communities for success. We examine the possibility of reconciliation between these disciplines, and assert that research on tiger conservation needs to allow for an increasingly interdisciplinary approach. We call for a more integrated approach to tiger conservation, to examine the values inherent in conservation and to shed more light on the social factors that affect tiger conservation schemes. Copyright © 2012 Elsevier Ltd. All rights reserved.

Computational performance of Free Mesh Method applied to continuum mechanics problems

PubMed Central

YAGAWA, Genki

2011-01-01

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics. PMID:21558753

3D SPH numerical simulation of the wave generated by the Vajont rockslide

NASA Astrophysics Data System (ADS)

Vacondio, R.; Mignosa, P.; Pagani, S.

2013-09-01

A 3D numerical modeling of the wave generated by the Vajont slide, one of the most destructive ever occurred, is presented in this paper. A meshless Lagrangian Smoothed Particle Hydrodynamics (SPH) technique was adopted to simulate the highly fragmented violent flow generated by the falling slide in the artificial reservoir. The speed-up achievable via General Purpose Graphic Processing Units (GP-GPU) allowed to adopt the adequate resolution to describe the phenomenon. The comparison with the data available in literature showed that the results of the numerical simulation reproduce satisfactorily the maximum run-up, also the water surface elevation in the residual lake after the event. Moreover, the 3D velocity field of the flow during the event and the discharge hydrograph which overtopped the dam, were obtained.

Emerging conservation challenges and prospects in an era of offshore hydrocarbon exploration and exploitation.

PubMed

Kark, Salit; Brokovich, Eran; Mazor, Tessa; Levin, Noam

2015-12-01

Globally, extensive marine areas important for biodiversity conservation and ecosystem functioning are undergoing exploration and extraction of oil and natural gas resources. Such operations are expanding to previously inaccessible deep waters and other frontier regions, while conservation-related legislation and planning is often lacking. Conservation challenges arising from offshore hydrocarbon development are wide-ranging. These challenges include threats to ecosystems and marine species from oil spills, negative impacts on native biodiversity from invasive species colonizing drilling infrastructure, and increased political conflicts that can delay conservation actions. With mounting offshore operations, conservationists need to urgently consider some possible opportunities that could be leveraged for conservation. Leveraging options, as part of multi-billion dollar marine hydrocarbon operations, include the use of facilities and costly equipment of the deep and ultra-deep hydrocarbon industry for deep-sea conservation research and monitoring and establishing new conservation research, practice, and monitoring funds and environmental offsetting schemes. The conservation community, including conservation scientists, should become more involved in the earliest planning and exploration phases and remain involved throughout the operations so as to influence decision making and promote continuous monitoring of biodiversity and ecosystems. A prompt response by conservation professionals to offshore oil and gas developments can mitigate impacts of future decisions and actions of the industry and governments. New environmental decision support tools can be used to explicitly incorporate the impacts of hydrocarbon operations on biodiversity into marine spatial and conservation plans and thus allow for optimum trade-offs among multiple objectives, costs, and risks. © 2015 Society for Conservation Biology.

Can private land conservation reduce wildfire risk to homes? A case study in San Diego County, California, USA

USGS Publications Warehouse

Butsic, Van; Syphard, Alexandra D.; Keeley, Jon E.; Bar-Massada, Avi

2017-01-01

The purchase of private land for conservation purposes is a common way to prevent the exploitation of sensitive ecological areas. However, private land conservation can also provide other benefits, one of these being natural hazard reduction. Here, we investigated the impacts of private land conservation on fire risk to homes in San Diego County, California. We coupled an econometric land use change model with a model that estimates the probability of house loss due to fire in order to compare fire risk at the county and municipality scale under alternative private land purchasing schemes and over a 20 year time horizon. We found that conservation purchases could reduce fire risk on this landscape, and the amount of risk reduction was related to the targeting approach used to choose which parcels were conserved. Conservation land purchases that targeted parcels designated as high fire hazard resulted in lower fire risk to homes than purchases that targeted low costs or high likelihood to subdivide. This result was driven by (1) preventing home placement in fire prone areas and (2) taking land off the market, and hence increasing development densities in other areas. These results raise the possibility that resource conservation and fire hazard reduction may benefit from combining efforts. With adequate planning, future conservation purchases could have synergistic effects beyond just protecting ecologically sensitive areas.

A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows

NASA Astrophysics Data System (ADS)

Joshi, Vaibhav; Jaiman, Rajeev K.

2018-05-01

We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen-Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen-Cahn phase-field equation with the incompressible Navier-Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen-Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace-Young law and a sloshing tank problem. Two- and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase-field solver for a practical offshore engineering application of wave-structure interaction.

Quantum Monte Carlo calculations of NiO

NASA Astrophysics Data System (ADS)

Maezono, Ryo; Towler, Mike D.; Needs, Richard. J.

2008-03-01

We describe variational and diffusion quantum Monte Carlo (VMC and DMC) calculations [1] of NiO using a 1024-electron simulation cell. We have used a smooth, norm-conserving, Dirac-Fock pseudopotential [2] in our work. Our trial wave functions were of Slater-Jastrow form, containing orbitals generated in Gaussian-basis UHF periodic calculations. Jastrow factor is optimized using variance minimization with optimized cutoff lengths using the same scheme as our previous work. [4] We apply the lattice regulated scheme [5] to evaluate non-local pseudopotentials in DMC and find the scheme improves the smoothness of the energy-volume curve. [1] CASINO ver.2.1 User Manual, University of Cambridge (2007). [2] J.R. Trail et.al., J. Chem. Phys. 122, 014112 (2005). [3] CRYSTAL98 User's Manual, University of Torino (1998). [4] Ryo Maezono et.al., Phys. Rev. Lett., 98, 025701 (2007). [5] Michele Casula, Phys. Rev. B 74, 161102R (2006).

A new class of accurate, mesh-free hydrodynamic simulation methods

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2015-06-01

We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both SPH and grid-based/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a high-order matrix gradient estimator and a Riemann solver acting over the volume `overlap'. We implement and test a parallel, second-order version of the method with self-gravity and cosmological integration, in the code GIZMO:1 this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require `artificial diffusion' terms; and allows the fluid elements to move with the flow, so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages versus SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced `particle noise' and numerical viscosity, more accurate sub-sonic flow evolution, and sharp shock-capturing. Advantages versus non-moving meshes include: automatic adaptivity, dramatically reduced advection errors and numerical overmixing, velocity-independent errors, accurate coupling to gravity, good angular momentum conservation and elimination of `grid alignment' effects. We can, for example, follow hundreds of orbits of gaseous discs, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize `grid noise'. These differences are important for a range of astrophysical problems.

The effect of sampling scheme in the survey of atmospheric deposition of heavy metals in Albania by using moss biomonitoring.

PubMed

Qarri, Flora; Lazo, Pranvera; Bekteshi, Lirim; Stafilov, Trajce; Frontasyeva, Marina; Harmens, Harry

2015-02-01

The atmospheric deposition of heavy metals in Albania was investigated by using a carpet-forming moss species (Hypnum cupressiforme) as bioindicator. Sampling was done in the dry seasons of autumn 2010 and summer 2011. Two different sampling schemes are discussed in this paper: a random sampling scheme with 62 sampling sites distributed over the whole territory of Albania and systematic sampling scheme with 44 sampling sites distributed over the same territory. Unwashed, dried samples were totally digested by using microwave digestion, and the concentrations of metal elements were determined by inductively coupled plasma atomic emission spectroscopy (ICP-AES) and AAS (Cd and As). Twelve elements, such as conservative and trace elements (Al and Fe and As, Cd, Cr, Cu, Ni, Mn, Pb, V, Zn, and Li), were measured in moss samples. Li as typical lithogenic element is also included. The results reflect local emission points. The median concentrations and statistical parameters of elements were discussed by comparing two sampling schemes. The results of both sampling schemes are compared with the results of other European countries. Different levels of the contamination valuated by the respective contamination factor (CF) of each element are obtained for both sampling schemes, while the local emitters identified like iron-chromium metallurgy and cement industry, oil refinery, mining industry, and transport have been the same for both sampling schemes. In addition, the natural sources, from the accumulation of these metals in mosses caused by metal-enriched soil, associated with wind blowing soils were pointed as another possibility of local emitting factors.

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

Implementation of the high-order schemes QUICK and LECUSSO in the COMMIX-1C Program

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

Sakai, K.; Sun, J.G.; Sha, W.T.

Multidimensional analysis computer programs based on the finite volume method, such as COMMIX-1C, have been commonly used to simulate thermal-hydraulic phenomena in engineering systems such as nuclear reactors. In COMMIX-1C, the first-order schemes with respect to both space and time are used. In many situations such as flow recirculations and stratifications with steep gradient of velocity and temperature fields, however, high-order difference schemes are necessary for an accurate prediction of the fields. For these reasons, two second-order finite difference numerical schemes, QUICK (Quadratic Upstream Interpolation for Convective Kinematics) and LECUSSO (Local Exact Consistent Upwind Scheme of Second Order), have beenmore » implemented in the COMMIX-1C computer code. The formulations were derived for general three-dimensional flows with nonuniform grid sizes. Numerical oscillation analyses for QUICK and LECUSSO were performed. To damp the unphysical oscillations which occur in calculations with high-order schemes at high mesh Reynolds numbers, a new FRAM (Filtering Remedy and Methodology) scheme was developed and implemented. To be consistent with the high-order schemes, the pressure equation and the boundary conditions for all the conservation equations were also modified to be of second order. The new capabilities in the code are listed. Test calculations were performed to validate the implementation of the high-order schemes. They include the test of the one-dimensional nonlinear Burgers equation, two-dimensional scalar transport in two impinging streams, von Karmann vortex shedding, shear driven cavity flow, Couette flow, and circular pipe flow. The calculated results were compared with available data; the agreement is good.« less

Distributed Relaxation for Conservative Discretizations

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2001-01-01

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Adaptive mesh fluid simulations on GPU

NASA Astrophysics Data System (ADS)

Wang, Peng; Abel, Tom; Kaehler, Ralf

2010-10-01

We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be mapped naturally on this architecture. Using the method of lines approach with the second order total variation diminishing Runge-Kutta time integration scheme, piecewise linear reconstruction, and a Harten-Lax-van Leer Riemann solver, we achieve an overall speedup of approximately 10 times faster execution on one graphics card as compared to a single core on the host computer. We attain this speedup in uniform grid runs as well as in problems with deep AMR hierarchies. Our framework can readily be applied to more general systems of conservation laws and extended to higher order shock capturing schemes. This is shown directly by an implementation of a magneto-hydrodynamic solver and comparing its performance to the pure hydrodynamic case. Finally, we also combined our CUDA parallel scheme with MPI to make the code run on GPU clusters. Close to ideal speedup is observed on up to four GPUs.

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.

Natural Resource Management Schemes as Entry Points for Integrated Landscape Approaches: Evidence from Ghana and Burkina Faso.

PubMed

Foli, Samson; Ros-Tonen, Mirjam A F; Reed, James; Sunderland, Terry

2018-07-01

In recognition of the failures of sectoral approaches to overcome global challenges of biodiversity loss, climate change, food insecurity and poverty, scientific discourse on biodiversity conservation and sustainable development is shifting towards integrated landscape governance arrangements. Current landscape initiatives however very much depend on external actors and funding, raising the question of whether, and how, and under what conditions, locally embedded resource management schemes can serve as entry points for the implementation of integrated landscape approaches. This paper assesses the entry point potential for three established natural resource management schemes in West Africa that target landscape degradation with involvement of local communities: the Chantier d'Aménagement Forestier scheme encompassing forest management sites across Burkina Faso and the Modified Taungya System and community wildlife resource management initiatives in Ghana. Based on a review of the current literature, we analyze the extent to which design principles that define a landscape approach apply to these schemes. We found that the CREMA meets most of the desired criteria, but that its scale may be too limited to guarantee effective landscape governance, hence requiring upscaling. Conversely, the other two initiatives are strongly lacking in their design principles on fundamental components regarding integrated approaches, continual learning, and capacity building. Monitoring and evaluation bodies and participatory learning and negotiation platforms could enhance the schemes' alignment with integrated landscape approaches.

Student Involvement with the Regionally Important Geomorphological Site (RIGS) Scheme: An Opportunity to Learn Geomorphology and Gain Transferable Skills.

ERIC Educational Resources Information Center

McEwen, Lindsey

1996-01-01

Outlines student involvement with a conservation project that aims to develop a Regionally Important Geological/Geomorphological Site network (RIGS) at a county level in the United Kingdom. Emphasis is placed on identifying, describing, evaluating, and documenting land forms of educational, research, historical, and/or aesthetic value. (MJP)

Effects of weighting schemes on the identification of wildlife corridors generated with least-cost methods

Treesearch

Sean A. Parks; Kevin S. McKelvey; Michael K. Schwartz

2012-01-01

The importance of movement corridors for maintaining connectivity within metapopulations of wild animals is a cornerstone of conservation. One common approach for determining corridor locations is least-cost corridor (LCC) modeling, which uses algorithms within a geographic information system to search for routes with the lowest cumulative resistance between target...

Neotropical migratory landbird species and their habitats of special concern within the Southeast Region

Treesearch

William C. Hunter; David N. Pashley; Ronald E. F. Escano

1993-01-01

The Southeast Management Working Group for Partners in Flight initiated a prioritization scheme in April 1991 to help guide regional and local conservation efforts for Neotropical migratory landbirds. Preliminary breeding season priorities have been established in each of 24 physiographic areas for species and habitats, with some non-breeding season priorities set as...

Section 1: Looking Broadly at the Politics of Privatization: The Politics of Privatization in American Education

ERIC Educational Resources Information Center

Boyd, William L.

2007-01-01

The long-sustained effort of conservatives and their think tanks and media outlets to win support for school choice, market forces, and privatization schemes in education is paying off. But it is encountering steady resistance from the public education establishment and its supporting teachers' unions. Actions, reactions, strategies, and the…

Corrigendum to "On the relation between conservation and dual consistency for summation-by-parts schemes" [J. Comput. Phys. 344 (2017) 437-439

NASA Astrophysics Data System (ADS)

Nordström, Jan; Ghasemi, Fatemeh

2018-05-01

A few notational errors were recently discovered in the above publication. The notation used in the note is valid for fluxes of the form fL (u) =AL u ,fR (v) =AR v where AL =AR is m × m constant symmetric matrix.

Monitoring change in the abundance and distribution of insects using butterflies and other indicator groups

PubMed Central

Thomas, J.A

2005-01-01

Conservative estimates suggest that 50–90% of the existing insect species on Earth have still to be discovered, yet the named insects alone comprise more than half of all known species of organism. With such poor baseline knowledge, monitoring change in insect diversity poses a formidable challenge to scientists and most attempts to generalize involve large extrapolations from a few well-studied taxa. Butterflies are often the only group for which accurate measures of change can be obtained. Four schemes, used successfully to assess change in British butterflies, that are increasingly being applied across the world are described: Red Data Books (RDB) list the best judgements of experts of the conservation status of species in their field of expertise; mapping schemes plot the changing distributions of species at scales of 1–100 km2; transect monitoring schemes generate time series of changes in abundance in sample populations of species on fixed sites across the UK; and occasional surveys measure the number, boundaries and size of all populations of a (usually RDB) species at intervals of 10–30 years. All schemes describe consistent patterns of change, but if they are to be more generally useful, it is important to understand how well butterflies are representative of other taxa. Comparisons with similarly measured changes in native bird and plant species suggest that butterflies have declined more rapidly that these other groups in Britain; it should soon be possible to test whether this pattern exists elsewhere. It is also demonstrated that extinction rates in British butterflies are similar to those in a range of other insect groups over 100 years once recording bias is accounted for, although probably lower than in aquatic or parasitic taxa. It is concluded that butterflies represent adequate indicators of change for many terrestrial insect groups, but recommended that similar schemes be extended to other popular groups, especially dragonflies, bumblebees, hoverflies and ants. Given institutional backing, similar projects could be employed internationally and standardized. Finally, a range of schemes designed to monitor change in communities of aquatic macro-invertebrates is described. Although designed to use invertebrates as a bio-indicator of water quality for human use, these programmes could be extended to monitor the 2010 biodiversity targets of the World Summit on Sustainable Development. PMID:15814349

Monitoring change in the abundance and distribution of insects using butterflies and other indicator groups.

PubMed

Thomas, J A

2005-02-28

Conservative estimates suggest that 50-90% of the existing insect species on Earth have still to be discovered, yet the named insects alone comprise more than half of all known species of organism. With such poor baseline knowledge, monitoring change in insect diversity poses a formidable challenge to scientists and most attempts to generalize involve large extrapolations from a few well-studied taxa. Butterflies are often the only group for which accurate measures of change can be obtained. Four schemes, used successfully to assess change in British butterflies, that are increasingly being applied across the world are described: Red Data Books (RDB) list the best judgements of experts of the conservation status of species in their field of expertise; mapping schemes plot the changing distributions of species at scales of 1-100 km2; transect monitoring schemes generate time series of changes in abundance in sample populations of species on fixed sites across the UK; and occasional surveys measure the number, boundaries and size of all populations of a (usually RDB) species at intervals of 10-30 years. All schemes describe consistent patterns of change, but if they are to be more generally useful, it is important to understand how well butterflies are representative of other taxa. Comparisons with similarly measured changes in native bird and plant species suggest that butterflies have declined more rapidly that these other groups in Britain; it should soon be possible to test whether this pattern exists elsewhere. It is also demonstrated that extinction rates in British butterflies are similar to those in a range of other insect groups over 100 years once recording bias is accounted for, although probably lower than in aquatic or parasitic taxa. It is concluded that butterflies represent adequate indicators of change for many terrestrial insect groups, but recommended that similar schemes be extended to other popular groups, especially dragonflies, bumblebees, hoverflies and ants. Given institutional backing, similar projects could be employed internationally and standardized. Finally, a range of schemes designed to monitor change in communities of aquatic macro-invertebrates is described. Although designed to use invertebrates as a bio-indicator of water quality for human use, these programmes could be extended to monitor the 2010 biodiversity targets of the World Summit on Sustainable Development.

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

A Green Media Access Method for IEEE 802.15.6 Wireless Body Area Network.

PubMed

Jacob, Anil K; Jacob, Lillykutty

2017-09-30

It is of utmost importance to conserve battery energy to the maximum possible extent in WBAN nodes while collecting and transferring medical data. The IEEE 802.15.6 WBAN standard does not specify any method to conserve energy. This paper focuses on a method to conserve energy in IEEE 802.15.6 WBAN nodes when using CSMA/CA, while simultaneously restricting data delivery delay to the required value as specified in medical applications. The technique is to allow the nodes to sleep all the times except for receiving beacons and for transmitting data frames whenever a data frame enters an empty buffer. The energy consumed by the nodes and the average latency of data frame for periodical arrival of data are found out analytically. The analytical results are validated and also the proposed method is compared with other energy conserving schemes, using Castalia simulation studies. The proposed method shows superior performance in both device lifetime and latency of emergency medical data.

A Discrete Constraint for Entropy Conservation and Sound Waves in Cloud-Resolving Modeling

NASA Technical Reports Server (NTRS)

Zeng, Xi-Ping; Tao, Wei-Kuo; Simpson, Joanne

2003-01-01

Ideal cloud-resolving models contain little-accumulative errors. When their domain is so large that synoptic large-scale circulations are accommodated, they can be used for the simulation of the interaction between convective clouds and the large-scale circulations. This paper sets up a framework for the models, using moist entropy as a prognostic variable and employing conservative numerical schemes. The models possess no accumulative errors of thermodynamic variables when they comply with a discrete constraint on entropy conservation and sound waves. Alternatively speaking, the discrete constraint is related to the correct representation of the large-scale convergence and advection of moist entropy. Since air density is involved in entropy conservation and sound waves, the challenge is how to compute sound waves efficiently under the constraint. To address the challenge, a compensation method is introduced on the basis of a reference isothermal atmosphere whose governing equations are solved analytically. Stability analysis and numerical experiments show that the method allows the models to integrate efficiently with a large time step.

Incorporating genetic sampling in long-term monitoring and adaptive management in the San Diego County Management Strategic Plan Area, Southern California

USGS Publications Warehouse

Vandergast, Amy G.

2017-06-02

Habitat and species conservation plans usually rely on monitoring to assess progress towards conservation goals. Southern California, USA, is a hotspot of biodiversity and home to many federally endangered and threatened species. Here, several regional multi-species conservation plans have been implemented to balance development and conservation goals, including in San Diego County. In the San Diego County Management Strategic Plan Area (MSPA), a monitoring framework for the preserve system has been developed with a focus on species monitoring, vegetation monitoring, threats monitoring and abiotic monitoring. Genetic sampling over time (genetic monitoring) has proven useful in gathering species presence and abundance data and detecting population trends, particularly related to species and threats monitoring objectives. This report reviews genetic concepts and techniques of genetics that relate to monitoring goals and outlines components of a genetic monitoring scheme that could be applied in San Diego or in other monitoring frameworks throughout the Nation.

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.

2014-09-01

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

NASA Technical Reports Server (NTRS)

Bridgeman, J. O.; Steger, J. L.; Caradonna, F. X.

1982-01-01

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Multigrid Relaxation of a Factorizable, Conservative Discretization of the Compressible Flow Equations

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Sidilkover, David; Thomas, J. L.

2000-01-01

The second-order factorizable discretization of the compressible Euler equations developed by Sidilkover is extended to conservation form on general curvilinear body-fitted grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Solutions for flow in a channel with Mach numbers ranging from 0.0001 to a supercritical Mach number are shown, demonstrating uniform convergence rates and no loss of accuracy in the incompressible limit. A solution for the flow around the leading edge of a semi-infinite parabolic body demonstrates that the scheme maintains rapid convergence for a flow containing a stagnation point.

Home retrofitting for energy conservation and solar considerations

NASA Astrophysics Data System (ADS)

1981-10-01

A manual which explains both the key concepts behind the need for and the home energy efficiency improvement is reviewed. A comprehensive picture of how home energy use is effected by the inhabitants and by the structure itself is presented. The manual explains: looking at energy, how the heat transfer occurs between houses and humans, energy audits and how to use them, energy conservation actions to do now to reduce energy use. Schemes to reduce infiltration, how to increase insulation, and what to do with windows and doors, heating and heat distribution systems, and water heaters are included. Solar energy options are explained, as well as financing and tax credits.

A Godunov-like point-centered essentially Lagrangian hydrodynamic approach

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

Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.

We present an essentially Lagrangian hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedron meshes. The scheme reduces to a purely Lagrangian approach when the flow is linear or if the mesh size is equal to zero; as a result, we use the term essentially Lagrangian for the proposed approach. The motivation for developing a hydrodynamic method for tetrahedron meshes is because tetrahedron meshes have some advantages over other mesh topologies. Notable advantages include reduced complexity in generating conformal meshes, reduced complexity in mesh reconnection, and preserving tetrahedron cells with automatic mesh refinement. A challenge, however, is tetrahedron meshesmore » do not correctly deform with a lower order (i.e. piecewise constant) staggered-grid hydrodynamic scheme (SGH) or with a cell-centered hydrodynamic (CCH) scheme. The SGH and CCH approaches calculate the strain via the tetrahedron, which can cause artificial stiffness on large deformation problems. To resolve the stiffness problem, we adopt the point-centered hydrodynamic approach (PCH) and calculate the evolution of the flow via an integration path around the node. The PCH approach stores the conserved variables (mass, momentum, and total energy) at the node. The evolution equations for momentum and total energy are discretized using an edge-based finite element (FE) approach with linear basis functions. A multidirectional Riemann-like problem is introduced at the center of the tetrahedron to account for discontinuities in the flow such as a shock. Conservation is enforced at each tetrahedron center. The multidimensional Riemann-like problem used here is based on Lagrangian CCH work [8, 19, 37, 38, 44] and recent Lagrangian SGH work [33-35, 39, 45]. In addition, an approximate 1D Riemann problem is solved on each face of the nodal control volume to advect mass, momentum, and total energy. The 1D Riemann problem produces fluxes [18] that remove a volume error in the PCH discretization. A 2-stage Runge–Kutta method is used to evolve the solution in time. The details of the new hydrodynamic scheme are discussed; likewise, results from numerical test problems are presented.« less

A Godunov-like point-centered essentially Lagrangian hydrodynamic approach

DOE PAGES

Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...

2014-10-28

We present an essentially Lagrangian hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedron meshes. The scheme reduces to a purely Lagrangian approach when the flow is linear or if the mesh size is equal to zero; as a result, we use the term essentially Lagrangian for the proposed approach. The motivation for developing a hydrodynamic method for tetrahedron meshes is because tetrahedron meshes have some advantages over other mesh topologies. Notable advantages include reduced complexity in generating conformal meshes, reduced complexity in mesh reconnection, and preserving tetrahedron cells with automatic mesh refinement. A challenge, however, is tetrahedron meshesmore » do not correctly deform with a lower order (i.e. piecewise constant) staggered-grid hydrodynamic scheme (SGH) or with a cell-centered hydrodynamic (CCH) scheme. The SGH and CCH approaches calculate the strain via the tetrahedron, which can cause artificial stiffness on large deformation problems. To resolve the stiffness problem, we adopt the point-centered hydrodynamic approach (PCH) and calculate the evolution of the flow via an integration path around the node. The PCH approach stores the conserved variables (mass, momentum, and total energy) at the node. The evolution equations for momentum and total energy are discretized using an edge-based finite element (FE) approach with linear basis functions. A multidirectional Riemann-like problem is introduced at the center of the tetrahedron to account for discontinuities in the flow such as a shock. Conservation is enforced at each tetrahedron center. The multidimensional Riemann-like problem used here is based on Lagrangian CCH work [8, 19, 37, 38, 44] and recent Lagrangian SGH work [33-35, 39, 45]. In addition, an approximate 1D Riemann problem is solved on each face of the nodal control volume to advect mass, momentum, and total energy. The 1D Riemann problem produces fluxes [18] that remove a volume error in the PCH discretization. A 2-stage Runge–Kutta method is used to evolve the solution in time. The details of the new hydrodynamic scheme are discussed; likewise, results from numerical test problems are presented.« less

The global palm oil sector must change to save biodiversity and improve food security in the tropics.

PubMed

Azhar, Badrul; Saadun, Norzanalia; Prideaux, Margi; Lindenmayer, David B

2017-12-01

Most palm oil currently available in global markets is sourced from certified large-scale plantations. Comparatively little is sourced from (typically uncertified) smallholders. We argue that sourcing sustainable palm oil should not be determined by commercial certification alone and that the certification process should be revisited. There are so-far unrecognized benefits of sourcing palm oil from smallholders that should be considered if genuine biodiversity conservation is to be a foundation of 'environmentally sustainable' palm oil production. Despite a lack of certification, smallholder production is often more biodiversity-friendly than certified production from large-scale plantations. Sourcing palm oil from smallholders also alleviates poverty among rural farmers, promoting better conservation outcomes. Yet, certification schemes - the current measure of 'sustainability' - are financially accessible only for large-scale plantations that operate as profit-driven monocultures. Industrial palm oil is expanding rapidly in regions with weak environmental laws and enforcement. This warrants the development of an alternative certification scheme for smallholders. Greater attention should be directed to deforestation-free palm oil production in smallholdings, where production is less likely to cause large scale biodiversity loss. These small-scale farmlands in which palm oil is mixed with other crops should be considered by retailers and consumers who are interested in promoting sustainable palm oil production. Simultaneously, plantation companies should be required to make their existing production landscapes more compatible with enhanced biodiversity conservation. Copyright © 2017 Elsevier Ltd. All rights reserved.

In Vitro Conservation of Sweet Potato Genotypes

PubMed Central

Arrigoni-Blank, Maria de Fátima; Tavares, Fernanda Ferreira; dos Santos, Maria Clézia; Menezes, Thays Saynara Alves; de Santana, Aléa Dayane Dantas

2014-01-01

The aim of this study was to develop a protocol for the in vitro conservation of sweet potato genotypes using the slow growth technique. The first experiment was conducted in a 4 × 5 × 2 factorial scheme, testing four genotypes (IPB-007, IPB-052, IPB-072, and IPB-137), five concentrations of abscisic acid (ABA) (0.0, 1.0, 2.0, 4.0, and 8.0 mg·L−1), and two temperatures (18 and 25°C). The second experiment was conducted in a 4 × 3 × 3 factorial scheme at 18°C, testing four genotypes (IPB-007, IPB-052, IPB-072, and IPB-137), three variations of MS salts (50, 75, and 100%), and three concentrations of sucrose (10, 20, and 30 g·L−1). Every three months, we evaluated the survival (%), shoot height, and shoot viability. In vitro conservation of the sweet potato genotypes IPB-052 and IPB-007 was obtained over three and six months, respectively, using MS medium plus 2.0 mg·L−1 of ABA at either 18 or 25°C. Genotypes IPB-072 and IPB-137 can be kept for three and six months, respectively, in MS medium without ABA at 18°C. It is possible to store IPB-052 and IPB-072 for six months and IPB-007 and IPB-137 for nine months using 30 g·L−1 of sucrose and 50% MS salts. PMID:24563627

The PLUTO code for astrophysical gasdynamics .

NASA Astrophysics Data System (ADS)

Mignone, A.

Present numerical codes appeal to a consolidated theory based on finite difference and Godunov-type schemes. In this context we have developed a versatile numerical code, PLUTO, suitable for the solution of high-mach number flow in 1, 2 and 3 spatial dimensions and different systems of coordinates. Different hydrodynamic modules and algorithms may be independently selected to properly describe Newtonian, relativistic, MHD, or relativistic MHD fluids. The modular structure exploits a general framework for integrating a system of conservation laws, built on modern Godunov-type shock-capturing schemes. The code is freely distributed under the GNU public license and it is available for download to the astrophysical community at the URL http://plutocode.to.astro.it.

Block structured adaptive mesh and time refinement for hybrid, hyperbolic + N-body systems

NASA Astrophysics Data System (ADS)

Miniati, Francesco; Colella, Phillip

2007-11-01

We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels. We implement a code based on a higher order, conservative and directionally unsplit Godunov’s method for hydrodynamics; a symmetric, time centered modified symplectic scheme for collisionless component; and a multilevel, multigrid relaxation algorithm for the elliptic equation coupling the two components. Numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented.

Adaptive control schemes for improving dynamic performance of efficiency-optimized induction motor drives.

PubMed

Kumar, Navneet; Raj Chelliah, Thanga; Srivastava, S P

2015-07-01

Model Based Control (MBC) is one of the energy optimal controllers used in vector-controlled Induction Motor (IM) for controlling the excitation of motor in accordance with torque and speed. MBC offers energy conservation especially at part-load operation, but it creates ripples in torque and speed during load transition, leading to poor dynamic performance of the drive. This study investigates the opportunity for improving dynamic performance of a three-phase IM operating with MBC and proposes three control schemes: (i) MBC with a low pass filter (ii) torque producing current (iqs) injection in the output of speed controller (iii) Variable Structure Speed Controller (VSSC). The pre and post operation of MBC during load transition is also analyzed. The dynamic performance of a 1-hp, three-phase squirrel-cage IM with mine-hoist load diagram is tested. Test results are provided for the conventional field-oriented (constant flux) control and MBC (adjustable excitation) with proposed schemes. The effectiveness of proposed schemes is also illustrated for parametric variations. The test results and subsequent analysis confer that the motor dynamics improves significantly with all three proposed schemes in terms of overshoot/undershoot peak amplitude of torque and DC link power in addition to energy saving during load transitions. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Large-eddy simulation of flow past a circular cylinder

NASA Technical Reports Server (NTRS)

Mittal, R.

1995-01-01

Some of the most challenging applications of large-eddy simulation are those in complex geometries where spectral methods are of limited use. For such applications more conventional methods such as finite difference or finite element have to be used. However, it has become clear in recent years that dissipative numerical schemes which are routinely used in viscous flow simulations are not good candidates for use in LES of turbulent flows. Except in cases where the flow is extremely well resolved, it has been found that upwind schemes tend to damp out a significant portion of the small scales that can be resolved on the grid. Furthermore, it has been found that even specially designed higher-order upwind schemes that have been used successfully in the direct numerical simulation of turbulent flows produce too much dissipation when used in conjunction with large-eddy simulation. The objective of the current study is to perform a LES of incompressible flow past a circular cylinder at a Reynolds number of 3900 using a solver which employs an energy-conservative second-order central difference scheme for spatial discretization and compare the results obtained with those of Beaudan & Moin (1994) and with the experiments in order to assess the performance of the central scheme for this relatively complex geometry.

High-order conservative finite difference GLM-MHD schemes for cell-centered MHD

NASA Astrophysics Data System (ADS)

Mignone, Andrea; Tzeferacos, Petros; Bodo, Gianluigi

2010-08-01

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. [J. Comput. Phys. 175 (2002) 645-673]. The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.

Hydrodynamic Simulations of Protoplanetary Disks with GIZMO

NASA Astrophysics Data System (ADS)

Rice, Malena; Laughlin, Greg

2018-01-01

Over the past several decades, the field of computational fluid dynamics has rapidly advanced as the range of available numerical algorithms and computationally feasible physical problems has expanded. The development of modern numerical solvers has provided a compelling opportunity to reconsider previously obtained results in search for yet undiscovered effects that may be revealed through longer integration times and more precise numerical approaches. In this study, we compare the results of past hydrodynamic disk simulations with those obtained from modern analytical resources. We focus our study on the GIZMO code (Hopkins 2015), which uses meshless methods to solve the homogeneous Euler equations of hydrodynamics while eliminating problems arising as a result of advection between grid cells. By comparing modern simulations with prior results, we hope to provide an improved understanding of the impact of fluid mechanics upon the evolution of protoplanetary disks.

Smoothed particle hydrodynamics method from a large eddy simulation perspective

NASA Astrophysics Data System (ADS)

Di Mascio, A.; Antuono, M.; Colagrossi, A.; Marrone, S.

2017-03-01

The Smoothed Particle Hydrodynamics (SPH) method, often used for the modelling of the Navier-Stokes equations by a meshless Lagrangian approach, is revisited from the point of view of Large Eddy Simulation (LES). To this aim, the LES filtering procedure is recast in a Lagrangian framework by defining a filter that moves with the positions of the fluid particles at the filtered velocity. It is shown that the SPH smoothing procedure can be reinterpreted as a sort of LES Lagrangian filtering, and that, besides the terms coming from the LES convolution, additional contributions (never accounted for in the SPH literature) appear in the equations when formulated in a filtered fashion. Appropriate closure formulas are derived for the additional terms and a preliminary numerical test is provided to show the main features of the proposed LES-SPH model.

Solution of Grad-Shafranov equation by the method of fundamental solutions

NASA Astrophysics Data System (ADS)

Nath, D.; Kalra, M. S.; Kalra

2014-06-01

In this paper we have used the Method of Fundamental Solutions (MFS) to solve the Grad-Shafranov (GS) equation for the axisymmetric equilibria of tokamak plasmas with monomial sources. These monomials are the individual terms appearing on the right-hand side of the GS equation if one expands the nonlinear terms into polynomials. Unlike the Boundary Element Method (BEM), the MFS does not involve any singular integrals and is a meshless boundary-alone method. Its basic idea is to create a fictitious boundary around the actual physical boundary of the computational domain. This automatically removes the involvement of singular integrals. The results obtained by the MFS match well with the earlier results obtained using the BEM. The method is also applied to Solov'ev profiles and it is found that the results are in good agreement with analytical results.

Meshless modelling of dynamic behaviour of glasses under intense shock loadings: Application to matter ejection during high velocity impacts on thin brittle targets

NASA Astrophysics Data System (ADS)

Michel, Y.; Chevalier, J.-M.; Durin, C.; Espinosa, C.; Malaise, F.; Barrau, J.-J.

2006-08-01

The purpose of this study is to present a new material model adapted to SPH modelling of dynamic behaviour of glasses under shock loadings. This model has the ability to reproduce fragmentation and densification of glasses under compression as well as brittle tensile failure. It has been implemented in Ls-Dyna software and coupled with a SPH code. By comparison with CEA-CESTA experimental data the model has been validated for fused silica and Pyrex glass for stress level up to 35GPa. For Laser MegaJoule applications, the present material model was applied to 3D high velocity impacts on thin brittle targets with good agreement with experimental data obtained using CESTA's double stage light gas gun in term of damages and matter ejection.

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

NASA Astrophysics Data System (ADS)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For code development, a one-dimensional solver for the Euler equations was developed. This work is an extension of Chang's work on the fourth-order CESE method for solving a one-dimensional scalar convection equation. A generic formulation for the nth-order CESE method, where n ≥ 4, was derived. Indeed, numerical implementation of the scheme confirmed that the order of convergence was consistent with the order of the scheme. For the two- and three-dimensional solvers, SOLVCON was used as the basic framework for code implementation. A new solver kernel for the fourth-order CESE method has been developed and integrated into the framework provided by SOLVCON. The main part of SOLVCON, which deals with unstructured meshes and parallel computing, remains intact. The SOLVCON code for data transmission between computer nodes for High Performance Computing (HPC). To validate and verify the newly developed high-order CESE algorithms, several one-, two- and three-dimensional simulations where conducted. For the arbitrary order, one-dimensional, CESE solver, three sets of governing equations were selected for simulation: (i) the linear convection equation, (ii) the linear acoustic equations, (iii) the nonlinear Euler equations. All three systems of equations were used to verify the order of convergence through mesh refinement. In addition the Euler equations were used to solve the Shu-Osher and Blastwave problems. These two simulations demonstrated that the new high-order CESE methods can accurately resolve discontinuities in the flow field.For the two-dimensional, fourth-order CESE solver, the Euler equation was employed in four different test cases. The first case was used to verify the order of convergence through mesh refinement. The next three cases demonstrated the ability of the new solver to accurately resolve discontinuities in the flows. This was demonstrated through: (i) the interaction between acoustic waves and an entropy pulse, (ii) supersonic flow over a circular blunt body, (iii) supersonic flow over a guttered wedge. To validate and verify the three-dimensional, fourth-order CESE solver, two different simulations where selected. The first used the linear convection equations to demonstrate fourth-order convergence. The second used the Euler equations to simulate supersonic flow over a spherical body to demonstrate the scheme's ability to accurately resolve shocks. All test cases used are well known benchmark problems and as such, there are multiple sources available to validate the numerical results. Furthermore, the simulations showed that the high-order CESE solver was stable at a CFL number near unity.

Sampling affects the detection of genetic subdivision and conservation implications for fisher in the Sierra Nevada

Treesearch

Jody M. Tucker; Michael K. Schwartz; Richard L. Truex; Samantha M. Wisely; Fred W. Allendorf

2014-01-01

The small population of fisher (Pekania pennanti) in the southern Sierra Nevada is completely geographically and genetically isolated putting it at increased risk of extinction. Previous research using a clustered sampling scheme found a high amount of genetic subdivision within the southern Sierra Nevada population hypothesized to be caused by the Kings River Canyon....

Finite difference methods for the solution of unsteady potential flows

NASA Technical Reports Server (NTRS)

Caradonna, F. X.

1982-01-01

Various problems which are confronted in the development of an unsteady finite difference potential code are reviewed mainly in the context of what is done for a typical small disturbance and full potential method. The issues discussed include choice of equations, linearization and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three dimensional rotor calculations, are demonstrated.

The Switch to Private Pension Plans for Teachers, 1982-2002: A Case of Freedom of Choice or Financial Scandal?

ERIC Educational Resources Information Center

Griggs, Clive

2009-01-01

In the early 1980s the Conservative Administration introduced legislation to promote private personal pension plans for public sector workers. An army of commission-driven sales staff from the financial services industry sought to persuade teachers and others to abandon their inflation-proof pension schemes for those offered by private companies.…