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Sample records for 2d finite volume

  1. Use of finite volume radiation for predicting the Knudsen minimum in 2D channel flow

    SciTech Connect

    Malhotra, Chetan P.; Mahajan, Roop L.

    2014-12-09

    In an earlier paper we employed an analogy between surface-to-surface radiation and free-molecular flow to model Knudsen flow through tubes and onto planes. In the current paper we extend the analogy between thermal radiation and molecular flow to model the flow of a gas in a 2D channel across all regimes of rarefaction. To accomplish this, we break down the problem of gaseous flow into three sub-problems (self-diffusion, mass-motion and generation of pressure gradient) and use the finite volume method for modeling radiation through participating media to model the transport in each sub-problem as a radiation problem. We first model molecular self-diffusion in the stationary gas by modeling the transport of the molecular number density through the gas starting from the analytical asymptote for free-molecular flow to the kinetic theory limit of gaseous self-diffusion. We then model the transport of momentum through the gas at unit pressure gradient to predict Poiseuille flow and slip flow in the 2D gas. Lastly, we predict the generation of pressure gradient within the gas due to molecular collisions by modeling the transport of the forces generated due to collisions per unit volume of gas. We then proceed to combine the three radiation problems to predict flow of the gas over the entire Knudsen number regime from free-molecular to transition to continuum flow and successfully capture the Knudsen minimum at Kn ∼ 1.

  2. Effects of mesh resolution and topographic representation in 2D finite volume models of shallow water fluvial flow

    NASA Astrophysics Data System (ADS)

    Horritt, M. S.; Bates, P. D.; Mattinson, M. J.

    2006-09-01

    SummaryThe effects of mesh resolution and topographic data quality on the predictions of a 2D finite volume model of channel flow are investigated. 25 cm resolution side scan sonar swath bathymetry of a 7 km reach of the river Thames, UK, provides topography for a series of finite volume models with resolutions ranging from 2.5 to 50 m. Results from the coarser meshes are compared with the 2.5 m simulation which is used as a benchmark. The model shows greater sensitivity to mesh resolution than topographic sampling. Sensitivity to mesh resolution is attributed to two effects of roughly equal magnitude. Small elements are able to represent hydraulic features such as recirculation zones, and a more accurate representation of the domain boundary helps to drive these flow features. In practical terms, a models at a resolution of 20 and 50 m require 50 m cross-sections, whereas the 10 m model predictions are improved by using all the bathymetry data.

  3. 2-d Finite Element Code Postprocessor

    1996-07-15

    ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forcesmore » along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.« less

  4. Moving finite elements in 2-D

    NASA Technical Reports Server (NTRS)

    Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.

    1983-01-01

    The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.

  5. 2-D Finite Element Heat Conduction

    1989-10-30

    AYER is a finite element program which implicitly solves the general two-dimensional equation of thermal conduction for plane or axisymmetric bodies. AYER takes into account the effects of time (transient problems), in-plane anisotropic thermal conductivity, a three-dimensional velocity distribution, and interface thermal contact resistance. Geometry and material distributions are arbitrary, and input is via subroutines provided by the user. As a result, boundary conditions, material properties, velocity distributions, and internal power generation may be mademore » functions of, e.g., time, temperature, location, and heat flux.« less

  6. Twisted mass finite volume effects

    SciTech Connect

    Colangelo, Gilberto; Wenger, Urs; Wu, Jackson M. S.

    2010-08-01

    We calculate finite-volume effects on the pion masses and decay constant in twisted mass lattice QCD at finite lattice spacing. We show that the lighter neutral pion in twisted mass lattice QCD gives rise to finite-volume effects that are exponentially enhanced when compared to those arising from the heavier charged pions. We demonstrate that the recent two flavor twisted mass lattice data can be better fitted when twisted mass effects in finite-volume corrections are taken into account.

  7. ELLIPT2D: A Flexible Finite Element Code Written Python

    SciTech Connect

    Pletzer, A.; Mollis, J.C.

    2001-03-22

    The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research.

  8. Finite Element Analysis of 2-D Elastic Contacts Involving FGMs

    NASA Astrophysics Data System (ADS)

    Abhilash, M. N.; Murthy, H.

    2014-05-01

    The response of elastic indenters in contact with Functionally Graded Material (FGM) coated homogeneous elastic half space has been presented in the current paper. Finite element analysis has been used due to its ability to handle complex geometry, material, and boundary conditions. Indenters of different typical surface profiles have been considered and the problem has been idealized as a two-dimensional (2D) plane strain problem considering only normal loads. Initially, indenters were considered to be rigid and the results were validated with the solutions presented in the literature. The analysis has then been extended to the case of elastic indenters on FGM-coated half spaces and the results are discussed.

  9. AnisWave2D: User's Guide to the 2d Anisotropic Finite-DifferenceCode

    SciTech Connect

    Toomey, Aoife

    2005-01-06

    This document describes a parallel finite-difference code for modeling wave propagation in 2D, fully anisotropic materials. The code utilizes a mesh refinement scheme to improve computational efficiency. Mesh refinement allows the grid spacing to be tailored to the velocity model, so that fine grid spacing can be used in low velocity zones where the seismic wavelength is short, and coarse grid spacing can be used in zones with higher material velocities. Over-sampling of the seismic wavefield in high velocity zones is therefore avoided. The code has been implemented to run in parallel over multiple processors and allows large-scale models and models with large velocity contrasts to be simulated with ease.

  10. Predicting Fracture Using 2D Finite Element Modeling

    PubMed Central

    MacNeil, J.A.M.; Adachi, J.D; Goltzman, D; Josse, R.G; Kovacs, C.S; Prior, J.C; Olszynski, W; Davison, K.S.; Kaiser, S.M

    2013-01-01

    A decrease in bone density at the hip or spine has been shown to increase the risk of fracture. A limitation of the bone mineral density (BMD) measurement is that it provides only a measure of a bone samples average density when projected onto a 2D surface. Effectively, what determines bone fracture is whether an applied load exceeds ultimate strength, with both bone tissue material properties (can be approximated through bone density), and geometry playing a role. The goal of this project was to use bone geometry and BMD obtained from radiographs and DXA measurements respectively to estimate fracture risk, using a two-dimensional finite element model (FEM) of the sagittal plane of lumbar vertebrae. The Canadian Multicenter Osteoporosis Study (CaMos) data was used for this study. There were 4194 men and women over the age of 50 years, with 786 having fractures. Each subject had BMD testing and radiographs of their lumbar vertebrae. A single two dimensional FEM of the first to fourth lumbar vertebra was automatically generated for each subject. Bone tissue stiffness was assigned based on the BMD of the individual vertebrae, and adjusted for patient age. Axial compression boundary conditions were applied with a force proportional to body mass. The resulting overall strain from the applied force was found. Men and women were analyzed separately. At baseline, the sensitivity of BMD to predict fragility fractures in women and men was 3.77 % and 0.86 %, while the sensitivity of FEM to predict fragility fractures for women and men was 10.8 % and 11.3 %. The FEM ROC curve demonstrated better performance compared to BMD. The relative risk of being considered at high fracture risk using FEM at baseline, was a better predictor of 5 year incident fragility fracture risk compared to BMD. PMID:21959170

  11. STEALTH - a Lagrange explicit finite-difference code for solid, structural, and thermohydraulic analysis. Volume 8A: STEALTH/WHAMSE - a 2-D fluid-structure interaction code. Computer code manual

    SciTech Connect

    Gross, M.B.

    1984-10-01

    STEALTH is a family of computer codes that can be used to calculate a variety of physical processes in which the dynamic behavior of a continuum is involved. The version of STEALTH described in this volume is designed for calculations of fluid-structure interaction. This version of the program consists of a hydrodynamic version of STEALTH which has been coupled to a finite-element code, WHAMSE. STEALTH computes the transient response of the fluid continuum, while WHAMSE computes the transient response of shell and beam structures under external fluid loadings. The coupling between STEALTH and WHAMSE is performed during each cycle or step of a calculation. Separate calculations of fluid response and structural response are avoided, thereby giving a more accurate model of the dynamic coupling between fluid and structure. This volume provides the theoretical background, the finite-difference equations, the finite-element equations, a discussion of several sample problems, a listing of the input decks for the sample problems, a programmer's manual and a description of the input records for the STEALTH/WHAMSE computer program.

  12. Automatic differentiation of the TACO2D finite element code using ADIFOR

    SciTech Connect

    Carle, A.; Fagan, M.

    1996-04-01

    The need for sensitivities in particular applications is becoming increasingly important in problems such as optimal design or control. In this study, the authors use ADIFOR to generate derivative code for TACO2D, a finite element heat transfer code. The study of TACO2D indicates that ADIFOR-generated derivatives yield accurate derivatives at a fraction of the time requirements of finite difference approximations, and space requirements proportional to the number of variables. The primary focus on TACO2D was for the design of chemical vapor deposition reactors.

  13. Finite Temperature Response of a 2D Dipolar Bose Gas at Different Dipolar Tilt Angles

    NASA Astrophysics Data System (ADS)

    Shen, Pengtao; Quader, Khandker

    We calculate finite temperature (T) response of a 2D Bose gas, subject to dipolar interaction, within the random phase approximation (RPA). We evaluate the appropriate 2D finite-T pair bubble diagram needed in RPA, and explore ranges of density and temperature for various dipolar tilt angles. We find the system to exhibit a collapse transition and a finite momentum instability, signaling a density wave or striped phase. We construct phase diagrams depicting these instabilities and resulting phases, including a normal Bose gas phase. We also consider the finite-T response of a quasi-2D dipolar Bose gas. We discuss how our results may apply to ultracold dense Bose gas of polar molecules, such as 41K87Rb, that has been realized experimentally. Acknowledge partial support from Institute for Complex Adaptive Matter (ICAM).

  14. Finite volume hydromechanical simulation in porous media

    NASA Astrophysics Data System (ADS)

    Nordbotten, Jan Martin

    2014-05-01

    Cell-centered finite volume methods are prevailing in numerical simulation of flow in porous media. However, due to the lack of cell-centered finite volume methods for mechanics, coupled flow and deformation is usually treated either by coupled finite-volume-finite element discretizations, or within a finite element setting. The former approach is unfavorable as it introduces two separate grid structures, while the latter approach loses the advantages of finite volume methods for the flow equation. Recently, we proposed a cell-centered finite volume method for elasticity. Herein, we explore the applicability of this novel method to provide a compatible finite volume discretization for coupled hydromechanic flows in porous media. We detail in particular the issue of coupling terms, and show how this is naturally handled. Furthermore, we observe how the cell-centered finite volume framework naturally allows for modeling fractured and fracturing porous media through internal boundary conditions. We support the discussion with a set of numerical examples: the convergence properties of the coupled scheme are first investigated; second, we illustrate the practical applicability of the method both for fractured and heterogeneous media.

  15. Finite volume hydromechanical simulation in porous media

    PubMed Central

    Nordbotten, Jan Martin

    2014-01-01

    Cell-centered finite volume methods are prevailing in numerical simulation of flow in porous media. However, due to the lack of cell-centered finite volume methods for mechanics, coupled flow and deformation is usually treated either by coupled finite-volume-finite element discretizations, or within a finite element setting. The former approach is unfavorable as it introduces two separate grid structures, while the latter approach loses the advantages of finite volume methods for the flow equation. Recently, we proposed a cell-centered finite volume method for elasticity. Herein, we explore the applicability of this novel method to provide a compatible finite volume discretization for coupled hydromechanic flows in porous media. We detail in particular the issue of coupling terms, and show how this is naturally handled. Furthermore, we observe how the cell-centered finite volume framework naturally allows for modeling fractured and fracturing porous media through internal boundary conditions. We support the discussion with a set of numerical examples: the convergence properties of the coupled scheme are first investigated; second, we illustrate the practical applicability of the method both for fractured and heterogeneous media. PMID:25574061

  16. Extracting excited mesons from the finite volume

    SciTech Connect

    Doring, Michael

    2014-12-01

    As quark masses come closer to their physical values in lattice simulations, finite volume effects dominate the level spectrum. Methods to extract excited mesons from the finite volume are discussed, like moving frames in the presence of coupled channels. Effective field theory can be used to stabilize the determination of the resonance spectrum.

  17. Finite-volume scheme for anisotropic diffusion

    NASA Astrophysics Data System (ADS)

    van Es, Bram; Koren, Barry; de Blank, Hugo J.

    2016-02-01

    In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

  18. Critical behavior and finite volume

    SciTech Connect

    Ivanchenko, Yu.M.; Filippov, A.E.; Lisyanskii, A.A.

    1986-10-01

    An exactly solvable model is used to investigate the influence of the finite size of a system on its critical behavior. The renormalization of the critical temperature is calculated together with the critical exponents and the correlation function. A crossover of the critical exponents from their scaling values to the exponents of mean field theory is obtained. The possibility of complete disappearance of the region of scaling under the influence of the finite size of the system is demonstrated.

  19. Effects of 2D and Finite Density Fluctuations on O-X Correlation Reflectometry

    SciTech Connect

    G.J. Kramer; R. Nazikian; E. Valeo

    2001-07-05

    The correlation between O-mode and X-mode reflectometer signals is studied with a 1D and 2D reflectometer model in order to explore its feasibilities as a q-profile diagnostic. It was found that 2D effects and finite fluctuation levels both decrease the O-X correlation. At very low fluctuation levels, which are usually present in the plasma core, there is good possibility to determine the local magnetic field strength and use that as a constraint for the equilibrium reconstruction.

  20. Dynamic Analysis of 2D Electromagnetic Resonant Optical Scanner Using 3D Finite Element Method

    NASA Astrophysics Data System (ADS)

    Hirata, Katsuhiro; Hong, Sara; Maeda, Kengo

    The optical scanner is a scanning device in which a laser beam is reflected by a mirror that can be rotated or oscillated. In this paper, we propose a new 2D electromagnetic resonant optical scanner that employs electromagnets and leaf springs. Torque characteristics and resonance characteristics of the scanner are analyzed using the 3D finite element method. The validity of the analysis is shown by comparing the characteristics inferred from the analysis with the characteristics of the prototype. Further, 2D resonance is investigated by introducing a superimposed-frequency current in a single coil.

  1. 2D-3D hybrid stabilized finite element method for tsunami runup simulations

    NASA Astrophysics Data System (ADS)

    Takase, S.; Moriguchi, S.; Terada, K.; Kato, J.; Kyoya, T.; Kashiyama, K.; Kotani, T.

    2016-09-01

    This paper presents a two-dimensional (2D)-three-dimensional (3D) hybrid stabilized finite element method that enables us to predict a propagation process of tsunami generated in a hypocentral region, which ranges from offshore propagation to runup to urban areas, with high accuracy and relatively low computational costs. To be more specific, the 2D shallow water equation is employed to simulate the propagation of offshore waves, while the 3D Navier-Stokes equation is employed for the runup in urban areas. The stabilized finite element method is utilized for numerical simulations for both of the 2D and 3D domains that are independently discretized with unstructured meshes. The multi-point constraint and transmission methods are applied to satisfy the continuity of flow velocities and pressures at the interface between the resulting 2D and 3D meshes, since neither their spatial dimensions nor node arrangements are consistent. Numerical examples are presented to demonstrate the performance of the proposed hybrid method to simulate tsunami behavior, including offshore propagation and runup to urban areas, with substantially lower computation costs in comparison with full 3D computations.

  2. 2D-3D hybrid stabilized finite element method for tsunami runup simulations

    NASA Astrophysics Data System (ADS)

    Takase, S.; Moriguchi, S.; Terada, K.; Kato, J.; Kyoya, T.; Kashiyama, K.; Kotani, T.

    2016-05-01

    This paper presents a two-dimensional (2D)-three-dimensional (3D) hybrid stabilized finite element method that enables us to predict a propagation process of tsunami generated in a hypocentral region, which ranges from offshore propagation to runup to urban areas, with high accuracy and relatively low computational costs. To be more specific, the 2D shallow water equation is employed to simulate the propagation of offshore waves, while the 3D Navier-Stokes equation is employed for the runup in urban areas. The stabilized finite element method is utilized for numerical simulations for both of the 2D and 3D domains that are independently discretized with unstructured meshes. The multi-point constraint and transmission methods are applied to satisfy the continuity of flow velocities and pressures at the interface between the resulting 2D and 3D meshes, since neither their spatial dimensions nor node arrangements are consistent. Numerical examples are presented to demonstrate the performance of the proposed hybrid method to simulate tsunami behavior, including offshore propagation and runup to urban areas, with substantially lower computation costs in comparison with full 3D computations.

  3. 2D resistivity inversion using conjugate gradients for a finite element discretization

    NASA Astrophysics Data System (ADS)

    Bortolozo, C. A.; Santos, F. M.; Porsani, J. L.

    2014-12-01

    In this work we present a DC 2D inversion algorithm using conjugate gradients relaxation to solve the maximum likelihood inverse equations. We apply, according to Zhang (1995), the maximum likelihood inverse theory developed by Tarantola and Valette (1982) to our 2D resistivity inversion. This algorithm was chosen to this research because it doesn't need to calculate the field's derivatives. Since conjugate gradient techniques only need the results of the sensitivity matrix à or its transpose ÃT multiplying a vector, the actual computation of the sensitivity matrix are not performed, according to the methodology described in Zhang (1995). In Zhang (1995), the terms Ãx and ÃTy, are dependent of the stiffness matrix K and its partial derivative ∂K⁄∂ρ. The inversion methodology described in Zhang (1995) is for the case of 3D electrical resistivity by finite differences discretization. So it was necessary to make a series of adjustments to obtain a satisfactory result for 2D electrical inversion using finite element method. The difference between the modeling of 3D resistivity with finite difference and the 2D finite element method are in the integration variable, used in the 2D case. In the 2D case the electrical potential are initially calculated in the transformed domain, including the stiffness matrix, and only in the end is transformed in Cartesian domain. In the case of 3D, described by Zhang (1995) this is done differently, the calculation is done directly in the Cartesian domain. In the literature was not found any work describing how to deal with this problem. Because the calculations of Ãx and ÃTy must be done without having the real stiffness matrix, the adaptation consist in calculate the stiffness matrix and its partial derivative using a set of integration variables. We transform those matrix in the same form has in the potential case, but with different sets of variables. The results will be presented and are very promising.

  4. Adaptive finite element modeling of direct current resistivity in 2-D generally anisotropic structures

    NASA Astrophysics Data System (ADS)

    Yan, Bo; Li, Yuguo; Liu, Ying

    2016-07-01

    In this paper, we present an adaptive finite element (FE) algorithm for direct current (DC) resistivity modeling in 2-D generally anisotropic conductivity structures. Our algorithm is implemented on an unstructured triangular mesh that readily accommodates complex structures such as topography and dipping layers and so on. We implement a self-adaptive, goal-oriented grid refinement algorithm in which the finite element analysis is performed on a sequence of refined grids. The grid refinement process is guided by an a posteriori error estimator. The problem is formulated in terms of total potentials where mixed boundary conditions are incorporated. This type of boundary condition is superior to the Dirichlet type of conditions and improves numerical accuracy considerably according to model calculations. We have verified the adaptive finite element algorithm using a two-layered earth with azimuthal anisotropy. The FE algorithm with incorporation of mixed boundary conditions achieves high accuracy. The relative error between the numerical and analytical solutions is less than 1% except in the vicinity of the current source location, where the relative error is up to 2.4%. A 2-D anisotropic model is used to demonstrate the effects of anisotropy upon the apparent resistivity in DC soundings.

  5. Justification for a 2D versus 3D fingertip finite element model during static contact simulations.

    PubMed

    Harih, Gregor; Tada, Mitsunori; Dolšak, Bojan

    2016-10-01

    The biomechanical response of a human hand during contact with various products has not been investigated in details yet. It has been shown that excessive contact pressure on the soft tissue can result in discomfort, pain and also cumulative traumatic disorders. This manuscript explores the benefits and limitations of a simplified two-dimensional vs. an anatomically correct three-dimensional finite element model of a human fingertip. Most authors still use 2D FE fingertip models due to their simplicity and reduced computational costs. However we show that an anatomically correct 3D FE fingertip model can provide additional insight into the biomechanical behaviour. The use of 2D fingertip FE models is justified when observing peak contact pressure values as well as displacement during the contact for the given studied cross-section. On the other hand, an anatomically correct 3D FE fingertip model provides a contact pressure distribution, which reflects the fingertip's anatomy. PMID:26856769

  6. Effect of River Training Project on Hydrodynamics Flow Circumstances by 2D Finite Element Numerical Model

    NASA Astrophysics Data System (ADS)

    Zou, B.; Li, D. F.; Hu, H. J.; Zhang, H. W.; Lou, L. H.; Chen, M.; Lv, Z. Y.

    Based on the verified two dimensional(2D) finite element model for river flow simulation, the effect of estuary training levees on the water flow and sediment movement in the Yellow River estuary is analyzed. For disclosing the effect of setting the two training levees on the flow and sediment motion, the calculation and analysis for the two projects, (one is no levees, the other is setting up two no levees) are given. The results show that when setting up two training levees, water flow is bound by levees and the water flows become more concentrated. As a result, velocity increases in the main channel, sediment carrying capacity of water flow increases correspondingly.

  7. Finite-size scaling in a 2D disordered electron gas with spectral nodes

    NASA Astrophysics Data System (ADS)

    Sinner, Andreas; Ziegler, Klaus

    2016-08-01

    We study the DC conductivity of a weakly disordered 2D electron gas with two bands and spectral nodes, employing the field theoretical version of the Kubo–Greenwood conductivity formula. Disorder scattering is treated within the standard perturbation theory by summing up ladder and maximally crossed diagrams. The emergent gapless (diffusion) modes determine the behavior of the conductivity on large scales. We find a finite conductivity with an intermediate logarithmic finite-size scaling towards smaller conductivities but do not obtain the logarithmic divergence of the weak-localization approach. Our results agree with the experimentally observed logarithmic scaling of the conductivity in graphene with the formation of a plateau near {{e}2}/π h .

  8. Finite-size scaling in a 2D disordered electron gas with spectral nodes.

    PubMed

    Sinner, Andreas; Ziegler, Klaus

    2016-08-01

    We study the DC conductivity of a weakly disordered 2D electron gas with two bands and spectral nodes, employing the field theoretical version of the Kubo-Greenwood conductivity formula. Disorder scattering is treated within the standard perturbation theory by summing up ladder and maximally crossed diagrams. The emergent gapless (diffusion) modes determine the behavior of the conductivity on large scales. We find a finite conductivity with an intermediate logarithmic finite-size scaling towards smaller conductivities but do not obtain the logarithmic divergence of the weak-localization approach. Our results agree with the experimentally observed logarithmic scaling of the conductivity in graphene with the formation of a plateau near [Formula: see text]. PMID:27270084

  9. Diagonal multisoliton matrix elements in finite volume

    NASA Astrophysics Data System (ADS)

    Pálmai, T.; Takács, G.

    2013-02-01

    We consider diagonal matrix elements of local operators between multisoliton states in finite volume in the sine-Gordon model and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Takács which were only valid for diagonal scattering. In order to test the conjecture, we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.

  10. Finite volume renormalization scheme for fermionic operators

    SciTech Connect

    Monahan, Christopher; Orginos, Kostas

    2013-11-01

    We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.

  11. Moving finite elements in 2-D. Technical progress report, year 3

    SciTech Connect

    Gelinas, R.J.

    1984-04-03

    The moving finite element (MFE) method has emerged as a potentially potent and interesting method for solving partial differential equations (PDE's) with large gradients. The principal feature of the MFE method is that the grid node co-ordinates, themselves, are dependent variables and are calculated at each time step so as to minimize a PDE residual in some norm. This has the effect of moving the grid nodes continuously and systematically to those positions which minimize PDE numerical solution errors. Research on the MFE method to this time has been advanced by a relatively small number of groups and individual investigators. Of these, the presently proposing group at Science Applications, Inc. (SAI), in Pleasanton, California, has pursued simultaneously developments of the basic theory, numerical analysis, and real-world applications under sponsorship of the DOE and others. The results of our MFE research to date in both 1-D and 2-D transient PDE systems have been quite positive, as well as laden with indicators for further advancements. We report the progress of this third year of 2-D MFE research and indicate those research tasks which should now be pursued into their next logical stages of advancement for large-gradient PDE problems in 2-D.

  12. Ablation problems using a finite control volume technique

    SciTech Connect

    Blackwell, B.F.; Thornton, A.L.; Hogan, R.E.

    1993-03-01

    An element based finite control volume procedure is applied to the solution of ablation problems for 2-D axisymmetric geometries. A mesh consisting of four node quadrilateral elements was used. The nodes are allowed to move in response to the surface recession rate. The computational domain is divided into a region with a structured mesh with moving nodes and a region with an unstructured mesh with stationary nodes. The mesh is costrained to move along spines associated with the original mesh. Example problems are presented for the ablation of a realistic nose tip geometry exposed to aerodynamic heating from a uniform free stream environment.

  13. Ablation problems using a finite control volume technique

    SciTech Connect

    Blackwell, B.F.; Thornton, A.L.; Hogan, R.E.

    1993-01-01

    An element based finite control volume procedure is applied to the solution of ablation problems for 2-D axisymmetric geometries. A mesh consisting of four node quadrilateral elements was used. The nodes are allowed to move in response to the surface recession rate. The computational domain is divided into a region with a structured mesh with moving nodes and a region with an unstructured mesh with stationary nodes. The mesh is costrained to move along spines associated with the original mesh. Example problems are presented for the ablation of a realistic nose tip geometry exposed to aerodynamic heating from a uniform free stream environment.

  14. 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.

  15. Numerical method of crack analysis in 2D finite magnetoelectroelastic media

    NASA Astrophysics Data System (ADS)

    Zhao, Minghao; Xu, Guangtao; Fan, Cuiying

    2010-04-01

    The present paper extends the hybrid extended displacement discontinuity fundamental solution method (HEDD-FSM) (Eng Anal Bound Elem 33:592-600, 2009) to analysis of cracks in 2D finite magnetoelectroelastic media. The solution of the crack is expressed approximately by a linear combination of fundamental solutions of the governing equations, which includes the extended point force fundamental solutions with sources placed at chosen points outside the domain of the problem under consideration, and the extended Crouch fundamental solutions with extended displacement discontinuities placed on the crack. The coefficients of the fundamental solutions are determined by letting the approximated solution satisfy the prescribed boundary conditions on the boundary of the domain and on the crack face. The Crouch fundamental solution for a parabolic element at the crack tip is derived to model the square root variations of near tip fields. The extended stress intensity factors are calculated under different electric and magnetic boundary conditions.

  16. A framework for grand scale parallelization of the combined finite discrete element method in 2d

    NASA Astrophysics Data System (ADS)

    Lei, Z.; Rougier, E.; Knight, E. E.; Munjiza, A.

    2014-09-01

    Within the context of rock mechanics, the Combined Finite-Discrete Element Method (FDEM) has been applied to many complex industrial problems such as block caving, deep mining techniques (tunneling, pillar strength, etc.), rock blasting, seismic wave propagation, packing problems, dam stability, rock slope stability, rock mass strength characterization problems, etc. The reality is that most of these were accomplished in a 2D and/or single processor realm. In this work a hardware independent FDEM parallelization framework has been developed using the Virtual Parallel Machine for FDEM, (V-FDEM). With V-FDEM, a parallel FDEM software can be adapted to different parallel architecture systems ranging from just a few to thousands of cores.

  17. 2D time-domain finite-difference modeling for viscoelastic seismic wave propagation

    NASA Astrophysics Data System (ADS)

    Fan, Na; Zhao, Lian-Feng; Xie, Xiao-Bi; Ge, Zengxi; Yao, Zhen-Xing

    2016-07-01

    Real Earth media are not perfectly elastic. Instead, they attenuate propagating mechanical waves. This anelastic phenomenon in wave propagation can be modeled by a viscoelastic mechanical model consisting of several standard linear solids. Using this viscoelastic model, we approximate a constant Q over a frequency band of interest. We use a four-element viscoelastic model with a tradeoff between accuracy and computational costs to incorporate Q into 2D time-domain first-order velocity-stress wave equations. To improve the computational efficiency, we limit the Q in the model to a list of discrete values between 2 and 1000. The related stress and strain relaxation times that characterize the viscoelastic model are pre-calculated and stored in a database for use by the finite-difference calculation. A viscoelastic finite-difference scheme that is second-order in time and fourth-order in space is developed based on the MacCormack algorithm. The new method is validated by comparing the numerical result with analytical solutions that are calculated using the generalized reflection/transmission coefficient method. The synthetic seismograms exhibit greater than 95 per cent consistency in a two-layer viscoelastic model. The dispersion generated from the simulation is consistent with the Kolsky-Futterman dispersion relationship.

  18. Optimal implicit 2-D finite differences to model wave propagation in poroelastic media

    NASA Astrophysics Data System (ADS)

    Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.

    2016-05-01

    Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite-differences to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (<10kHz). We validate the numerical solution by comparing it to an analytical-transient solution obtaining clear seismic wavefields including fast P, slow P and S waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High order explicit finite-differences (FD) can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.

  19. 2D wave-front shaping in optical superlattices using nonlinear volume holography.

    PubMed

    Yang, Bo; Hong, Xu-Hao; Lu, Rong-Er; Yue, Yang-Yang; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan

    2016-07-01

    Nonlinear volume holography is employed to realize arbitrary wave-front shaping during nonlinear processes with properly designed 2D optical superlattices. The concept of a nonlinear polarization wave in nonlinear volume holography is investigated. The holographic imaging of irregular patterns was performed using 2D LiTaO3 crystals with fundamental wave propagating along the spontaneous polarization direction, and the results agree well with the theoretical predictions. This Letter not only extends the application area of optical superlattices, but also offers an efficient method for wave-front shaping technology. PMID:27367067

  20. Diverse Geological Applications For Basil: A 2d Finite-deformation Computational Algorithm

    NASA Astrophysics Data System (ADS)

    Houseman, Gregory A.; Barr, Terence D.; Evans, Lynn

    Geological processes are often characterised by large finite-deformation continuum strains, on the order of 100% or greater. Microstructural processes cause deformation that may be represented by a viscous constitutive mechanism, with viscosity that may depend on temperature, pressure, or strain-rate. We have developed an effective com- putational algorithm for the evaluation of 2D deformation fields produced by Newto- nian or non-Newtonian viscous flow. With the implementation of this algorithm as a computer program, Basil, we have applied it to a range of diverse applications in Earth Sciences. Viscous flow fields in 2D may be defined for the thin-sheet case or, using a velocity-pressure formulation, for the plane-strain case. Flow fields are represented using 2D triangular elements with quadratic interpolation for velocity components and linear for pressure. The main matrix equation is solved by an efficient and compact conjugate gradient algorithm with iteration for non-Newtonian viscosity. Regular grids may be used, or grids based on a random distribution of points. Definition of the prob- lem requires that velocities, tractions, or some combination of the two, are specified on all external boundary nodes. Compliant boundaries may also be defined, based on the idea that traction is opposed to and proportional to boundary displacement rate. In- ternal boundary segments, allowing fault-like displacements within a viscous medium have also been developed, and we find that the computed displacement field around the fault tip is accurately represented for Newtonian and non-Newtonian viscosities, in spite of the stress singularity at the fault tip. Basil has been applied by us and colleagues to problems that include: thin sheet calculations of continental collision, Rayleigh-Taylor instability of the continental mantle lithosphere, deformation fields around fault terminations at the outcrop scale, stress and deformation fields in and around porphyroblasts, and

  1. Massless sunset diagrams in finite asymmetric volumes

    NASA Astrophysics Data System (ADS)

    Niedermayer, F.; Weisz, P.

    2016-06-01

    This paper discusses the methods and the results used in an accompanying paper describing the matching of effective chiral Lagrangians in dimensional and lattice regularizations. We present methods to compute 2-loop massless sunset diagrams in finite asymmetric volumes in the framework of these regularizations. We also consider 1-loop sums in both regularizations, extending the results of Hasenfratz and Leutwyler for the case of dimensional regularization and we introduce a new method to calculate precisely the expansion coefficients of the 1-loop lattice sums.

  2. Simulations of SH wave scattering due to cracks by the 2-D finite difference method

    NASA Astrophysics Data System (ADS)

    Suzuki, Y.; Kawahara, J.; Okamoto, T.; Miyashita, K.

    2006-05-01

    We simulate SH wave scattering by 2-D parallel cracks using the finite difference method (FDM), instead of the popularly used boundary integral equation method (BIEM). Here special emphasis is put on simplicity; we apply a standard FDM (fourth-order velocity-stress scheme with a staggered grid) to media in cluding traction-freecracks, which are expressed by arrays of grid points with zero traction. Two types of accuracy tests based oncomparison with a reliable BIEM, suggest that the present method gives practically sufficient accuracy, except for the wavefields in the vicinity of cracks, which can be well handled if the second-order FDM is used instead. As an application of this method, we also simulate wave propagation in media with randomly distributed cracks of the same length. We experimentally determine the attenuation and velocity dispersion induced by scattering from the synthetic seismograms, using a waveform averaging technique. It is shown that the results are well explained by a theory based on the Foldy approximation for crack densities of up to about 01. The presence of a free surface does not affect the validity of the theory. A preliminary experiment also suggests that the validity will not change even for multi-scale cracks.

  3. Optimal implicit 2-D finite differences to model wave propagation in poroelastic media

    NASA Astrophysics Data System (ADS)

    Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.

    2016-08-01

    Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite differences (FD) to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (<10 kHz). We validate the numerical solution by comparing it to an analytical-transient solution obtaining clear seismic wavefields including fast P and slow P and S waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High-order explicit FD can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here, we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.

  4. Combination 3D TOP with 2D PC MRA Techique for cerebral blood flow volume measurement.

    PubMed

    Guo, G; Wu, R H; Zhang, Y P; Guan, J T; Guo, Y L; Cheng, Y; terBrugge, K; Mikulis, D J

    2006-01-01

    To demonstrate the discrepancy of cerebral blood flow volume (BFV) estimation with 2D phase-contrast (2D PC) MRA guided with 3D time-of-flight (3D TOF) MR localization by using an "internal" standard. 20 groups of the common (CCA), internal (ICA), and external (ECA) carotid arteries in 10 healthy subjects were examined with 2D PC MRA guided by 3D TOF MR angiograms. The sum BFV of the internal and external carotid arteries was then compared with the ipsilateral common carotid artery flow. An accurate technique would demonstrate no difference. The difference was therefore a measure of accuracy of the method. 3D TOF MRA localization is presented to allow the determination of a slice orientation to improve the accuracy of 2D PC MRA in estimate the BFV. By using the combined protocols, there was better correlation in BFV estimate between the sum of ICA+ECA with the ipsilateral CCA (R2=0.729, P=0.000). The inconsistency (mean +/- SD) was found to be 6.95 +/- 5.95% for estimate the BFV in ICA+ECA and ipsilateral CCA. The main inconsistency was contributed to the ECA and its branches. Guided with 3D TOF MRA localization, 2D PC MRA is more accurate in the determination of blood flow volume in the carotid arteries. PMID:17946401

  5. LARGE volume string compactifications at finite temperature

    NASA Astrophysics Data System (ADS)

    Anguelova, Lilia; Calò, Vincenzo; Cicoli, Michele

    2009-10-01

    We present a detailed study of the finite-temperature behaviour of the LARGE Volume type IIB flux compactifications. We show that certain moduli can thermalise at high temperatures. Despite that, their contribution to the finite-temperature effective potential is always negligible and the latter has a runaway behaviour. We compute the maximal temperature Tmax, above which the internal space decompactifies, as well as the temperature T*, that is reached after the decay of the heaviest moduli. The natural constraint T* < Tmax implies a lower bound on the allowed values of the internal volume Script V. We find that this restriction rules out a significant range of values corresponding to smaller volumes of the order Script V ~ 104ls6, which lead to standard GUT theories. Instead, the bound favours values of the order Script V ~ 1015ls6, which lead to TeV scale SUSY desirable for solving the hierarchy problem. Moreover, our result favours low-energy inflationary scenarios with density perturbations generated by a field, which is not the inflaton. In such a scenario, one could achieve both inflation and TeV-scale SUSY, although gravity waves would not be observable. Finally, we pose a two-fold challenge for the solution of the cosmological moduli problem. First, we show that the heavy moduli decay before they can begin to dominate the energy density of the Universe. Hence they are not able to dilute any unwanted relics. And second, we argue that, in order to obtain thermal inflation in the closed string moduli sector, one needs to go beyond the present EFT description.

  6. SIMULATIONS OF 2D AND 3D THERMOCAPILLARY FLOWS BY A LEAST-SQUARES FINITE ELEMENT METHOD. (R825200)

    EPA Science Inventory

    Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank-Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matri...

  7. CLFE2D: A generalized plane strain finite element program laminated composites subject to mechanical and hygrothermal loading

    NASA Technical Reports Server (NTRS)

    Buczek, M. B.; Gregory, M. A.; Herakovich, C. T.

    1983-01-01

    CLFE2D is a two dimensional generalized plane strain finite element code, using a linear, four node, general quadrilateral, isoparametric element. The program is developed to calculate the displacements, strains, stresses, and strain energy densities in a finite width composite laminate. CLFE2D offers any combination of the following load types: nodal displacements, nodal forces, uniform normal strain, or hygrothermal. The program allows the user to input one set of three dimensional orthotropic material properties. The user can then specify the angle of material principal orientation for each element in the mesh. Output includes displacements, stresses, strains and strain densities at points selected by the user. An option is also available to plot the underformed and deformed finite element meshes.

  8. Cancer multicellular spheroids: volume assessment from a single 2D projection.

    PubMed

    Piccinini, Filippo; Tesei, Anna; Arienti, Chiara; Bevilacqua, Alessandro

    2015-02-01

    Volume is one of the most important features for the characterization of a tumour on a macroscopic scale. It is often used to assess the effectiveness of care treatments, thus making its correct evaluation a crucial issue for patient care. Similarly, volume is a key feature on a microscopic scale. Multicellular cancer spheroids are 3D tumour models widely employed in pre-clinical studies to test the effects of drugs and radiotherapy treatments. Very few methods have been proposed to estimate the tumour volume arising from a 2D projection of multicellular spheroids, and even fewer have been designed to provide a 3D reconstruction of the tumour shape. In this work, we propose Reconstruction and Visualization from a Single Projection (ReViSP), an automatic method conceived to reconstruct the 3D surface and estimate the volume of single cancer multicellular spheroids, or even of spheroid cultures. As the input parameter ReViSP requires only one 2D projection, which could be a widefield microscope image. We assessed the effectiveness of our method by comparing it with other approaches. To this purpose, we used a new strategy that allowed us to achieve accurate volume measurements based on the analysis of home-made 3D objects, built by mimicking the spheroid morphology. The results confirmed the effectiveness of our method for both 3D reconstruction and volume assessment. ReViSP software is distributed as an open source tool. PMID:25561413

  9. High-Order Spectral Volume Method for 2D Euler Equations

    NASA Technical Reports Server (NTRS)

    Wang, Z. J.; Zhang, Laiping; Liu, Yen; Kwak, Dochan (Technical Monitor)

    2002-01-01

    The Spectral Volume (SV) method is extended to the 2D Euler equations. The focus of this paper is to study the performance of the SV method on multidimensional non-linear systems. Implementation details including total variation diminishing (TVD) and total variation bounded (TVB) limiters are presented. Solutions with both smooth features and discontinuities are utilized to demonstrate the overall capability of the SV method.

  10. 2D-3D Registration of CT Vertebra Volume to Fluoroscopy Projection: A Calibration Model Assessment

    NASA Astrophysics Data System (ADS)

    Bifulco, P.; Cesarelli, M.; Allen, R.; Romano, M.; Fratini, A.; Pasquariello, G.

    2009-12-01

    This study extends a previous research concerning intervertebral motion registration by means of 2D dynamic fluoroscopy to obtain a more comprehensive 3D description of vertebral kinematics. The problem of estimating the 3D rigid pose of a CT volume of a vertebra from its 2D X-ray fluoroscopy projection is addressed. 2D-3D registration is obtained maximising a measure of similarity between Digitally Reconstructed Radiographs (obtained from the CT volume) and real fluoroscopic projection. X-ray energy correction was performed. To assess the method a calibration model was realised a sheep dry vertebra was rigidly fixed to a frame of reference including metallic markers. Accurate measurement of 3D orientation was obtained via single-camera calibration of the markers and held as true 3D vertebra position; then, vertebra 3D pose was estimated and results compared. Error analysis revealed accuracy of the order of 0.1 degree for the rotation angles of about 1 mm for displacements parallel to the fluoroscopic plane, and of order of 10 mm for the orthogonal displacement.

  11. A mixed finite element-finite volume formulation of the Black-Oil model

    SciTech Connect

    Bergamaschi, L.; Mantica, S.; Manzini, G.

    1999-01-01

    In this paper the authors mainly address the compressible model where three independent components (oil, gas, and water) form the three phases (liquid, vapor, and aqua) present in the reservoir. This model is usually known under the name of Black-Oil, and its main feature is the description of mass-exchange processes between all phases. In this paper a sequential coupling of mixed finite element and shock-capturing finite volume techniques is proposed, in order to numerically solve the system of partial differential equations arising from the Black-Oil model. The Brezzi-Douglas-Marini space of degree one is used to approximate the Darcy`s velocity in the parabolic-type pressure equation, while the system of mass conservation laws is solved by a higher order Godunov-type scheme, here extended to triangle-based unstructured grids. Numerical results on 1-D and 2-D test cases prove the effectiveness and the robustness of the coupling, which seems particularly suited to handling high heterogeneities and at the same time accurately resolving steep gradients without spurious oscillations.

  12. Extreme value statistics of 2D Gaussian free field: effect of finite domains

    NASA Astrophysics Data System (ADS)

    Cao, X.; Rosso, A.; Santachiara, R.

    2016-01-01

    We study minima statistics of the 2D Gaussian free field (GFF) on circles in the unit disk with Dirichlet boundary condition. Free energy distributions of the associated random energy models are exactly calculated in the high temperature phase, and shown to satisfy the duality property, which enables us to predict the minima distribution by assuming the freezing scenario. Numerical tests are provided. Related questions concerning the GFF on a sphere are also considered.

  13. A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

    NASA Technical Reports Server (NTRS)

    Kandil, Osama A.

    1998-01-01

    Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

  14. TOPAZ - a finite element heat conduction code for analyzing 2-D solids

    SciTech Connect

    Shapiro, A.B.

    1984-03-01

    TOPAZ is a two-dimensional implicit finite element computer code for heat conduction analysis. This report provides a user's manual for TOPAZ and a description of the numerical algorithms used. Sample problems with analytical solutions are presented. TOPAZ has been implemented on the CRAY and VAX computers.

  15. Finite volume corrections to the electromagnetic mass of composite particles

    NASA Astrophysics Data System (ADS)

    Lee, Jong-Wan; Tiburzi, Brian C.

    2016-02-01

    The long-range electromagnetic interaction presents a challenge for numerical computations in QCD +QED . In addition to power-law finite volume effects, the standard lattice gauge theory approach introduces nonlocality through removal of photon zero-momentum modes. The resulting finite volume effects must be quantitatively understood; and, to this end, nonrelativistic effective field theories are an efficient tool, especially in the case of composite particles. Recently an oddity related to nonlocality of the standard lattice approach was uncovered by the Budapest-Marseille-Wuppertal collaboration. Explicit contributions from antiparticles appear to be required so that finite volume QED results for a pointlike fermion can be reproduced in the effective field theory description. We provide transparency for this argument by considering pointlike scalars and spinors in finite volume QED using the method of regions. For the more germane case of composite particles, we determine that antiparticle modes contribute to the finite volume electromagnetic mass of composite spinors through terms proportional to the squares of timelike form factors evaluated at threshold. We extend existing finite volume calculations to one order higher, which is particularly relevant for the electromagnetic mass of light nuclei. Additionally, we verify that the analogous finite volume contributions to the nucleon mass in chiral perturbation theory vanish in accordance with locality.

  16. Exact ground state for the four-electron problem in a 2D finite honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Trencsényi, Réka; Glukhov, Konstantin; Gulácsi, Zsolt

    2014-07-01

    Working in a subspace with dimensionality much smaller than the dimension of the full Hilbert space, we deduce exact four-particle ground states in 2D samples containing hexagonal repeat units and described by Hubbard type of models. The procedure identifies first a small subspace ? in which the ground state ? is placed, than deduces ? by exact diagonalization in ?. The small subspace is obtained by the repeated application of the Hamiltonian ? on a carefully chosen starting wave vector describing the most interacting particle configuration, and the wave vectors resulting from the application of ?, till the obtained system of equations closes in itself. The procedure which can be applied in principle at fixed but arbitrary system size and number of particles is interesting on its own since it provides exact information for the numerical approximation techniques which use a similar strategy, but apply non-complete basis for ?. The diagonalization inside ? provides an incomplete image of the low lying part of the excitation spectrum, but provides the exact ?. Once the exact ground state is obtained, its properties can be easily analysed. The ? is found always as a singlet state whose energy, interestingly, saturates in the ? limit. The unapproximated results show that the emergence probabilities of different particle configurations in the ground state presents 'Zittern' (trembling) characteristics which are absent in 2D square Hubbard systems. Consequently, the manifestation of the local Coulomb repulsion in 2D square and honeycomb types of systems presents differences, which can be a real source in the differences in the many-body behaviour.

  17. A 2D finite element wave equation solver based on triangular base elements

    NASA Astrophysics Data System (ADS)

    Van Eester, D.; Lerche, E.; Evrard, M.

    2009-11-01

    A finite element method based on the subdivision of the physical domain in triangular sub-domains in which simple local 'areale' coordinates are adopted is explored. The advantage of the method is that it straightforwardly allows grid refinement in regions where higher precision is required. The plasma model was kept simple for this 'proof-of-principle' exercise. Rather than accounting for the actual differential or integro-differential dielectric tensor, its locally uniform plasma equivalent was adopted for 3 possible choices: the cold plasma response, the full hot Stix/Swanson plasma tensor retaining all orders in finite Larmor radius (FLR) and the more common hot tensor, truncated at terms of second order in the Larmor radius.

  18. A 2D finite element wave equation solver based on triangular base elements

    SciTech Connect

    Van Eester, D.; Lerche, E.; Evrard, M.

    2009-11-26

    A finite element method based on the subdivision of the physical domain in triangular sub-domains in which simple local 'areale' coordinates are adopted is explored. The advantage of the method is that it straightforwardly allows grid refinement in regions where higher precision is required. The plasma model was kept simple for this 'proof-of-principle' exercise. Rather than accounting for the actual differential or integro-differential dielectric tensor, its locally uniform plasma equivalent was adopted for 3 possible choices: the cold plasma response, the full hot Stix/Swanson plasma tensor retaining all orders in finite Larmor radius (FLR) and the more common hot tensor, truncated at terms of second order in the Larmor radius.

  19. Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation

    DOE PAGESBeta

    Chen, Zhangxin; Cockburn, Bernardo; Jerome, Joseph W.; Shu, Chi-Wang

    1995-01-01

    In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions. The method combines a standard mixed finite element method, used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing the performance of the new method are displayed, and the results compared with those obtained by using Essentially Nonoscillatory (ENO) finite difference schemes. Frommore » the perspective of device modeling, these methods are robust, since they are capable of encompassing broad parameter ranges, including those for which shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but we have tested them much more generally with considerable success.« less

  20. Finite element nonlinear flutter and fatigue life of 2-D panels with temperature effects

    NASA Technical Reports Server (NTRS)

    Mei, Chuh; Xue, David Y.

    1991-01-01

    A frequency domain method for two-dimensional nonlinear panel flutter with thermal effects obtained from a consistent finite element formulation is presented. The von Karman nonlinear strain-displacement relation is used to account for large deflections, and the quasi-steady first-order piston theory is employed for aerodynamic loading. The finite element frequency domain results are compared with analytical time domain solutions. In a limit-cycle motion, the panel frequency and stress can be determined, thus fatigue life can be predicted. The influence of temperature and dynamic pressure on panel fatigue life is presented. An endurance dynamic pressure can be established at a given temperature from the present method.

  1. A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene

    SciTech Connect

    Brinkman, D.; Heitzinger, C.; Markowich, P.A.

    2014-01-15

    We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac–Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac–Poisson system where potentials act as beam splitters or Veselago lenses.

  2. A new spectral finite volume method for elastic wave modelling on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Zhang, Wensheng; Zhuang, Yuan; Chung, Eric T.

    2016-04-01

    In this paper, we consider a new spectral finite volume method for the elastic wave equations. Our new finite volume method is based on a piecewise constant approximation on a fine mesh and a high-order polynomial reconstruction on a coarser mesh. Our new method is constructed based on two existing techniques, the high-order finite volume method and the spectral finite volume method. In fact, we will construct a new method to take advantage of both methods. More precisely, our method has two distinctive features. The first one is that the local polynomial reconstructions are performed on the coarse triangles, and the reconstruction matrices for all the coarse triangles are the same. This fact enhances the parallelization of our algorithm. We will present a parallel implementation of our method and show excellent efficiency results. The second one is that, by using a suitable number of finer triangles with a coarse triangle, we obtain an over-determined reconstruction system, which can enhance the robustness of the reconstruction process. To derive our scheme, standard finite volume technique is applied to each fine triangle, and the high-order reconstructed polynomials, computed on coarse triangles, are used to compute numerical fluxes. We will present numerical results to show the performance of our method. Our method is presented for 2D problems, but the same methodology can be applied to 3D.

  3. Using Multithreading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes

    NASA Technical Reports Server (NTRS)

    Heber, Gerd; Biswas, Rupak; Thulasiraman, Parimala; Gao, Guang R.; Bailey, David H. (Technical Monitor)

    1998-01-01

    In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes. The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the question phase of FE applications on triangular meshes, and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments on EARTH-SP2, an implementation of EARTH on the IBM SP2, with different load balancing strategies that are built into the runtime system.

  4. Using Multi-threading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes

    NASA Technical Reports Server (NTRS)

    Heber, Gerd; Biswas, Rupak; Thulasiraman, Parimala; Gao, Guang R.; Saini, Subhash (Technical Monitor)

    1998-01-01

    In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the adaption phase of FE applications oil triangular meshes and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments oil EARTH-SP2, on implementation of EARTH on the IBM SP2 with different load balancing strategies that are built into the runtime system.

  5. Coupling finite and boundary element methods for 2-D elasticity problems

    NASA Technical Reports Server (NTRS)

    Krishnamurthy, T.; Raju, I. S.; Sistla, R.

    1993-01-01

    A finite element-boundary element (FE-BE) coupling method for two-dimensional elasticity problems is developed based on a weighted residual variational method in which a portion of the domain of interest is modeled by FEs and the remainder of the region by BEs. The performance of the FE-BE coupling method is demonstrated via applications to a simple 'patch test' problem and three-crack problems. The method passed the patch tests for various modeling configurations and yielded accurate strain energy release rates for the crack problems studied.

  6. Electromagnetic induction by finite wavenumber source fields in 2-D lateral heterogeneities - The transverse electric mode

    NASA Technical Reports Server (NTRS)

    Hermance, J. F.

    1984-01-01

    Electromagnetic induction in a laterally homogeneous earth is analyzed in terms of a source field with finite dimensions. Attention is focused on a time-varying two-dimensional current source directed parallel to the strike of a two-dimensional anomalous structure within the earth, i.e., the E-parallel mode. The spatially harmonic source field is expressed as discontinuities in the magnetic (or electric) field of the current in the source. The model is applied to describing the magnetic gradients across megatectonic features, and may be used to predict the magnetic fields encountered by a satellite orbiting above the ionosphere.

  7. Comparison of different precondtioners for nonsymmtric finite volume element methods

    SciTech Connect

    Mishev, I.D.

    1996-12-31

    We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.

  8. Finite-size effects for anisotropic 2D Ising model with various boundary conditions

    NASA Astrophysics Data System (ADS)

    Izmailian, N. Sh

    2012-12-01

    We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa)) obtained by Kaufman (1949 Phys. Rev. 76 1232), Wu and Hu (2002 J. Phys. A: Math. Gen. 35 5189) and Kastening (2002 Phys. Rev. E 66 057103)). We express the partition functions in terms of the partition functions Zα, β(J, k) with (α, β) = (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2), J is an interaction coupling and k is an anisotropy parameter. Based on such expressions, we then extend the algorithm of Ivashkevich et al (2002 J. Phys. A: Math. Gen. 35 5543) to derive the exact asymptotic expansion of the logarithm of the partition function for all boundary conditions mentioned above. Our result is f = fbulk + ∑∞p = 0fp(ρ, k)S-p - 1, where f is the free energy of the system, fbulk is the free energy of the bulk, S = MN is the area of the lattice and ρ = M/N is the aspect ratio. All coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio ρeff = ρ/sinh 2Jc and show that for pp and aa boundary conditions all finite size correction terms are invariant under the transformation ρeff → 1/ρeff. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.

  9. Comparison of truncation error of finite-difference and finite-volume formulations of convection terms

    NASA Technical Reports Server (NTRS)

    Leonard, B. P.

    1992-01-01

    Judging by errors in the computational-fluid-dynamics literature in recent years, it is not generally well understood that (above first-order) there are significant differences in spatial truncation error between formulations of convection involving a finite-difference approximation of the first derivative, on the one hand, and a finite-volume model of flux differences across a control-volume cell, on the other. The difference between the two formulations involves a second-order truncation-error term (proportional to the third-derivative of the convected variable). Hence, for example, a third (or higher) order finite-difference approximation for the first-derivative convection term is only second-order accurate when written in conservative control-volume form as a finite-volume formulation, and vice versa.

  10. ZONE - a finite element mesh generator. [2-D, for CDC 7600

    SciTech Connect

    Burger, M.J.

    1980-03-12

    The ZONE computer program is a finite element mesh generator that produces the nodes and element description of any two-dimensional geometry. The geometry is subdivided into a mesh of quadrilateral and triangular zones arranged sequentially in an ordered march through the geometry. The order of march can be chosen so that the minimum bandwidth is obtained. The node points are defined in terms of the x and y coordinates in a global rectangular coordinate system. The zones generated are quadrilaterals or triangles defined by four node points in a counterclockwise sequence. Node points defining the outside boundary are generated for slide lines and to describe pressure boundary conditions. The mesh that is generated can be used as input to any two dimensional as well as any axisymmetrical structure program. The following points are taken up: program concept and characteristics; regions; layers; meridians (offset, circular arc, ellipse); rays; common characterstics - rays and meridians, ZONE input description; output files; examples; and program availability. Also generated is the input to the program PLOT. 15 figures. (RWR)

  11. An energy stable, hexagonal finite difference scheme for the 2D phase field crystal amplitude equations

    NASA Astrophysics Data System (ADS)

    Guan, Zhen; Heinonen, Vili; Lowengrub, John; Wang, Cheng; Wise, Steven M.

    2016-09-01

    In this paper we construct an energy stable finite difference scheme for the amplitude expansion equations for the two-dimensional phase field crystal (PFC) model. The equations are formulated in a periodic hexagonal domain with respect to the reciprocal lattice vectors to achieve a provably unconditionally energy stable and solvable scheme. To our knowledge, this is the first such energy stable scheme for the PFC amplitude equations. The convexity of each part in the amplitude equations is analyzed, in both the semi-discrete and fully-discrete cases. Energy stability is based on a careful convexity analysis for the energy (in both the spatially continuous and discrete cases). As a result, unique solvability and unconditional energy stability are available for the resulting scheme. Moreover, we show that the scheme is point-wise stable for any time and space step sizes. An efficient multigrid solver is devised to solve the scheme, and a few numerical experiments are presented, including grain rotation and shrinkage and grain growth studies, as examples of the strength and robustness of the proposed scheme and solver.

  12. Accurate 2d finite element calculations for hydrogen in magnetic fields of arbitrary strength

    NASA Astrophysics Data System (ADS)

    Schimeczek, C.; Wunner, G.

    2014-02-01

    Recent observations of hundreds of hydrogen-rich magnetic white dwarf stars with magnetic fields up to 105 T (103 MG) have called for more comprehensive and accurate databases for wavelengths and oscillator strengths of the H atom in strong magnetic fields for all states evolving from the field-free levels with principal quantum numbers n≤10. We present a code to calculate the energy eigenvalues and wave functions of such states which is capable of covering the entire regime of field strengths B=0 T to B˜109 T. We achieve this high flexibility by using a two-dimensional finite element expansion of the wave functions in terms of B-splines in the directions parallel and perpendicular to the magnetic field, instead of using asymptotically valid basis expansions in terms of spherical harmonics or Landau orbitals. We have paid special attention to the automation of the program such that the data points for the magnetic field strengths at which the energy of a given state are calculated can be selected automatically. Furthermore, an elaborate method for varying the basis parameters is applied to ensure that the results reach a pre-selected precision, which also can be adjusted freely. Energies and wave functions are stored in a convenient format for further analysis, e.g. for the calculation of transition energies and oscillator strengths. The code has been tested to work for 300 states with an accuracy of better than 10-6 Rydberg across several symmetry subspaces over the entire regime of magnetic field strengths.

  13. User's manual for DYNA2D: an explicit two-dimensional hydrodynamic finite-element code with interactive rezoning

    SciTech Connect

    Hallquist, J.O.

    1982-02-01

    This revised report provides an updated user's manual for DYNA2D, an explicit two-dimensional axisymmetric and plane strain finite element code for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. A contact-impact algorithm permits gaps and sliding along material interfaces. By a specialization of this algorithm, such interfaces can be rigidly tied to admit variable zoning without the need of transition regions. Spatial discretization is achieved by the use of 4-node solid elements, and the equations-of motion are integrated by the central difference method. An interactive rezoner eliminates the need to terminate the calculation when the mesh becomes too distorted. Rather, the mesh can be rezoned and the calculation continued. The command structure for the rezoner is described and illustrated by an example.

  14. 2D simultaneous spatial and temporal focusing multiphoton microscopy for fast volume imaging with improved sectioning ability

    NASA Astrophysics Data System (ADS)

    Song, Qiyuan; Isobe, Keisuke; Hirosawa, Kenichi; Midorikawa, Katsumi; Kannari, Fumihiko

    2015-03-01

    Simultaneous spatial and temporal focusing (SSTF) multiphoton microscopy offers us widefield imaging with sectioning ability. As extending the idea to 2D SSTF, people can utilize a 2D spectral disperser. In this study, we use a 2D spectral disperser via a virtually-imaged phased-array (VIPA) and a diffraction grating to fulfill the back aperture of objective lens with a spectrum matrix. This offers us an axial resolution enhanced by a factor of ~1.7 compared with conventional SSTF microscopy. Furthermore, the small free spectral range (FSR) of VIPA will reduce the temporal self-imaging effect around out-of-focus region and thus will reduce the out-of-focus multiphoton excited fluorescence (MPEF) signal of 2D SSTF microscopy. We experimentally show that inside a sample with dense MPEF, the contrast of the sectioning image is increased in our 2D SSTF microscope compared with SSTF microscope. In our microscope, we use a 1 kHz chirped amplification laser, a piezo stage and a sCMOS camera integrated with 2D SSTF to realize high speed volume imaging at a speed of 50 volumes per second as well as improved sectioning ability. Volume imaging of Brownian motions of fluorescent beads as small as 1μm has been demonstrated. Not only the lateral motion but also the axial motion could be traced.

  15. AC Loss Calculation of REBCO Cables by the Combination of Electric Circuit Model and 2D Finite Element Method

    NASA Astrophysics Data System (ADS)

    Noji, H.

    This study investigates the losses in a two conducting-layer REBCO cable fabricated by researchers at Furukawa Electric Co. Ltd. The losses were calculated using a combination of my electric circuit (EC) model with a two-dimensional finite element method (2D FEM). The helical pitches of the tapes in each layer, P1 and P2, were adjusted to equalize the current in both cable layers, although the loss calculation assumed infinite helical pitches and the same current in each layer at first. The results showed that the losses depended on the relative tape-position angle between the layers (θ/θ'), because the vertical field between adjacent tapes in the same layer varied with θ/θ'. When simulating the real cable, the helical pitches were adjusted and the layer currents were calculated by the EC model. These currents were input to the 2D FEM to compute the losses. The losses changed along the cable length because the difference between P1 and P2 altered the θ/θ' along this direction. The average angle-dependent and position-dependent losses were equal and closely approximated the measured losses. As an example to reduce the loss in this cable, the angle and the helical pitches were fixed at θ/θ' = 0.5 and P1 = P2 = 100 mm (S-direction). The calculation with these conditions indicated that the loss is about one order of magnitude lower than the measurement.

  16. Two-Nucleon Systems in a Finite Volume

    SciTech Connect

    Briceno, Raul

    2014-11-01

    I present the formalism and methodology for determining the nucleon-nucleon scattering parameters from the finite volume spectra obtained from lattice quantum chromodynamics calculations. Using the recently derived energy quantization conditions and the experimentally determined scattering parameters, the bound state spectra for finite volume systems with overlap with the 3S1-3D3 channel are predicted for a range of volumes. It is shown that the extractions of the infinite-volume deuteron binding energy and the low-energy scattering parameters, including the S-D mixing angle, are possible from Lattice QCD calculations of two-nucleon systems with boosts of |P| <= 2pi sqrt{3}/L in volumes with spatial extents L satisfying fm <~ L <~ 14 fm.

  17. Gray-Matter Volume, Midbrain Dopamine D2/D3 Receptors and Drug Craving in Methamphetamine Users

    PubMed Central

    Morales, Angelica A.; Kohno, Milky; Robertson, Chelsea L.; Dean, Andy C.; Mandelkern, Mark A.; London, Edythe D.

    2015-01-01

    Dysfunction of the mesocorticolimbic system plays a critical role in clinical features of addiction. Despite evidence suggesting that midbrain dopamine receptors influence amphetamine-induced dopamine release and that dopamine is involved in methamphetamine-induced neurotoxicity, associations between dopamine receptors and gray-matter volume have been unexplored in methamphetamine users. Here we used magnetic resonance imaging and [18F]fallypride positron emission tomography, respectively, to measure gray-matter volume (in 58 methamphetamine users) and dopamine D2/D3 receptor availability (binding potential relative to nondisplaceable uptake of the radiotracer, BPnd) (in 31 methamphetamine users and 37 control participants). Relationships between these measures and self-reported drug craving were examined. Although no difference in midbrain D2/D3 BPnd was detected between methamphetamine and control groups, midbrain D2/D3 BPnd was positively correlated with gray-matter volume in the striatum, prefrontal cortex, insula, hippocampus and temporal cortex in methamphetamine users, but not in control participants (group-by-midbrain D2/D3 BPnd interaction, p<0.05 corrected for multiple comparisons). Craving for methamphetamine was negatively associated with gray-matter volume in the insula, prefrontal cortex, amygdala, temporal cortex, occipital cortex, cerebellum, and thalamus (p<0.05 corrected for multiple comparisons). A relationship between midbrain D2/D3 BPnd and methamphetamine craving was not detected. Lower midbrain D2/D3 BPnd may increase vulnerability to deficits in gray-matter volume in mesocorticolimbic circuitry in methamphetamine users, possibly reflecting greater dopamine-induced toxicity. Identifying factors that influence prefrontal and limbic volume, such as midbrain BPnd, may be important for understanding the basis of drug craving, a key factor in the maintenance of substance use disorders. PMID:25896164

  18. Quantum electrodynamics in finite volume and nonrelativistic effective field theories

    NASA Astrophysics Data System (ADS)

    Fodor, Z.; Hoelbling, C.; Katz, S. D.; Lellouch, L.; Portelli, A.; Szabo, K. K.; Toth, B. C.

    2016-04-01

    Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.

  19. PDE-based geophysical modelling using finite elements: examples from 3D resistivity and 2D magnetotellurics

    NASA Astrophysics Data System (ADS)

    Schaa, R.; Gross, L.; du Plessis, J.

    2016-04-01

    We present a general finite-element solver, escript, tailored to solve geophysical forward and inverse modeling problems in terms of partial differential equations (PDEs) with suitable boundary conditions. Escript’s abstract interface allows geoscientists to focus on solving the actual problem without being experts in numerical modeling. General-purpose finite element solvers have found wide use especially in engineering fields and find increasing application in the geophysical disciplines as these offer a single interface to tackle different geophysical problems. These solvers are useful for data interpretation and for research, but can also be a useful tool in educational settings. This paper serves as an introduction into PDE-based modeling with escript where we demonstrate in detail how escript is used to solve two different forward modeling problems from applied geophysics (3D DC resistivity and 2D magnetotellurics). Based on these two different cases, other geophysical modeling work can easily be realized. The escript package is implemented as a Python library and allows the solution of coupled, linear or non-linear, time-dependent PDEs. Parallel execution for both shared and distributed memory architectures is supported and can be used without modifications to the scripts.

  20. Finite volume effects for nucleon and heavy meson masses

    SciTech Connect

    Colangelo, Gilberto; Fuhrer, Andreas; Lanz, Stefan

    2010-08-01

    We apply the resummed version of the Luescher formula to analyze finite volume corrections to the mass of the nucleon and of heavy mesons. We show that by applying the subthreshold expansion of the scattering amplitudes one can express the finite volume corrections in terms of only a few physical observables and the size of the box. In the case of the nucleon, the available information about the quark mass dependence of these physical quantities is discussed and used to assess the finite volume corrections to the nucleon mass as a function of the quark mass including a detailed analysis of the remaining uncertainties. For heavy mesons, the Luescher formula is derived both fully relativistically and in a nonrelativistic approximation and a first attempt at a numerical analysis is made.

  1. Spectral (Finite) Volume Method for One Dimensional Euler Equations

    NASA Technical Reports Server (NTRS)

    Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

    2002-01-01

    Consider a mesh of unstructured triangular cells. Each cell is called a Spectral Volume (SV), denoted by Si, which is further partitioned into subcells named Control Volumes (CVs), indicated by C(sub i,j). To represent the solution as a polynomial of degree m in two dimensions (2D) we need N = (m+1)(m+2)/2 pieces of independent information, or degrees of freedom (DOFs). The DOFs in a SV method are the volume-averaged mean variables at the N CVs. For example, to build a quadratic reconstruction in 2D, we need at least (2+1)(3+1)/2 = 6 DOFs. There are numerous ways of partitioning a SV, and not every partition is admissible in the sense that the partition may not be capable of producing a degree m polynomial. Once N mean solutions in the CVs of a SV are given, a unique polynomial reconstruction can be obtained.

  2. Finite-volume goal-oriented mesh adaptation for aerodynamics using functional derivative with respect to nodal coordinates

    NASA Astrophysics Data System (ADS)

    Todarello, Giovanni; Vonck, Floris; Bourasseau, Sébastien; Peter, Jacques; Désidéri, Jean-Antoine

    2016-05-01

    A new goal-oriented mesh adaptation method for finite volume/finite difference schemes is extended from the structured mesh framework to a more suitable setting for adaptation of unstructured meshes. The method is based on the total derivative of the goal with respect to volume mesh nodes that is computable after the solution of the goal discrete adjoint equation. The asymptotic behaviour of this derivative is assessed on regularly refined unstructured meshes. A local refinement criterion is derived from the requirement of limiting the first order change in the goal that an admissible node displacement may cause. Mesh adaptations are then carried out for classical test cases of 2D Euler flows. Efficiency and local density of the adapted meshes are presented. They are compared with those obtained with a more classical mesh adaptation method in the framework of finite volume/finite difference schemes [46]. Results are very close although the present method only makes usage of the current grid.

  3. Topological phases for bound states moving in a finite volume

    SciTech Connect

    Bour, Shahin; Koenig, Sebastian; Hammer, H.-W.; Lee, Dean; Meissner, Ulf-G.

    2011-11-01

    We show that bound states moving in a finite periodic volume have an energy correction which is topological in origin and universal in character. The topological volume corrections contain information about the number and mass of the constituents of the bound states. These results have broad applications to lattice calculations involving nucleons, nuclei, hadronic molecules, and cold atoms. We illustrate and verify the analytical results with several numerical lattice calculations.

  4. Modeling of composite piezoelectric structures with the finite volume method.

    PubMed

    Bolborici, Valentin; Dawson, Francis P; Pugh, Mary C

    2012-01-01

    Piezoelectric devices, such as piezoelectric traveling- wave rotary ultrasonic motors, have composite piezoelectric structures. A composite piezoelectric structure consists of a combination of two or more bonded materials, at least one of which is a piezoelectric transducer. Piezoelectric structures have mainly been numerically modeled using the finite element method. An alternative approach based on the finite volume method offers the following advantages: 1) the ordinary differential equations resulting from the discretization process can be interpreted directly as corresponding circuits; and 2) phenomena occurring at boundaries can be treated exactly. This paper presents a method for implementing the boundary conditions between the bonded materials in composite piezoelectric structures modeled with the finite volume method. The paper concludes with a modeling example of a unimorph structure. PMID:22293746

  5. a Finite Nucleon Extended Volume Model for Nuclear Matter

    NASA Astrophysics Data System (ADS)

    Rocha, Alberto S. S.; Vasconcellos, César A. Z.; Coelho, Helio T.

    We investigate the effects of a finite volume extension for nucleons immersed in nuclear matter. We wish in this way to explore the role played by this non-vanishing (but fixed) volume in shaping nuclear matter properties, in contrast with other models of nuclear physics in which nucleons are treated as point-like particles. We introduce a model characterized by an exclusion volume à la Van der Waals, as well as an effective non-relativistic approximation to model meson-exchange interactions between nucleons. The model is consistent with experimental values of saturation density and binding energy of nuclear matter in the domain of typical densities for neutron stars.

  6. Development of a hip joint model for finite volume simulations.

    PubMed

    Cardiff, P; Karač, A; FitzPatrick, D; Ivanković, A

    2014-01-01

    This paper establishes a procedure for numerical analysis of a hip joint using the finite volume method. Patient-specific hip joint geometry is segmented directly from computed tomography and magnetic resonance imaging datasets and the resulting bone surfaces are processed into a form suitable for volume meshing. A high resolution continuum tetrahedral mesh has been generated, where a sandwich model approach is adopted; the bones are represented as a stiffer cortical shells surrounding more flexible cancellous cores. Cartilage is included as a uniform thickness extruded layer and the effect of layer thickness is investigated. To realistically position the bones, gait analysis has been performed giving the 3D positions of the bones for the full gait cycle. Three phases of the gait cycle are examined using a finite volume based custom structural contact solver implemented in open-source software OpenFOAM. PMID:24141555

  7. Simulations of P-SV wave scattering due to cracks by the 2-D finite difference method

    NASA Astrophysics Data System (ADS)

    Suzuki, Yuji; Shiina, Takahiro; Kawahara, Jun; Okamoto, Taro; Miyashita, Kaoru

    2013-12-01

    We simulate P-SV wave scattering by 2-D parallel cracks using the finite difference method (FDM). Here, special emphasis is put on simplicity; we apply a standard FDM (second-order velocity-stress scheme with a staggered grid) to media including traction-free, infinitesimally thin cracks, which are expressed in a simple manner. As an accuracy test of the present method, we calculate the displacement discontinuity along an isolated crack caused by harmonic waves using the method, which is compared with the corresponding results based on a reliable boundary integral equation method. The test resultantly indicates that the present method yields sufficient accuracy. As an application of this method, we also simulate wave propagation in media with randomly distributed cracks. We experimentally determine the attenuation and velocity dispersion induced by scattering from the synthetic seismograms, using a waveform averaging technique. It is shown that the results are well explained by a theory based on the Foldy approximation, if the crack density is sufficiently low. The theory appears valid with a crack density up to at least 0.1 for SV wave incidence, whereas the validity limit appears lower for P wave incidence.

  8. LOCA hydroloads calculations with multidimensional nonlinear fluid/structure interaction. Volume 2: STEALTH 2D/WHAMSE 2D single-phse fluid and elastic structure studies. Final report. [PWR

    SciTech Connect

    Chang, F.H.; Santee, G.E. Jr.; Mortensen, G.A.; Brockett, G.F.; Gross, M.B.; Silling, S.A.; Belytschko, T.

    1981-03-01

    This report, the second in a series of reports for RP-1065, describes the second step in the stepwise approach for developing the three-dimensional, nonlinear, fluid/structure interaction methodology to assess the hydroloads on a large PWR during the subcooled portions of a hypothetical LOCA. The second step in the methodology considers enhancements and special modifications to the 2D STEALTH-HYDRO computer program and the 2D WHAMSE computer program. The 2D STEALTH-HYDRO enhancements consist of a fluid-fluid coupling control-volume model and an orifice control-volume model. The enhancements to 2D WHAMSE include elimination of the implicit integration routines, material models, and structural elements not required for the hydroloads application. In addition the logic for coupling the 2D STEALTH-HYDRO computer program to the 2D WHAMSE computer program is discussed.

  9. Finite volume and finite element methods applied to 3D laminar and turbulent channel flows

    SciTech Connect

    Louda, Petr; Příhoda, Jaromír; Sváček, Petr; Kozel, Karel

    2014-12-10

    The work deals with numerical simulations of incompressible flow in channels with rectangular cross section. The rectangular cross section itself leads to development of various secondary flow patterns, where accuracy of simulation is influenced by numerical viscosity of the scheme and by turbulence modeling. In this work some developments of stabilized finite element method are presented. Its results are compared with those of an implicit finite volume method also described, in laminar and turbulent flows. It is shown that numerical viscosity can cause errors of same magnitude as different turbulence models. The finite volume method is also applied to 3D turbulent flow around backward facing step and good agreement with 3D experimental results is obtained.

  10. The finite element method: Is weighted volume integration essential?

    NASA Astrophysics Data System (ADS)

    Narasimhan, T. N.

    In developing finite element equations for steady state and transient diffusion-type processes, weighted volume integration is generally assumed to be an intrinsic requirement. It is shown that such finite element equations can be developed directly and with ease on the basis of the elementary notion of a surface integral. Although weighted volume integration is mathematically correct, the algebraic equations stemming from it are no more informative than those derived directly on the basis of a surface integral. An interesting upshot is that the derivation based on surface integration does not require knowledge of a partial differential equation but yet is logically rigorous. It is commonly stated that weighted volume integration of the differential equation helps one carry out analyses of errors, convergence and existence, and therefore, weighted volume integration is preferable. It is suggested that because the direct derivation is logically consistent, numerical solutions emanating from it must be testable for accuracy and internal consistency in ways that the style of which may differ from the classical procedures of error- and convergence-analysis. In addition to simplifying the teaching of the finite element method, the thoughts presented in this paper may lead to establishing the finite element method independently in its own right, rather than it being a surrogate of the differential equation. The purpose of this paper is not to espouse any one particular way of formulating the finite element equations. Rather, it is one of introspection. The desire is to critically examine our traditional way of doing things and inquire whether alternate approaches may reveal to us new and interesting insights.

  11. Effective finite-difference modelling methods with 2D acoustic wave equation using a combination of cross and rhombus stencils

    NASA Astrophysics Data System (ADS)

    Wang, Enjiang; Liu, Yang; Sen, Mrinal K.

    2016-07-01

    The 2D acoustic wave equation is commonly solved numerically by finite-difference (FD) methods in which the accuracy of solution is significantly affected by the FD stencils. The commonly used cross stencil can reach either only second-order accuracy for space domain dispersion-relation-based FD method or (2 M)th-order accuracy along eight specific propagation directions for time-space domain dispersion-relation-based FD method, if the conventional (2 M)th-order spatial FD and second-order temporal FD are used to discretize the equation. One other newly developed rhombus stencil can reach arbitrary even-order accuracy. However, this stencil adds significantly computational cost when the operator length is large. To achieve a balance between the solution accuracy and efficiency, we develop a new FD stencil to solve the 2D acoustic wave equation. This stencil is a combination of the cross stencil and rhombus stencil. A cross stencil with an operator length parameter M is used to approximate the spatial partial derivatives while a rhombus stencil with an operator length parameter N together with the conventional 2nd-order temporal FD is employed in approximating the temporal partial derivatives. Using this stencil, a new FD scheme is developed; we demonstrate that this scheme can reach (2 M)th-order accuracy in space and (2 N)th-order accuracy in time when spatial FD coefficients and temporal FD coefficients are derived from respective dispersion relation using Taylor-series expansion (TE) method. To further increase the accuracy, we derive the FD coefficients by employing the time-space domain dispersion relation of this FD scheme using TE. We also use least-squares (LS) optimization method to reduce dispersion at high wavenumbers. Dispersion analysis, stability analysis and modelling examples demonstrate that our new scheme has greater accuracy and better stability than conventional FD schemes, and thus can adopt large time steps. To reduce the extra computational

  12. Register cardiac fiber orientations from 3D DTI volume to 2D ultrasound image of rat hearts

    NASA Astrophysics Data System (ADS)

    Qin, Xulei; Wang, Silun; Shen, Ming; Zhang, Xiaodong; Lerakis, Stamatios; Wagner, Mary B.; Fei, Baowei

    2015-03-01

    Two-dimensional (2D) ultrasound or echocardiography is one of the most widely used examinations for the diagnosis of cardiac diseases. However, it only supplies the geometric and structural information of the myocardium. In order to supply more detailed microstructure information of the myocardium, this paper proposes a registration method to map cardiac fiber orientations from three-dimensional (3D) magnetic resonance diffusion tensor imaging (MR-DTI) volume to the 2D ultrasound image. It utilizes a 2D/3D intensity based registration procedure including rigid, log-demons, and affine transformations to search the best similar slice from the template volume. After registration, the cardiac fiber orientations are mapped to the 2D ultrasound image via fiber relocations and reorientations. This method was validated by six images of rat hearts ex vivo. The evaluation results indicated that the final Dice similarity coefficient (DSC) achieved more than 90% after geometric registrations; and the inclination angle errors (IAE) between the mapped fiber orientations and the gold standards were less than 15 degree. This method may provide a practical tool for cardiologists to examine cardiac fiber orientations on ultrasound images and have the potential to supply additional information for diagnosis of cardiac diseases.

  13. Finite volume solution of the compressible boundary-layer equations

    NASA Technical Reports Server (NTRS)

    Loyd, B.; Murman, E. M.

    1986-01-01

    A box-type finite volume discretization is applied to the integral form of the compressible boundary layer equations. Boundary layer scaling is introduced through the grid construction: streamwise grid lines follow eta = y/h = const., where y is the normal coordinate and h(x) is a scale factor proportional to the boundary layer thickness. With this grid, similarity can be applied explicity to calculate initial conditions. The finite volume method preserves the physical transparency of the integral equations in the discrete approximation. The resulting scheme is accurate, efficient, and conceptually simple. Computations for similar and non-similar flows show excellent agreement with tabulated results, solutions computed with Keller's Box scheme, and experimental data.

  14. A nonlocal finite difference scheme for simulation of wave propagation in 2D models with reduced numerical dispersion

    NASA Astrophysics Data System (ADS)

    Martowicz, A.; Ruzzene, M.; Staszewski, W. J.; Rimoli, J. J.; Uhl, T.

    2014-03-01

    The work deals with the reduction of numerical dispersion in simulations of wave propagation in solids. The phenomenon of numerical dispersion naturally results from time and spatial discretization present in a numerical model of mechanical continuum. Although discretization itself makes possible to model wave propagation in structures with complicated geometries and made of different materials, it inevitably causes simulation errors when improper time and length scales are chosen for the simulations domains. Therefore, by definition, any characteristic parameter for spatial and time resolution must create limitations on maximal wavenumber and frequency for a numerical model. It should be however noted that expected increase of the model quality and its functionality in terms of affordable wavenumbers, frequencies and speeds should not be achieved merely by denser mesh and reduced time integration step. The computational cost would be simply unacceptable. The authors present a nonlocal finite difference scheme with the coefficients calculated applying a Fourier series, which allows for considerable reduction of numerical dispersion. There are presented the results of analyses for 2D models, with isotropic and anisotropic materials, fulfilling the planar stress state. Reduced numerical dispersion is shown in the dispersion surfaces for longitudinal and shear waves propagating for different directions with respect to the mesh orientation and without dramatic increase of required number of nonlocal interactions. A case with the propagation of longitudinal wave in composite material is studied with given referential solution of the initial value problem for verification of the time-domain outcomes. The work gives a perspective of modeling of any type of real material dispersion according to measurements and with assumed accuracy.

  15. Numerical Modeling of Six Historical Transoceanic Tsunami Events Using a Robust Finite Volume Method on GPUs

    NASA Astrophysics Data System (ADS)

    Jalali Farahani, R.; Li, S.; Mohammed, F.; Astill, S.; Williams, C. R.; Lee, R.; Wilson, P. S.; Srinvias, B.

    2014-12-01

    Six transoceanic historical tsunami events including Japan Tohoku tsunami (2011), Chile Maule tsunami (2010), Indian Ocean tsunami (2004), Japan Nankai tsunami (1946), Chile Valdivia tsunami (1960), and Alaska tsunami (1964) have been modeled using a 2D well-balanced shallow water numerical model. The model solves the nonlinear 2D shallow water equations using an upwind finite volume method and is shown in this study to be capable of modeling the tsunami waves and resulting inundations over complex topography and bathymetry. The finite volume method is capable of modeling the wetting and drying of the bed surface at the coastline with no numerical instabilities and the inundation is modeled by allowing the computational cells to dynamically change from dry to wet. The numerical model implements parallel computations on Graphics Processing Units (GPUs), which enables the model to implement detailed modeling of inundation of small-scale coastal regions in a short simulation time. The slip distribution and seismic moment of the six earthquake driven tsunami events are introduced to the model as the initial condition including coastal uplift and subsidence. Both local regions and far-field regions affected by these tsunami waves are numerically studied and the resulting run-up and tsunami inundations are compared with the recorded observation data provided by National Oceanic and Atmospheric Administration (NOAA) including coastal tide gauges and eyewitness observation data. The GPU-based finite volume model indicates accuracy and robustness as well as short simulation time that can be used for transoceanic tsunami waves modeling including real-time numerical modeling of tsunami events and their inland inundations.

  16. Finite-volume cumulant expansion in QCD-colorless plasma

    NASA Astrophysics Data System (ADS)

    Ladrem, M.; Ahmed, M. A. A.; Alfull, Z. Z.; Cherif, S.

    2015-09-01

    Due to the finite-size effects, the localization of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite-volume transition point T0(V) of the QCD deconfinement phase transition to a colorless QGP, we have developed a new approach using the finite-size cumulant expansion of the order parameter and the L_{mn}-method. The first six cumulants C_{1,2,3,4,5,6} with the corresponding under-normalized ratios (skewness Σ kurtosis κ , pentosis \\varPi _{± }, and hexosis {H}_{1,2,3}) and three unnormalized combinations of them, ({O}={{σ }2 {κ } }{{Σ }^{-1} }, {U} ={{σ }^{-2} {Σ }^{-1} }, {N} = {σ }2 {κ }) are calculated and studied as functions of ( T, V). A new approach, unifying in a clear and consistent way the definitions of cumulant ratios, is proposed. A numerical FSS analysis of the obtained results has allowed us to locate accurately the finite-volume transition point. The extracted transition temperature value T0(V) agrees with that expected T0N(V) from the order parameter and the thermal susceptibility χ T( T,V) , according to the standard procedure of localization to within about 2 %. In addition to this, a very good correlation factor is obtained proving the validity of our cumulants method. The agreement of our results with those obtained by means of other models is remarkable.

  17. A Coupled Finite-Volume Model for 2-D Surface and 3-D Subsurface Flows

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Surface-subsurface interactions are an intrinsic component of the hydrologic response within a watershed; therefore, hydrologic modeling tools should consider these interactions to provide reliable predictions, especially during rainfall-runoff processes. This paper presents a fully implicit coupled...

  18. Edge gradients evaluation for 2D hybrid finite volume method model

    Technology Transfer Automated Retrieval System (TEKTRAN)

    In this study, a two-dimensional depth-integrated hydrodynamic model was developed using FVM on a hybrid unstructured collocated mesh system. To alleviate the negative effects of mesh irregularity and non-uniformity, a conservative evaluation method for edge gradients based on the second-order Tayl...

  19. Stimulating rupture surfaces in a finite rock volume

    NASA Astrophysics Data System (ADS)

    Krüger, O. S.; Shapiro, S. A.; Dinske, C.

    2012-12-01

    Pore fluids in rocks and pore pressure perturbations can trigger earthquakes. Sometimes fluid injections into boreholes are able to induce potentially damaging seismic events. For instance, this was the case by stimulations at such Enhanced Geothermal Systems like the ones at Basel, in Cooper Basin, at The Geysers field and at Soultz. Fluid-induced microearthquakes in hydrocarbon or geothermal reservoirs, aftershocks of tectonic earthquakes or seismic emission in rock samples are examples of seismicity resulting from a seismogenic activation of finite volumes of rocks. Such a finiteness can influence frequency-magnitude statistics of the seismicity. Previously we have observed that fluid-induced large-magnitude events at geothermal and hydrocarbon reservoirs are frequently underrepresented in comparison with the Gutenberg-Richter statistics. This is an indication that the events are much more probable on rupture surfaces contained nearly completely within the stimulated volume. Here we theoretically analyse the influence of the finiteness of a perturbed volume on the frequency-magnitude statistics of induced events. Our analysis is a phenomenological one. It is possibly applicable to different types of the seismicity triggering like a triggering by pore-pressure perturbations or a triggering by rate-and-state processes. We approximate a stimulated volume by an ellipsoid or cuboid, and derive the magnitude statistics of induced events from the statistics of randomly orientated thin flat discs of different sizes, representing the rupture surfaces. We consider different possible scenarios of event triggering: rupture surfaces located completely within the stimulated volume and rupture surfaces which are intersecting with the stimulated volume. We derive lower and upper bounds of the probability to induce a given-magnitude event. The bounds depend on the characteristic scales of the stimulated volume. The minimum principal axis is the most influential geometric

  20. In vivo liver tracking with a high volume rate 4D ultrasound scanner and a 2D matrix array probe

    NASA Astrophysics Data System (ADS)

    Lediju Bell, Muyinatu A.; Byram, Brett C.; Harris, Emma J.; Evans, Philip M.; Bamber, Jeffrey C.

    2012-03-01

    The effectiveness of intensity-modulated radiation therapy (IMRT) is compromised by involuntary motion (e.g. respiration, cardiac activity). The feasibility of processing ultrasound echo data to automatically estimate 3D liver motion for real-time IMRT guidance was previously demonstrated, but performance was limited by an acquisition speed of 2 volumes per second due to hardware restrictions of a mechanical linear array probe. Utilizing a 2D matrix array probe with parallel receive beamforming offered increased acquisition speeds and an opportunity to investigate the benefits of higher volume rates. In vivo livers of three volunteers were scanned with and without respiratory motion at volume rates of 24 and 48 Hz, respectively. Respiration was suspended via voluntary breath hold. Correlation-based, phase-sensitive 3D speckle tracking was applied to consecutively acquired volumes of echo data. Volumes were omitted at fixed intervals and 3D speckle tracking was re-applied to study the effect of lower scan rates. Results revealed periodic motion that corresponded with the heart rate or breathing cycle in the absence or presence of respiration, respectively. For cardiac-induced motion, volume rates for adequate tracking ranged from 8 to 12 Hz and was limited by frequency discrepancies between tracking estimates from higher and lower frequency scan rates. Thus, the scan rate of volume data acquired without respiration was limited by the need to sample the frequency induced by the beating heart. In respiratory-dominated motion, volume rate limits ranged from 4 to 12 Hz, interpretable from the root-mean-squared deviation (RMSD) from tracking estimates at 24 Hz. While higher volume rates yielded RMSD values less than 1 mm in most cases, lower volume rates yielded RMSD values of 2-6 mm.

  1. Comparison of 3-D finite element model of ashlar masonry with 2-D numerical models of ashlar masonry

    NASA Astrophysics Data System (ADS)

    Beran, Pavel

    2016-06-01

    3-D state of stress in heterogeneous ashlar masonry can be also computed by several suitable chosen 2-D numerical models of ashlar masonry. The results obtained from 2-D numerical models well correspond to the results obtained from 3-D numerical model. The character of thermal stress is the same. While using 2-D models the computational time is reduced more than hundredfold and therefore this method could be used for computation of thermal stresses during long time periods with 10 000 of steps.

  2. High resolution finite volume scheme for the quantum hydrodynamic equations

    NASA Astrophysics Data System (ADS)

    Lin, Chin-Tien; Yeh, Jia-Yi; Chen, Jiun-Yeu

    2009-03-01

    The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10 -5 to 10 -12. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10 -4. To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were

  3. Location constraint based 2D-3D registration of fluoroscopic images and CT volumes for image-guided EP procedures

    NASA Astrophysics Data System (ADS)

    Liao, Rui; Xu, Ning; Sun, Yiyong

    2008-03-01

    Presentation of detailed anatomical structures via 3D Computed Tomographic (CT) volumes helps visualization and navigation in electrophysiology procedures (EP). Registration of the CT volume with the online fluoroscopy however is a challenging task for EP applications due to the lack of discernable features in fluoroscopic images. In this paper, we propose to use the coronary sinus (CS) catheter in bi-plane fluoroscopic images and the coronary sinus in the CT volume as a location constraint to accomplish 2D-3D registration. Two automatic registration algorithms are proposed in this study, and their performances are investigated on both simulated and real data. It is shown that compared to registration using mono-plane fluoroscopy, registration using bi-plane images results in substantially higher accuracy in 3D and enhanced robustness. In addition, compared to registering the projection of CS to the 2D CS catheter, it is more desirable to reconstruct a 3D CS catheter from the bi-plane fluoroscopy and then perform a 3D-3D registration between the CS and the reconstructed CS catheter. Quantitative validation based on simulation and visual inspection on real data demonstrates the feasibility of the proposed workflow in EP procedures.

  4. Gradient ROtating Outer Volume Excitation (GROOVE): A Novel Method for Single-Shot 2-D OVS

    PubMed Central

    Powell, Nathaniel J.; Jang, Albert; Park, Jang-Yeon; Valette, Julien; Garwood, Michael; Marjańska, Małgorzata

    2014-01-01

    Purpose A new outer volume suppression (OVS) technique is introduced that uses a single pulse and rotating gradients to accomplish frequency-swept excitation. This new technique, which is called Gradient ROtating Outer Volume Excitation (GROOVE), produces a circular or elliptical suppression band rather than suppressing the entire outer volume. Methods Theoretical and k-space descriptions of GROOVE are provided. The properties of GROOVE were investigated with simulations, phantom, and human experiments performed using a 4 T horizontal bore magnet equipped with a TEM coil. Results Similar suppression performance was obtained in phantom and human brain using GROOVE with circular and elliptical shapes. Simulations indicate that GROOVE requires less SAR and time than traditional OVS schemes, but traditional schemes provide a sharper transition zone and less residual signal. Conclusion GROOVE represents a new way of performing OVS in which spins are excited temporally in space on a trajectory which can be tailored to fit the shape of the suppression region. In addition, GROOVE is capable of suppressing tailored regions of space with more flexibility and in a shorter period of time than conventional methods. GROOVE provides a fast, low SAR alternative to conventional OVS methods in some applications (e.g., scalp suppression). PMID:24478130

  5. Compact finite volume methods for the diffusion equation

    NASA Technical Reports Server (NTRS)

    Rose, Milton E.

    1989-01-01

    The paper describes an approach to treating initial-boundary-value problems by finite volume methods in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second-order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and ADI methods.

  6. Compact finite volume methods for the diffusion equation

    NASA Technical Reports Server (NTRS)

    Rose, Milton E.

    1989-01-01

    An approach to treating initial-boundary value problems by finite volume methods is described, in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and alternating direction implicit (ADI) methods. The treatment of general curvilinear coordinates is shown to result from a specialization of these general results.

  7. Users manual for AUTOMESH-2D: A program of automatic mesh generation for two-dimensional scattering analysis by the finite element method

    NASA Technical Reports Server (NTRS)

    Hua, Chongyu; Volakis, John L.

    1990-01-01

    AUTOMESH-2D is a computer program specifically designed as a preprocessor for the scattering analysis of two dimensional bodies by the finite element method. This program was developed due to a need for reproducing the effort required to define and check the geometry data, element topology, and material properties. There are six modules in the program: (1) Parameter Specification; (2) Data Input; (3) Node Generation; (4) Element Generation; (5) Mesh Smoothing; and (5) Data File Generation.

  8. Full-vectorial finite element method based eigenvalue algorithm for the analysis of 2D photonic crystals with arbitrary 3D anisotropy.

    PubMed

    Hsu, Sen-Ming; Chang, Hung-Chun

    2007-11-26

    A full-vectorial finite element method based eigenvalue algorithm is developed to analyze the band structures of two-dimensional (2D) photonic crystals (PCs) with arbitray 3D anisotropy for in-planewave propagations, in which the simple transverse-electric (TE) or transverse-magnetic (TM) modes may not be clearly defined. By taking all the field components into consideration simultaneously without decoupling of the wave modes in 2D PCs into TE and TM modes, a full-vectorial matrix eigenvalue equation, with the square of the wavenumber as the eigenvalue, is derived. We examine the convergence behaviors of this algorithm and analyze 2D PCs with arbitrary anisotropy using this algorithm to demonstrate its correctness and usefulness by explaining the numerical results theoretically. PMID:19550864

  9. A mixed finite element/finite volume approach for solving biodegradation transport in groundwater

    NASA Astrophysics Data System (ADS)

    Gallo, Claudio; Manzini, Gianmarco

    1998-03-01

    A numerical model for the simulation of flow and transport of organic compounds undergoing bacterial oxygen- and nitrate-based respiration is presented. General assumptions regarding microbial population, bacteria metabolism and effects of oxygen, nitrogen and nutrient concentration on organic substrate rate of consumption are briefly described. The numerical solution techniques for solving both the flow and the transport are presented. The saturated flow equation is discretized using a high-order mixed finite element scheme, which provides a highly accurate estimation of the velocity field. The transport equation for a sorbing porous medium is approximated using a finite volume scheme enclosing an upwind TVD shock-capturing technique for capturing concentration-unsteady steep fronts. The performance and capabilities of the present approach in a bio-remediation context are assessed by considering a set of test problems. The reliability of the numerical results concerning solution accuracy and the computational efficiency in terms of cost and memory requirements are also estimated.

  10. Multichannel 1 → 2 transition amplitudes in a finite volume

    SciTech Connect

    Briceno, Raul A.; Hansen, Maxwell T.; Walker-Loud, Andre

    2015-02-03

    We perform a model-independent, non-perturbative investigation of two-point and three-point finite-volume correlation functions in the energy regime where two-particle states can go on-shell. We study three-point functions involving a single incoming particle and an outgoing two-particle state, relevant, for example, for studies of meson decays (e.g., B⁰ → K*l⁺l⁻) or meson photo production (e.g., πγ* → ππ). We observe that, while the spectrum solely depends upon the on-shell scattering amplitude, the correlation functions also depend upon off-shell amplitudes. The main result of this work is a non-perturbative generalization of the Lellouch-Luscher formula relating matrix elements of currents in finite and infinite spatial volumes. We extend that work by considering a theory with multiple, strongly-coupled channels and by accommodating external currents which inject arbitrary four-momentum as well as arbitrary angular-momentum. The result is exact up to exponentially suppressed corrections governed by the pion mass times the box size. We also apply our master equation to various examples, including two processes mentioned above as well as examples where the final state is an admixture of two open channels.

  11. A finite volume method for fluctuating hydrodynamics of simple fluids

    NASA Astrophysics Data System (ADS)

    Narayanan, Kiran; Samtaney, Ravi; Moran, Brian

    2015-11-01

    Fluctuating hydrodynamics accounts for stochastic effects that arise at mesoscopic and macroscopic scales. We present a finite volume method for numerical solutions of the fluctuating compressible Navier Stokes equations. Case studies for simple fluids are demonstrated via the use of two different equations of state (EOS) : a perfect gas EOS, and a Lennard-Jones EOS for liquid argon developed by Johnson et al. (Mol. Phys. 1993). We extend the fourth order conservative finite volume scheme originally developed by McCorquodale and Colella (Comm. in App. Math. & Comput. Sci. 2011), to evaluate the deterministic and stochastic fluxes. The expressions for the cell-centered discretizations of the stochastic shear stress and stochastic heat flux are adopted from Espanol, P (Physica A. 1998), where the discretizations were shown to satisfy the fluctuation-dissipation theorem. A third order Runge-Kutta scheme with weights proposed by Delong et al. (Phy. Rev. E. 2013) is used for the numerical time integration. Accuracy of the proposed scheme will be demonstrated. Comparisons of the numerical solution against theory for a perfect gas as well as liquid argon will be presented. Regularizations of the stochastic fluxes in the limit of zero mesh sizes will be discussed. Supported by KAUST Baseline Research Funds.

  12. Recent Developments in DAO's Finite-Volume Data Assimilation System

    NASA Technical Reports Server (NTRS)

    daSilva, Arlindo; Lin, S.-J.; Joiner, J.; Dee, D.; Frank, D.; Norris, P.; Poli, P.; Atlas, Robert (Technical Monitor)

    2001-01-01

    The Physical-space/Finite-volume Data Assimilation System (fvDAS) is the next generation global atmospheric data assimilation system in development at the Data Assimilation Office at NASA's Goddard Space Flight Center. It is based on a new finite-volume general circulation model jointly developed by NASA and NCAR and on the Physical-Space Statistical Analysis System (PSAS) developed at the DAO. The data assimilation method implemented in CODAS incorporates a simplified version of the model bias estimation and correction algorithm, as described by Dee and da Silva (1998). In this talk we will briefly describe the general system formulation, and focus on the impact of 3 data types recently introduced, namely: 1) cloud tracks winds from the Multi-angle Imaging Spectrometer by the US Air Force, and 3) temperature and moisture information derived from GPS refractivity occultation measurements. The impact of these data types on observation-minus-6hr forecast (O-F) statistics, as well as 5-day forecast skills will be discussed. In addition we will assess the impact of cloud assimilation on top of the atmosphere radiation fields estimated from CERES measurements.

  13. Finite Volume Numerical Methods for Aeroheating Rate Calculations from Infrared Thermographic Data

    NASA Technical Reports Server (NTRS)

    Daryabeigi, Kamran; Berry, Scott A.; Horvath, Thomas J.; Nowak, Robert J.

    2006-01-01

    The use of multi-dimensional finite volume heat conduction techniques for calculating aeroheating rates from measured global surface temperatures on hypersonic wind tunnel models was investigated. Both direct and inverse finite volume techniques were investigated and compared with the standard one-dimensional semi-infinite technique. Global transient surface temperatures were measured using an infrared thermographic technique on a 0.333-scale model of the Hyper-X forebody in the NASA Langley Research Center 20-Inch Mach 6 Air tunnel. In these tests the effectiveness of vortices generated via gas injection for initiating hypersonic transition on the Hyper-X forebody was investigated. An array of streamwise-orientated heating striations was generated and visualized downstream of the gas injection sites. In regions without significant spatial temperature gradients, one-dimensional techniques provided accurate aeroheating rates. In regions with sharp temperature gradients caused by striation patterns multi-dimensional heat transfer techniques were necessary to obtain more accurate heating rates. The use of the one-dimensional technique resulted in differences of 20% in the calculated heating rates compared to 2-D analysis because it did not account for lateral heat conduction in the model.

  14. A new spectral finite volume method for elastic wave modelling on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Zhang, Wensheng; Zhuang, Yuan; Chung, Eric T.

    2016-07-01

    In this paper, we consider a new spectral finite volume method (FVM) for the elastic wave equations. Our new FVM is based on a piecewise constant approximation on a fine mesh and a high-order polynomial reconstruction on a coarser mesh. Our new method is constructed based on two existing techniques, the high-order FVM and the spectral FVM. In fact, we will construct a new method to take advantage of both methods. More precisely, our method has two distinctive features. The first one is that the local polynomial reconstructions are performed on the coarse triangles and the reconstruction matrices for all the coarse triangles are the same. This fact enhances the parallelization of our algorithm. We will present a parallel implementation of our method and show excellent efficiency results. The second one is that, by using a suitable number of finer triangles with a coarse triangle, we obtain an overdetermined reconstruction system, which can enhance the robustness of the reconstruction process. To derive our scheme, standard finite volume technique is applied to each fine triangle, and the high-order reconstructed polynomials, computed on coarse triangles, are used to compute numerical fluxes. We will present numerical results to show the performance of our method. Our method is presented for 2-D problems, but the same methodology can be applied to 3-D.

  15. A Piecewise Linear Discontinuous Finite Element Spatial Discretization of the Transport Equation in 2D Cylindrical Geometry

    SciTech Connect

    Bailey, T S; Adams, M L; Chang, J H

    2008-10-01

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.

  16. Finite volume model for two-dimensional shallow environmental flow

    USGS Publications Warehouse

    Simoes, F.J.M.

    2011-01-01

    This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

  17. Vector coding the finite volume procedure for the CYBER 205

    NASA Astrophysics Data System (ADS)

    Rizzi, A.

    The architecture of supercomputers and fundamental principles of vector programming in FORTRAN are reviewed, and vector coding and execution of the finite volume procedure on the CYBER 205 are described. With the proper structure given to the data base each coordinate direction can be differenced throughout the entire grid in one vector operation. Boundary conditions must be interleaved, which inhibits the concurrency of the overall scheme. No data motion together with inner-loop vectorization is advocated. The computed example of transonic flow separating from the sharp leading edge of a delta wing demonstrates the performance of the procedure. Vectors over 20,000 elements long are obtained, and a rate of over 50 megaflops sustained over the entire computation indicates the high degree of vectorization achieved.

  18. An ADER-WENO Finite Volume AMR code for Astrophysics

    NASA Astrophysics Data System (ADS)

    Zanotti, O.; Dumbser, M.; Hidalgo, A.; Balsara, D.

    2014-09-01

    A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions is presented. A high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method, while a high order spatial accuracy is obtained through a WENO reconstruction. Thanks to the one-step nature of the underlying scheme, the resulting algorithm can be efficiently imported within an AMR framework on space-time adaptive meshes. We provide convincing evidence that the presented high order AMR scheme behaves better than traditional second order AMR methods. Tests are shown of the new scheme for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations and the equations of ideal magnetohydrodynamics. The proposed scheme is likely to become a useful tool in several astrophysical scenarios.

  19. SU(N) multi-Skyrmions at finite volume

    NASA Astrophysics Data System (ADS)

    Canfora, Fabrizio; Di Mauro, Marco; Kurkov, Maxim A.; Naddeo, Adele

    2015-09-01

    We study multi-soliton solutions of the four-dimensional SU(N) Skyrme model by combining the hedgehog ansatz for SU(N) based on the harmonic maps of S2 into CP^{N-1} and a geometrical trick which allows to analyze explicitly finite-volume effects without breaking the relevant symmetries of the ansatz. The geometric set-up allows to introduce a parameter which is related to the 't Hooft coupling of a suitable large N limit, in which N→ ∞ and the curvature of the background metric approaches zero, in such a way that their product is constant. The relevance of such a parameter to the physics of the system is pointed out. In particular, we discuss how the discrete symmetries of the configurations depend on it.

  20. Methods for Solving Gas Damping Problems in Perforated Microstructures Using a 2D Finite-Element Solver

    PubMed Central

    Veijola, Timo; Råback, Peter

    2007-01-01

    We present a straightforward method to solve gas damping problems for perforated structures in two dimensions (2D) utilising a Perforation Profile Reynolds (PPR) solver. The PPR equation is an extended Reynolds equation that includes additional terms modelling the leakage flow through the perforations, and variable diffusivity and compressibility profiles. The solution method consists of two phases: 1) determination of the specific admittance profile and relative diffusivity (and relative compressibility) profiles due to the perforation, and 2) solution of the PPR equation with a FEM solver in 2D. Rarefied gas corrections in the slip-flow region are also included. Analytic profiles for circular and square holes with slip conditions are presented in the paper. To verify the method, square perforated dampers with 16–64 holes were simulated with a three-dimensional (3D) Navier-Stokes solver, a homogenised extended Reynolds solver, and a 2D PPR solver. Cases for both translational (in normal to the surfaces) and torsional motion were simulated. The presented method extends the region of accurate simulation of perforated structures to cases where the homogenisation method is inaccurate and the full 3D Navier-Stokes simulation is too time-consuming.

  1. Richards Equation Solver; Rectangular Finite Volume Flux Updating Solution.

    2002-01-18

    Version: 00 POLYRES solves the transient, two-dimensional, Richards equation for water flow in unsaturated-saturated soils. The package is specifically designed to allow the user to easily model complex polygon-shaped regions. Flux, head, and unit gradient boundary conditions can be used. Spatial variation of the hydraulic properties can be defined across individual polygon-shaped subdomains, called objects. These objects combine to form a polygon-shaped model domain. Each object can have its own distribution of hydraulic parameters. Themore » resulting model domain and polygon-shaped internal objects are mapped onto a rectangular, finite-volume, computational grid by a preprocessor. This allows the user to specify model geometry independently of the underlying grid and greatly simplifies user input for complex geometries. In addition, this approach significantly reduces the computational requirements since complex geometries are actually modeled on a rectangular grid. This results in well-structured, finite difference-like systems of equations that require minimal storage and are very efficient to solve.« less

  2. A finite volume method for numerical grid generation

    NASA Astrophysics Data System (ADS)

    Beale, S. B.

    1999-07-01

    A novel method to generate body-fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables , and is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re-zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid-correction procedure. The scalar variables are re-mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet-Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local-boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point-by-point and whole-field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright

  3. Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

    NASA Technical Reports Server (NTRS)

    Gnoffo, Peter A.

    2006-01-01

    Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

  4. Splitting based finite volume schemes for ideal MHD equations

    NASA Astrophysics Data System (ADS)

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

    2009-02-01

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

  5. Efficient quadrature-free high-order spectral volume method on unstructured grids: Theory and 2D implementation

    SciTech Connect

    Harris, R.; Wang, Z.; Liu, Y.

    2007-11-19

    An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. For SV interfaces, a quadrature-free approach is compared with the Gauss quadrature approach to further evaluate the accuracy and efficiency. A simplified treatment of curved boundaries is also presented that avoids the need to store a separate reconstruction for each boundary cell. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and non-linear advection equations, and the Euler equations. Several well known inviscid flow test cases are utilized to show the effectiveness of the simplified curved boundary representation.

  6. Efficient quadrature-free high-order spectral volume method on unstructured grids: Theory and 2D implementation

    NASA Astrophysics Data System (ADS)

    Harris, Rob; Wang, Z. J.; Liu, Yen

    2008-01-01

    An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. For SV interfaces, a quadrature-free approach is compared with the Gauss quadrature approach to further evaluate the accuracy and efficiency. A simplified treatment of curved boundaries is also presented that avoids the need to store a separate reconstruction for each boundary cell. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and non-linear advection equations, and the Euler equations. Several well known inviscid flow test cases are utilized to show the effectiveness of the simplified curved boundary representation.

  7. Electromagnetic characterization of an MR volume coil with multilayered cylindrical load using a 2-D analytical approach

    NASA Astrophysics Data System (ADS)

    Tiberi, Gianluigi; Costagli, Mauro; Stara, Riccardo; Cosottini, Mirco; Tropp, James; Tosetti, Michela

    2013-05-01

    We present an analytical method for the analysis of Radio Frequency (RF) volume coils for Magnetic Resonance Imaging (MRI), using a 2-D full wave solution with loading by multilayered cylinders. This allows the characterization of radio-frequency E, H, B1, B1+ fields. Comparisons are provided with experimental data obtained at 7.0 T. The procedure permits us to clearly separate the solution to single line source problem (which we call the primordial solution) and the composite solution (i.e. full coil, i.e. the summations of primordial solutions according to the resonator drive configuration). The capability of separating the primordial solution and the composite one is fundamental for a thorough analysis of the phenomena of dielectric resonance, and of standing wave and multi-source interference. We show that dielectric resonance can be identified only by looking at the electromagnetic field from a single line source.

  8. Electromagnetic characterization of an MR volume coil with multilayered cylindrical load using a 2-D analytical approach.

    PubMed

    Tiberi, Gianluigi; Costagli, Mauro; Stara, Riccardo; Cosottini, Mirco; Tropp, James; Tosetti, Michela

    2013-05-01

    We present an analytical method for the analysis of Radio Frequency (RF) volume coils for Magnetic Resonance Imaging (MRI), using a 2-D full wave solution with loading by multilayered cylinders. This allows the characterization of radio-frequency E, H, B1, B1(+) fields. Comparisons are provided with experimental data obtained at 7.0 T. The procedure permits us to clearly separate the solution to single line source problem (which we call the primordial solution) and the composite solution (i.e. full coil, i.e. the summations of primordial solutions according to the resonator drive configuration). The capability of separating the primordial solution and the composite one is fundamental for a thorough analysis of the phenomena of dielectric resonance, and of standing wave and multi-source interference. We show that dielectric resonance can be identified only by looking at the electromagnetic field from a single line source. PMID:23548562

  9. Tunable 3D and 2D polystyrene nanoparticle assemblies using surface wettability, low volume fraction and surfactant effects

    NASA Astrophysics Data System (ADS)

    Pillai, S.; Hemmersam, A. G.; Mukhopadhyay, R.; Meyer, R. L.; Moghimi, S. M.; Besenbacher, F.; Kingshott, P.

    2009-01-01

    Polymer-based nanopatterning on metal surfaces is of increasing importance to a number of applications, including biosensors, bioelectronic devices and medical implants. Here we show that polycrystalline gold surfaces can be functionalized with monocomponent nanoparticle (NP) assemblies by a simple drop deposition method. Ordered 3D hexagonal close-packed structures consisting of 350 nm polystyrene (PS) NPs on hydrophobically modified gold surfaces from solutions of very low volume fraction (phiv = 0.0006) were obtained as a result of capillary force induced self-assembly, whilst 2D self-assembly of PS NPs was generated over large area on hydrophilic gold and TiO2 surfaces by spin coating. Furthermore, we show that when Triton X-100 is added to the PS NP suspending medium longer range ordering is obtained. Our observations may initiate interesting applications in the areas of nanoengineering of metal-based sensors and as a means to design new nanostructures for biocompatible implant surfaces.

  10. Finite Element Method for Analysis of Band Structures of 2D Phononic Crystals with Archimedean-like tilings

    NASA Astrophysics Data System (ADS)

    Li, Jianbao; Wang, Yue-Sheng; Zhang, Chuanzeng

    2010-05-01

    In this paper, a finite element method based on the ABAQUS code and user subroutine is presented to evaluate the propagation of acoustic waves in the two-dimensional phononic crystals with Archimedean-like tilings. Two systems composed of cylinder scatters embedded in a host in Ladybug and Bathroom lattices are considered. Complete and accurate band structures and transmission spectra are obtained to identify the band gaps and eigenmodes. We found that Archimedean-like structures can have some advantages over the traditional square lattice regarding the completeness of the gap and its position and width. Also, due to the same square primitive unit cell and the first Brillouin zone, the two square-like lattices have similar acoustic response in lower bands. The results indicate that the finite element method is precise for the band structure computation of the complex phononic crystals with Archimedean tilings.

  11. Meshing Preprocessor for the Mesoscopic 3D Finite Element Simulation of 2D and Interlock Fabric Deformation

    NASA Astrophysics Data System (ADS)

    Wendling, A.; Daniel, J. L.; Hivet, G.; Vidal-Sallé, E.; Boisse, P.

    2015-12-01

    Numerical simulation is a powerful tool to predict the mechanical behavior and the feasibility of composite parts. Among the available numerical approaches, as far as woven reinforced composites are concerned, 3D finite element simulation at the mesoscopic scale leads to a good compromise between realism and complexity. At this scale, the fibrous reinforcement is modeled by an interlacement of yarns assumed to be homogeneous that have to be accurately represented. Among the numerous issues induced by these simulations, the first one consists in providing a representative meshed geometrical model of the unit cell at the mesoscopic scale. The second one consists in enabling a fast data input in the finite element software (contacts definition, boundary conditions, elements reorientation, etc.) so as to obtain results within reasonable time. Based on parameterized 3D CAD modeling tool of unit-cells of dry fabrics already developed, this paper presents an efficient strategy which permits an automated meshing of the models with 3D hexahedral elements and to accelerate of several orders of magnitude the simulation data input. Finally, the overall modeling strategy is illustrated by examples of finite element simulation of the mechanical behavior of fabrics.

  12. Solution of the 2-D steady-state radiative transfer equation in participating media with specular reflections using SUPG and DG finite elements

    NASA Astrophysics Data System (ADS)

    Le Hardy, D.; Favennec, Y.; Rousseau, B.

    2016-08-01

    The 2D radiative transfer equation coupled with specular reflection boundary conditions is solved using finite element schemes. Both Discontinuous Galerkin and Streamline-Upwind Petrov-Galerkin variational formulations are fully developed. These two schemes are validated step-by-step for all involved operators (transport, scattering, reflection) using analytical formulations. Numerical comparisons of the two schemes, in terms of convergence rate, reveal that the quadratic SUPG scheme proves efficient for solving such problems. This comparison constitutes the main issue of the paper. Moreover, the solution process is accelerated using block SOR-type iterative methods, for which the determination of the optimal parameter is found in a very cheap way.

  13. Coupled 2D-3D finite element method for analysis of a skin panel with a discontinuous stiffener

    NASA Technical Reports Server (NTRS)

    Wang, J. T.; Lotts, C. G.; Davis, D. D., Jr.; Krishnamurthy, T.

    1992-01-01

    This paper describes a computationally efficient analysis method which was used to predict detailed stress states in a typical composite compression panel with a discontinuous hat stiffener. A global-local approach was used. The global model incorporated both 2D shell and 3D brick elements connected by newly developed transition elements. Most of the panel was modeled with 2D elements, while 3D elements were employed to model the stiffener flange and the adjacent skin. Both linear and geometrically nonlinear analyses were performed on the global model. The effect of geometric nonlinearity induced by the eccentric load path due to the discontinuous hat stiffener was significant. The local model used a fine mesh of 3D brick elements to model the region at the end of the stiffener. Boundary conditions of the local 3D model were obtained by spline interpolation of the nodal displacements from the global analysis. Detailed in-plane and through-the-thickness stresses were calculated in the flange-skin interface near the end of the stiffener.

  14. A Vertically Lagrangian Finite-Volume Dynamical Core for Global Models

    NASA Technical Reports Server (NTRS)

    Lin, Shian-Jiann

    2003-01-01

    A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.

  15. Development of an upwind, finite-volume code with finite-rate chemistry

    NASA Technical Reports Server (NTRS)

    Molvik, Gregory A.

    1994-01-01

    Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques, and a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical, and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data.

  16. An Analysis of Finite-Difference and Finite-Volume Formulations of Convervation Laws

    NASA Astrophysics Data System (ADS)

    Vinokur, Marcel

    1989-03-01

    Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations-potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

  17. An analysis of finite-difference and finite-volume formulations of conservation laws

    NASA Astrophysics Data System (ADS)

    Vinokur, Marcel

    1986-06-01

    Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

  18. An analysis of finite-difference and finite-volume formulations of conservation laws

    NASA Technical Reports Server (NTRS)

    Vinokur, Marcel

    1986-01-01

    Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

  19. An analysis of finite-difference and finite-volume formulations of conservation laws

    NASA Technical Reports Server (NTRS)

    Vinokur, Marcel

    1989-01-01

    Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

  20. Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

    NASA Astrophysics Data System (ADS)

    Xia, Yidong; Wang, Chuanjin; Luo, Hong; Christon, Mark; Bakosi, Jozsef

    2016-02-01

    Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in the simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, some form of solution verification has been attempted to identify sensitivities in the solution methods, and suggest best practices when using the Hydra-TH code.

  1. Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

    SciTech Connect

    Xia, Yidong; Wang, Chuanjin; Luo, Hong; Christon, Mark; Bakosi, Jozsef

    2015-12-15

    Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in the simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.

  2. Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

    DOE PAGESBeta

    Xia, Yidong; Wang, Chuanjin; Luo, Hong; Christon, Mark; Bakosi, Jozsef

    2015-12-15

    Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.« less

  3. Hybrid finite volume/ finite element method for radiative heat transfer in graded index media

    NASA Astrophysics Data System (ADS)

    Zhang, L.; Zhao, J. M.; Liu, L. H.; Wang, S. Y.

    2012-09-01

    The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89-101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.

  4. 3-D dynamic rupture simulations by a finite volume method

    NASA Astrophysics Data System (ADS)

    Benjemaa, M.; Glinsky-Olivier, N.; Cruz-Atienza, V. M.; Virieux, J.

    2009-07-01

    Dynamic rupture of a 3-D spontaneous crack of arbitrary shape is investigated using a finite volume (FV) approach. The full domain is decomposed in tetrahedra whereas the surface, on which the rupture takes place, is discretized with triangles that are faces of tetrahedra. First of all, the elastodynamic equations are described into a pseudo-conservative form for an easy application of the FV discretization. Explicit boundary conditions are given using criteria based on the conservation of discrete energy through the crack surface. Using a stress-threshold criterion, these conditions specify fluxes through those triangles that have suffered rupture. On these broken surfaces, stress follows a linear slip-weakening law, although other friction laws can be implemented. For The Problem Version 3 of the dynamic-rupture code verification exercise conducted by the SCEC/USGS, numerical solutions on a planar fault exhibit a very high convergence rate and are in good agreement with the reference one provided by a finite difference (FD) technique. For a non-planar fault of parabolic shape, numerical solutions agree satisfactorily well with those obtained with a semi-analytical boundary integral method in terms of shear stress amplitudes, stopping phases arrival times and stress overshoots. Differences between solutions are attributed to the low-order interpolation of the FV approach, whose results are particularly sensitive to the mesh regularity (structured/unstructured). We expect this method, which is well adapted for multiprocessor parallel computing, to be competitive with others for solving large scale dynamic ruptures scenarios of seismic sources in the near future.

  5. Coupled circuit based representation of piezoelectric structures modeled using the finite volume method.

    PubMed

    Bolborici, V; Dawson, F P

    2016-03-01

    This paper presents the methodology of generating a corresponding electrical circuit for a simple piezoelectric plate modeled with the finite volume method. The corresponding circuit is implemented using a circuit simulation software and the simulation results are compared to the finite volume modeling results for validation. It is noticed that both, the finite volume model and its corresponding circuit, generate identical results. The results of a corresponding circuit based on the finite volume model are also compared to the results of a corresponding circuit based on a simplified analytical model for a long piezoelectric plate, and to finite element simulation results for the same plate. It is observed that, for one control volume, the finite volume model corresponding circuit and the simplified analytical model corresponding circuit generate close results. It is also noticed that the results of the two corresponding circuits are different from the best approximation results obtained with high resolution finite element simulations due to the approximations made in the simplified analytical model and the fact that only one finite volume was used in the finite volume model. The implementation of the circuit can be automated for higher order systems by a program that takes as an input the matrix of the system and the forcing function vector, and returns a net list for the circuit. PMID:26639999

  6. Stress analysis of a rectangular implant in laminated composites using 2-D and 3-D finite elements

    NASA Technical Reports Server (NTRS)

    Chow, Wai T.; Graves, Michael J.

    1992-01-01

    An analysis method using the FEM based on the Hellinger-Reissner variation principle has been developed to determine the 3-D stresses and displacements near a rectangular implant inside a laminated composite material. Three-dimensional elements are employed in regions where the interlaminar stress is considered to be significant; 2-D elements are used in other areas. Uniaxially loaded graphite-epoxy laminates have been analyzed; the implant was modeled as four plies of 3501/6 epoxy located in the middle of the laminate. It is shown that the interlaminar stresses are an order of magnitude lower than the stress representing the applied far-field load. The stress concentration factors of both the interlaminar and in-plane stresses depend on the stacking sequence of the laminate.

  7. Comparison of 2D Finite Element Modeling Assumptions with Results From 3D Analysis for Composite Skin-Stiffener Debonding

    NASA Technical Reports Server (NTRS)

    Krueger, Ronald; Paris, Isbelle L.; OBrien, T. Kevin; Minguet, Pierre J.

    2004-01-01

    The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane-strain elements as well as three different generalized plane strain type approaches were performed. The computed skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with delamination length. For more accurate predictions, however, a three-dimensional analysis is required.

  8. Studying fast wave propagation and absorption at any cyclotron harmonic using a 2D finite element area coordinates wave equation solver

    SciTech Connect

    Lerche, Ernesto; Van Eester, Dirk

    2011-12-23

    Fourier analysis in the poloidal direction is a standard ingredient in present-day 2D wave equation solvers describing radio frequency waves in hot tokamak plasmas. Although a powerful and elegant technique, Fourier analysis has the disadvantage that a large number of modes is needed to describe the field pattern on a magnetic surface if a short wavelength mode exists on any - even very small - subpart of the particle trajectory. The present paper examines the potential of a method that does not suffer from this drawback: a finite element technique relying on simple linear or cubic area base functions that are defined on irregular elementary surfaces of triangular shape. The wave equation is solved in its weak Galerkin variational form and for realistic 2D tokamak geometry, accounting for the toroidal curvature but assuming the toroidal angle is ignorable, allowing to study the wave pattern for each of the independent toroidal modes excited by the antenna individually.The locally uniform full hot plasma dielectric tensor to all orders in finite Larmor radius was adopted. As the main intended application is the study of fast wave behavior (heating and current drive) at arbitrary harmonics, the wave vector complex amplitude appearing in the dielectric tensor is determined through a local dispersion root evaluation. High frequency fast wave propagation and damping is provided as an illustration in view of possible application of this type of current drive in future high density reactor-like tokamaks.

  9. A 2D finite element study on the role of material properties on eddy current losses in soft magnetic composites

    NASA Astrophysics Data System (ADS)

    Ren, Xiaotao; Corcolle, Romain; Daniel, Laurent

    2016-02-01

    The use of soft magnetic composites (SMCs) in electrical engineering applications is growing. SMCs provide an effective alternative to laminated steels because they exhibit a high permeability with low eddy current losses. Losses are a critical feature in the design of electrical machines, and it is necessary to evaluate the role of microstructure and constitutive properties of SMCs during the predesign stage. In this paper we propose a simplified finite element approach to compute eddy current losses in these materials. The computations allow to quantify the role of exciting source and material properties on eddy current losses. This analysis can later be used in the development of homogenization models for SMC. Contribution to the topical issue "Numelec 2015 - Elected submissions", edited by Adel Razek

  10. Finite-volume WENO scheme for viscous compressible multicomponent flows.

    PubMed

    Coralic, Vedran; Colonius, Tim

    2014-10-01

    We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin. PMID:25110358

  11. Finite volume methods for submarine debris flows and generated waves

    NASA Astrophysics Data System (ADS)

    Kim, Jihwan; Løvholt, Finn; Issler, Dieter

    2016-04-01

    Submarine landslides can impose great danger to the underwater structures and generate destructive tsunamis. Submarine debris flows often behave like visco-plastic materials, and the Herschel-Bulkley rheological model is known to be appropriate for describing the motion. In this work, we develop numerical schemes for the visco-plastic debris flows using finite volume methods in Eulerian coordinates with two horizontal dimensions. We provide parameter sensitivity analysis and demonstrate how common ad-hoc assumptions such as including a minimum shear layer depth influence the modeling of the landslide dynamics. Hydrodynamic resistance forces, hydroplaning, and remolding are all crucial terms for underwater landslides, and are hence added into the numerical formulation. The landslide deformation is coupled to the water column and simulated in the Clawpack framework. For the propagation of the tsunamis, the shallow water equations and the Boussinesq-type equations are employed to observe how important the wave dispersion is. Finally, two cases in central Norway, i.e. the subaerial quick clay landslide at Byneset in 2012, and the submerged tsunamigenic Statland landslide in 2014, are both presented for validation. The research leading to these results has received funding from the Research Council of Norway under grant number 231252 (Project TsunamiLand) and the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement 603839 (Project ASTARTE).

  12. Climate Simulations with an Isentropic Finite Volume Dynamical Core

    SciTech Connect

    Chen, Chih-Chieh; Rasch, Philip J.

    2012-04-15

    This paper discusses the impact of changing the vertical coordinate from a hybrid pressure to a hybrid-isentropic coordinate within the finite volume dynamical core of the Community Atmosphere Model (CAM). Results from a 20-year climate simulation using the new model coordinate configuration are compared to control simulations produced by the Eulerian spectral and FV dynamical cores of CAM which both use a pressure-based ({sigma}-p) coordinate. The same physical parameterization package is employed in all three dynamical cores. The isentropic modeling framework significantly alters the simulated climatology and has several desirable features. The revised model produces a better representation of heat transport processes in the atmosphere leading to much improved atmospheric temperatures. We show that the isentropic model is very effective in reducing the long standing cold temperature bias in the upper troposphere and lower stratosphere, a deficiency shared among most climate models. The warmer upper troposphere and stratosphere seen in the isentropic model reduces the global coverage of high clouds which is in better agreement with observations. The isentropic model also shows improvements in the simulated wintertime mean sea-level pressure field in the northern hemisphere.

  13. Finite-volume WENO scheme for viscous compressible multicomponent flows

    PubMed Central

    Coralic, Vedran; Colonius, Tim

    2014-01-01

    We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin. PMID:25110358

  14. Finite volume simulation for convective heat transfer in wavy channels

    NASA Astrophysics Data System (ADS)

    Aslan, Erman; Taymaz, Imdat; Islamoglu, Yasar

    2016-03-01

    The convective heat transfer characteristics for a periodic wavy channel have been investigated experimentally and numerically. Finite volume method was used in numerical study. Experiment results are used for validation the numerical results. Studies were conducted for air flow conditions where contact angle is 30°, and uniform heat flux 616 W/m2 is applied as the thermal boundary conditions. Reynolds number ( Re) is varied from 2000 to 11,000 and Prandtl number ( Pr) is taken 0.7. Nusselt number ( Nu), Colburn factor ( j), friction factor ( f) and goodness factor ( j/ f) against Reynolds number have been studied. The effects of the wave geometry and minimum channel height have been discussed. Thus, the best performance of flow and heat transfer characterization was determined through wavy channels. Additionally, it was determined that the computed values of convective heat transfer coefficients are in good correlation with experimental results for the converging diverging channel. Therefore, numerical results can be used for these channel geometries instead of experimental results.

  15. Finite volume effects in the chiral extrapolation of baryon masses

    NASA Astrophysics Data System (ADS)

    Lutz, M. F. M.; Bavontaweepanya, R.; Kobdaj, C.; Schwarz, K.

    2014-09-01

    We perform an analysis of the QCD lattice data on the baryon octet and decuplet masses based on the relativistic chiral Lagrangian. The baryon self-energies are computed in a finite volume at next-to-next-to-next-to-leading order (N3LO), where the dependence on the physical meson and baryon masses is kept. The number of free parameters is reduced significantly down to 12 by relying on large-Nc sum rules. Altogether we describe accurately more than 220 data points from six different lattice groups, BMW, PACS-CS, HSC, LHPC, QCDSF-UKQCD and NPLQCD. Values for all counterterms relevant at N3LO are predicted. In particular we extract a pion-nucleon sigma term of 39-1+2 MeV and a strangeness sigma term of the nucleon of σsN=84-4+28 MeV. The flavor SU(3) chiral limit of the baryon octet and decuplet masses is determined with (802±4) and (1103±6) MeV. Detailed predictions for the baryon masses as currently evaluated by the ETM lattice QCD group are made.

  16. Tsunami modelling with adaptively refined finite volume methods

    USGS Publications Warehouse

    LeVeque, R.J.; George, D.L.; Berger, M.J.

    2011-01-01

    Numerical modelling of transoceanic tsunami propagation, together with the detailed modelling of inundation of small-scale coastal regions, poses a number of algorithmic challenges. The depth-averaged shallow water equations can be used to reduce this to a time-dependent problem in two space dimensions, but even so it is crucial to use adaptive mesh refinement in order to efficiently handle the vast differences in spatial scales. This must be done in a 'wellbalanced' manner that accurately captures very small perturbations to the steady state of the ocean at rest. Inundation can be modelled by allowing cells to dynamically change from dry to wet, but this must also be done carefully near refinement boundaries. We discuss these issues in the context of Riemann-solver-based finite volume methods for tsunami modelling. Several examples are presented using the GeoClaw software, and sample codes are available to accompany the paper. The techniques discussed also apply to a variety of other geophysical flows. ?? 2011 Cambridge University Press.

  17. Anterior Cingulate Cortex Gray Matter Volume Mediates an Association between 2D:4D Ratio and Trait Aggression in Women but not Men

    PubMed Central

    Gorka, Adam X.; Norman, Rachel E.; Radtke, Spenser R.; Carré, Justin M.; Hariri, Ahmad R.

    2015-01-01

    Previous research demonstrates that prenatal testosterone exposure increases aggression, possibly through its effects on the structure and function of neural circuits supporting threat detection and emotion regulation. Here we examined associations between regional gray matter volume, trait aggression, and the ratio of the second and fourth digit of the hand (2D:4D ratio) as a putative index of prenatal testosterone exposure in 464 healthy young adult volunteers. Our analyses revealed a significant positive correlation between 2D:4D ratio and gray matter volume of the dorsal anterior cingulate cortex (dACC), a brain region supporting, emotion regulation, conflict monitoring, and behavioral inhibition. Subsequent analyses demonstrated that reduced (i.e., masculinized) gray matter volume in the dACC mediated the relationship between 2D:4D ratio and aggression in women, but not men. Expanding on this gender-specific mediation, additional analyses demonstrated that the shared variance between 2D:4D ratio, dACC gray matter volume, and aggression in women reflected the tendency to engage in cognitive reappraisal of emotionally provocative stimuli. Our results provide novel evidence that 2D:4D ratio is associated with masculinization of dACC gray matter volume, and that this neural phenotype mediates, in part, the expression of trait aggression in women. PMID:25827959

  18. Local finite element enrichment strategies for 2D contact computations and a corresponding post-processing scheme

    NASA Astrophysics Data System (ADS)

    Sauer, Roger A.

    2013-08-01

    Recently an enriched contact finite element formulation has been developed that substantially increases the accuracy of contact computations while keeping the additional numerical effort at a minimum reported by Sauer (Int J Numer Meth Eng, 87: 593-616, 2011). Two enrich-ment strategies were proposed, one based on local p-refinement using Lagrange interpolation and one based on Hermite interpolation that produces C 1-smoothness on the contact surface. Both classes, which were initially considered for the frictionless Signorini problem, are extended here to friction and contact between deformable bodies. For this, a symmetric contact formulation is used that allows the unbiased treatment of both contact partners. This paper also proposes a post-processing scheme for contact quantities like the contact pressure. The scheme, which provides a more accurate representation than the raw data, is based on an averaging procedure that is inspired by mortar formulations. The properties of the enrichment strategies and the corresponding post-processing scheme are illustrated by several numerical examples considering sliding and peeling contact in the presence of large deformations.

  19. Finite volume corrections to the two-particle decay of states with nonzero momentum

    SciTech Connect

    Christ, Norman H.; Kim, Changhoan; Yamazaki, Takeshi

    2005-12-01

    We study the effects of finite volume on the two-particle decay rate of an unstable state with nonzero momentum. First, Luescher's field-theoretic relation between the infinite-volume scattering phase shifts and the quantized energy levels of a finite-volume, two-particle system is generalized to the case of nonzero total momentum, confirming earlier results of Rummukainen and Gottlieb. We then use this result and the method of Lellouch and Luescher to determine the corrections needed for a finite-volume calculation of a two-particle decay amplitude when the decaying particle has nonvanishing center-of-mass momentum.

  20. Development of an upwind, finite-volume code with finite-rate chemistry

    NASA Technical Reports Server (NTRS)

    Molvik, Gregory A.

    1995-01-01

    Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques and of a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data. This report summarizes the research that took place from August 1,1994 to January 1, 1995.

  1. An implicit finite volume nodal point scheme for the solution of two-dimensional compressible Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Dutta, Vimala

    1993-07-01

    An implicit finite volume nodal point scheme has been developed for solving the two-dimensional compressible Navier-Stokes equations. The numerical scheme is evolved by efficiently combining the basic ideas of the implicit finite-difference scheme of Beam and Warming (1978) with those of nodal point schemes due to Hall (1985) and Ni (1982). The 2-D Navier-Stokes solver is implemented for steady, laminar/turbulent flows past airfoils by using C-type grids. Turbulence closure is achieved by employing the algebraic eddy-viscosity model of Baldwin and Lomax (1978). Results are presented for the NACA-0012 and RAE-2822 airfoil sections. Comparison of the aerodynamic coefficients with experimental results for the different test cases presented here establishes the validity and efficiency of the method.

  2. Coupled 2-dimensional cascade theory for noise an d unsteady aerodynamics of blade row interaction in turbofans. Volume 2: Documentation for computer code CUP2D

    NASA Technical Reports Server (NTRS)

    Hanson, Donald B.

    1994-01-01

    A two dimensional linear aeroacoustic theory for rotor/stator interaction with unsteady coupling was derived and explored in Volume 1 of this report. Computer program CUP2D has been written in FORTRAN embodying the theoretical equations. This volume (Volume 2) describes the structure of the code, installation and running, preparation of the input file, and interpretation of the output. A sample case is provided with printouts of the input and output. The source code is included with comments linking it closely to the theoretical equations in Volume 1.

  3. 2D wavelet-analysis-based calibration technique for flat-panel imaging detectors: application in cone beam volume CT

    NASA Astrophysics Data System (ADS)

    Tang, Xiangyang; Ning, Ruola; Yu, Rongfeng; Conover, David L.

    1999-05-01

    The application of the newly developed flat panel x-ray imaging detector in cone beam volume CT has attracted increasing interest recently. Due to an imperfect solid state array manufacturing process, however, defective elements, gain non-uniformity and offset image unavoidably exist in all kinds of flat panel x-ray imaging detectors, which will cause severe streak and ring artifacts in a cone beam reconstruction image and severely degrade image quality. A calibration technique, in which the artifacts resulting from the defective elements, gain non-uniformity and offset image can be reduced significantly, is presented in this paper. The detection of defective elements is distinctively based upon two-dimensional (2D) wavelet analysis. Because of its inherent localizability in recognizing singularities or discontinuities, wavelet analysis possesses the capability of detecting defective elements over a rather large x-ray exposure range, e.g., 20% to approximately 60% of the dynamic range of the detector used. Three-dimensional (3D) images of a low-contrast CT phantom have been reconstructed from projection images acquired by a flat panel x-ray imaging detector with and without calibration process applied. The artifacts caused individually by defective elements, gain non-uniformity and offset image have been separated and investigated in detail, and the correlation with each other have also been exposed explicitly. The investigation is enforced by quantitative analysis of the signal to noise ratio (SNR) and the image uniformity of the cone beam reconstruction image. It has been demonstrated that the ring and streak artifacts resulting from the imperfect performance of a flat panel x-ray imaging detector can be reduced dramatically, and then the image qualities of a cone beam reconstruction image, such as contrast resolution and image uniformity are improved significantly. Furthermore, with little modification, the calibration technique presented here is also applicable

  4. Finite Volume Based Computer Program for Ground Source Heat Pump System

    SciTech Connect

    Menart, James A.

    2013-02-22

    This report is a compilation of the work that has been done on the grant DE-EE0002805 entitled ?Finite Volume Based Computer Program for Ground Source Heat Pump Systems.? The goal of this project was to develop a detailed computer simulation tool for GSHP (ground source heat pump) heating and cooling systems. Two such tools were developed as part of this DOE (Department of Energy) grant; the first is a two-dimensional computer program called GEO2D and the second is a three-dimensional computer program called GEO3D. Both of these simulation tools provide an extensive array of results to the user. A unique aspect of both these simulation tools is the complete temperature profile information calculated and presented. Complete temperature profiles throughout the ground, casing, tube wall, and fluid are provided as a function of time. The fluid temperatures from and to the heat pump, as a function of time, are also provided. In addition to temperature information, detailed heat rate information at several locations as a function of time is determined. Heat rates between the heat pump and the building indoor environment, between the working fluid and the heat pump, and between the working fluid and the ground are computed. The heat rates between the ground and the working fluid are calculated as a function time and position along the ground loop. The heating and cooling loads of the building being fitted with a GSHP are determined with the computer program developed by DOE called ENERGYPLUS. Lastly COP (coefficient of performance) results as a function of time are provided. Both the two-dimensional and three-dimensional computer programs developed as part of this work are based upon a detailed finite volume solution of the energy equation for the ground and ground loop. Real heat pump characteristics are entered into the program and used to model the heat pump performance. Thus these computer tools simulate the coupled performance of the ground loop and the heat pump

  5. Recovery Act: Finite Volume Based Computer Program for Ground Source Heat Pump Systems

    SciTech Connect

    James A Menart, Professor

    2013-02-22

    This report is a compilation of the work that has been done on the grant DE-EE0002805 entitled Finite Volume Based Computer Program for Ground Source Heat Pump Systems. The goal of this project was to develop a detailed computer simulation tool for GSHP (ground source heat pump) heating and cooling systems. Two such tools were developed as part of this DOE (Department of Energy) grant; the first is a two-dimensional computer program called GEO2D and the second is a three-dimensional computer program called GEO3D. Both of these simulation tools provide an extensive array of results to the user. A unique aspect of both these simulation tools is the complete temperature profile information calculated and presented. Complete temperature profiles throughout the ground, casing, tube wall, and fluid are provided as a function of time. The fluid temperatures from and to the heat pump, as a function of time, are also provided. In addition to temperature information, detailed heat rate information at several locations as a function of time is determined. Heat rates between the heat pump and the building indoor environment, between the working fluid and the heat pump, and between the working fluid and the ground are computed. The heat rates between the ground and the working fluid are calculated as a function time and position along the ground loop. The heating and cooling loads of the building being fitted with a GSHP are determined with the computer program developed by DOE called ENERGYPLUS. Lastly COP (coefficient of performance) results as a function of time are provided. Both the two-dimensional and three-dimensional computer programs developed as part of this work are based upon a detailed finite volume solution of the energy equation for the ground and ground loop. Real heat pump characteristics are entered into the program and used to model the heat pump performance. Thus these computer tools simulate the coupled performance of the ground loop and the heat pump. The

  6. MARE2DEM: an open-source code for anisotropic inversion of controlled-source electromagnetic and magnetotelluric data using parallel adaptive 2D finite elements (Invited)

    NASA Astrophysics Data System (ADS)

    Key, K.

    2013-12-01

    This work announces the public release of an open-source inversion code named MARE2DEM (Modeling with Adaptively Refined Elements for 2D Electromagnetics). Although initially designed for the rapid inversion of marine electromagnetic data, MARE2DEM now supports a wide variety of acquisition configurations for both offshore and onshore surveys that utilize electric and magnetic dipole transmitters or magnetotelluric plane waves. The model domain is flexibly parameterized using a grid of arbitrarily shaped polygonal regions, allowing for complicated structures such as topography or seismically imaged horizons to be easily assimilated. MARE2DEM efficiently solves the forward problem in parallel by dividing the input data parameters into smaller subsets using a parallel data decomposition algorithm. The data subsets are then solved in parallel using an automatic adaptive finite element method that iterative solves the forward problem on successively refined finite element meshes until a specified accuracy tolerance is met, thus freeing the end user from the burden of designing an accurate numerical modeling grid. Regularized non-linear inversion for isotropic or anisotropic conductivity is accomplished with a new implementation of Occam's method referred to as fast-Occam, which is able to minimize the objective function in much fewer forward evaluations than the required by the original method. This presentation will review the theoretical considerations behind MARE2DEM and use a few recent offshore EM data sets to demonstrate its capabilities and to showcase the software interface tools that streamline model building and data inversion.

  7. Stable Artificial Dissipation Operators for Finite Volume Schemes on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Svard, Magnus; Gong, Jing; Nordstrom, Jan

    2006-01-01

    Our objective is to derive stable first-, second- and fourth-order artificial dissipation operators for node based finite volume schemes. Of particular interest are general unstructured grids where the strength of the finite volume method is fully utilized. A commonly used finite volume approximation of the Laplacian will be the basis in the construction of the artificial dissipation. Both a homogeneous dissipation acting in all directions with equal strength and a modification that allows different amount of dissipation in different directions are derived. Stability and accuracy of the new operators are proved and the theoretical results are supported by numerical computations.

  8. NUMERICAL MODELING OF CONTAMINANT TRANSPORT IN FRACTURED POROUS MEDIA USING MIXED FINITE ELEMENT AND FINITE VOLUME METHODS

    SciTech Connect

    Taylor, G.; Dong, C.; Sun, S.

    2010-03-18

    A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods, i.e. mixed finite element (MFE) and the finite volume methods. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocities field for both the fractures and matrix which are crucial to the convection part of the transport equation. The finite volume method and the standard MFE method are used to approximate the convection and dispersion terms respectively. The model is used to investigate the interaction of adsorption with transport and to extract information on effective adsorption distribution coefficients. Numerical examples in different fractured media illustrate the robustness and efficiency of the proposed numerical model.

  9. Verification of a non-hydrostatic dynamical core using the horizontal spectral element method and vertical finite difference method: 2-D aspects

    NASA Astrophysics Data System (ADS)

    Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.

    2014-11-01

    The non-hydrostatic (NH) compressible Euler equations for dry atmosphere were solved in a simplified two-dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. By using horizontal SEM, which decomposes the physical domain into smaller pieces with a small communication stencil, a high level of scalability can be achieved. By using vertical FDM, an easy method for coupling the dynamics and existing physics packages can be provided. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind-biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative and integral terms. For temporal integration, a time-split, third-order Runge-Kutta (RK3) integration technique was applied. The Euler equations that were used here are in flux form based on the hydrostatic pressure vertical coordinate. The equations are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate was implemented in this model. We validated the model by conducting the widely used standard tests: linear hydrostatic mountain wave, tracer advection, and gravity wave over the Schär-type mountain, as well as density current, inertia-gravity wave, and rising thermal bubble. The results from these tests demonstrated that the model using the horizontal SEM and the vertical FDM is accurate and robust provided sufficient diffusion is applied. The results with various horizontal resolutions also showed convergence of second-order accuracy due to the accuracy of the time integration scheme and that of the vertical direction, although high-order basis functions were used in the horizontal. By using the 2-D slice model, we effectively showed that the combined spatial

  10. Hybrid spectral difference/embedded finite volume method for conservation laws

    NASA Astrophysics Data System (ADS)

    Choi, Jung J.

    2015-08-01

    Recently, interests have been increasing towards applying the high-order methods to various engineering applications with complex geometries [30]. As a result, a family of discontinuous high-order methods, such as Discontinuous Galerkin (DG), Spectral Volume (SV) and Spectral Difference (SD) methods, is under active development. These methods provide high-order accurate solutions and are highly parallelizable due to the local solution reconstruction within each element. But, these methods suffer from the Gibbs phenomena when discontinuities are present in the flow fields. Various types of limiters [43-45] and artificial viscosity [46,48] have been employed to overcome this problem. A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in the flows with complex geometries. In the proposed hybrid approach, the finite volume (FV) element, consisting of structured FV subcells, is embedded in the base hexahedral element containing discontinuity, and an FV based high-order shock-capturing scheme is employed to overcome the Gibbs phenomena. Thus, a discontinuity is captured at the resolution of FV subcells within an embedded FV element. In the smooth flow region, the SD element is used in the base hexahedral element. Then, the governing equations are solved by the SD method. The SD method is chosen for its low numerical dissipation and computational efficiency preserving high-order accurate solutions. The coupling between the SD element and the FV element is achieved by the globally conserved mortar method [56]. In this paper, the 5th-order WENO scheme with the characteristic decomposition is employed as the shock-capturing scheme in the embedded FV element, and the 5th-order SD method is used in the smooth flow field. The order of accuracy study and various 1D and 2D test cases are carried out, which involve the discontinuities

  11. Slave finite elements for nonlinear analysis of engine structures, volume 1

    NASA Technical Reports Server (NTRS)

    Gellin, S.

    1991-01-01

    A 336 degrees of freedom slave finite element processing capability to analyze engine structures under severe thermomechanical loading is presented. Description of the theoretical development and demonstration of that element is presented in this volume.

  12. Finite-volume effects in the muon anomalous magnetic moment on the lattice

    NASA Astrophysics Data System (ADS)

    Aubin, Christopher; Blum, Thomas; Chau, Peter; Golterman, Maarten; Peris, Santiago; Tu, Cheng

    2016-03-01

    We investigate finite-volume effects in the hadronic vacuum polarization, with an eye toward the corresponding systematic error in the muon anomalous magnetic moment. We consider both recent lattice data as well as lowest-order, finite-volume chiral perturbation theory, in order to get a quantitative understanding. Even though leading-order chiral perturbation theory does not provide a good description of the hadronic vacuum polarization, it turns out that it gives a good representation of finite-volume effects. We find that finite-volume effects cannot be ignored when the aim is a few percent level accuracy for the leading-order hadronic contribution to the muon anomalous magnetic moment, even when using ensembles with mπL ≳4 and mπ˜200 MeV .

  13. Enhanced numerical inviscid and viscous fluxes for cell centered finite volume schemes

    NASA Astrophysics Data System (ADS)

    Eberle, Albrecht

    1991-07-01

    The most attractive features of cell centered finite volume schemes seem to be the easy introduction of the solid body boundary condition and the implementation of characteristic based methods for evaluating the convective fluxes at the cell faces of the finite volumes. For the viscous parts of the fluxes, however, cell centered finite volume schemes are not as well suited as cell vertex based discretizations since in a general grid, cell centered schemes usually are not linear flow preserving concerning the viscous terms. That means that the viscous stress tensor and the heat flux vector may spuriously vary in a flow field with linear velocity and/or temperature distribution. Several enhancements of the flux formulations for cell centered finite volume schemes are described.

  14. Deconfinement phase transition in a finite volume in the presence of massive particles

    SciTech Connect

    Ait El Djoudi, A.; Ghenam, L.

    2012-06-27

    We study the QCD deconfinement phase transition from a hadronic gas to a Quark-Gluon Plasma, in the presence of massive particles. Especially, the influence of some parameters as the finite volume, finite mass, flavors number N{sub f} on the transition point and on the order of the transition is investigated.

  15. O(2)-scaling in finite and infinite volume

    NASA Astrophysics Data System (ADS)

    Springer, Paul; Klein, Bertram

    2015-10-01

    The exact nature of the chiral crossover in QCD is still under investigation. In N_f=2 and N_f=(2+1) lattice simulations with staggered fermions the expected O( N)-scaling behavior was observed. However, it is still not clear whether this behavior falls into the O(2) or O(4) universality class. To resolve this issue, a careful scaling and finite-size scaling analysis of the lattice results are needed. We use a functional renormalization group to perform a new investigation of the finite-size scaling regions in O(2)- and O(4)-models. We also investigate the behavior of the critical fluctuations by means of the 4th-order Binder cumulant. The finite-size analysis of this quantity provides an additional way for determining the universality class of the chiral transition in lattice QCD.

  16. Silt motion simulation using finite volume particle method

    NASA Astrophysics Data System (ADS)

    Jahanbakhsh, E.; Vessaz, C.; Avellan, F.

    2014-03-01

    In this paper, we present a 3-D FVPM which features rectangular top-hat kernels. With this method, interaction vectors are computed exactly and efficiently. We introduce a new method to enforce the no-slip boundary condition. With this boundary enforcement, the interaction forces between fluid and wall are computed accurately. We employ the boundary force to predict the motion of rigid spherical silt particles inside the fluid. To validate the model, we simulate the 2-D sedimentation of a single particle in viscous fluid tank and compare results with benchmark data. The particle resolution is verified by convergence study. We also simulate the sedimentation of two particles exhibiting drafting, kissing and tumbling phenomena in 2-D and 3-D. We compare the results with other numerical solutions.

  17. Effects of finite volume on the KL – KS mass difference

    DOE PAGESBeta

    Christ, N.  H.; Feng, X.; Martinelli, G.; Sachrajda, C.  T.

    2015-06-24

    Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the KLmore » – KS mass difference ΔMK and the CP-violating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.« less

  18. Dynamic pulse buckling of cylindrical shells under axial impact: A comparison of 2D and 3D finite element calculations with experimental data

    SciTech Connect

    Hoffman, E.L.; Ammerman, D.J.

    1995-04-01

    A series of tests investigating dynamic pulse buckling of a cylindrical shell under axial impact is compared to several 2D and 3D finite element simulations of the event. The purpose of the work is to investigate the performance of various analysis codes and element types on a problem which is applicable to radioactive material transport packages, and ultimately to develop a benchmark problem to qualify finite element analysis codes for the transport package design industry. Four axial impact tests were performed on 4 in-diameter, 8 in-long, 304 L stainless steel cylinders with a 3/16 in wall thickness. The cylinders were struck by a 597 lb mass with an impact velocity ranging from 42.2 to 45.1 ft/sec. During the impact event, a buckle formed at each end of the cylinder, and one of the two buckles became unstable and collapsed. The instability occurred at the top of the cylinder in three tests and at the bottom in one test. Numerical simulations of the test were performed using the following codes and element types: PRONTO2D with axisymmetric four-node quadrilaterals; PRONTO3D with both four-node shells and eight-node hexahedrons; and ABAQUS/Explicit with axisymmetric two-node shells and four-node quadrilaterals, and 3D four-node shells and eight-node hexahedrons. All of the calculations are compared to the tests with respect to deformed shape and impact load history. As in the tests, the location of the instability is not consistent in all of the calculations. However, the calculations show good agreement with impact load measurements with the exception of an initial load spike which is proven to be the dynamic response of the load cell to the impact. Finally, the PRONIT02D calculation is compared to the tests with respect to strain and acceleration histories. Accelerometer data exhibited good qualitative agreement with the calculations. The strain comparisons show that measurements are very sensitive to gage placement.

  19. An Accuracy Evaluation of Unstructured Node-Centred Finite Volume Methods

    NASA Technical Reports Server (NTRS)

    Svard, Magnus; Gong, Jing; Nordstrom, Jan

    2006-01-01

    Node-centred edge-based finite volume approximations are very common in computational fluid dynamics since they are assumed to run on structured, unstructured and even on mixed grids. We analyse the accuracy properties of both first and second derivative approximations and conclude that these schemes can not be used on arbitrary grids as is often assumed. For the Euler equations first-order accuracy can be obtained if care is taken when constructing the grid. For the Navier-Stokes equations, the grid restrictions are so severe that these finite volume schemes have little advantage over structured finite difference schemes. Our theoretical results are verified through extensive computations.

  20. A triangle based mixed finite element-finite volume technique for modeling two phase flow through porous media

    SciTech Connect

    Durlofsky, L.J. )

    1993-04-01

    Triangle based discretization techniques offer great advantages relative to standard finite difference methods for the modeling of flow through geometrically complex geological features. The purpose of this paper is to develop and apply a triangle based method for the modeling of two phase flow through porous formations. The formulation includes the effects of gravity, compressibility, and capillary pressure. The technique entails a triangle based mixed finite element method for solution of the variable coefficient, parabolic pressure equation, and a second-order TVD-type (total variation diminishing) finite volume scheme for solution of the essentially hyperbolic saturation equation. The method is applied to a variety of example problems and is shown to perform very well on problems involving geometric complexity coupled with heterogeneous, generally anisotropic permeability descriptions. 20 refs., 20 figs.

  1. Consisitent and Accurate Finite Volume Methods for Coupled Flow and Geomechanics

    NASA Astrophysics Data System (ADS)

    Nordbotten, J. M.

    2014-12-01

    We introduce a new class of cell-centered finite volume methods for elasticity and poro-elasticity. As compared to lowest-order finite element discretizations, the new discretization has no additional degrees of freedom, and yet gives more accurate stress and flow fields. This finite volume discretization methods has furthermore the advantage that the mechanical discretization is fully compatible (in terms of grid and variables) with the standard cell-centered finite volume discretizations that are prevailing for commercial simulation of multi-phase flows in porous media. Theoretical analysis proves the convergence of the method. We give results showing that so-called numerical locking is avoided for a large class of structured and unstructured grids. The results are valid in both two and three spatial dimensions. The talk concludes with applications to problems with coupled multi-phase flow, transport and deformation, together with fractured porous media.

  2. A fast finite volume method for conservative space-fractional diffusion equations in convex domains

    NASA Astrophysics Data System (ADS)

    Jia, Jinhong; Wang, Hong

    2016-04-01

    We develop a fast finite volume method for variable-coefficient, conservative space-fractional diffusion equations in convex domains via a volume-penalization approach. The method has an optimal storage and an almost linear computational complexity. The method retains second-order accuracy without requiring a Richardson extrapolation. Numerical results are presented to show the utility of the method.

  3. Finite Volume Study of the Delta Magnetic Moments Using Dynamical Clover Fermions

    SciTech Connect

    Aubin, Christopher; Orginos, Konstantinos; Pascalutsa, Vladimir; Vanderhaeghen, Marc

    2009-01-01

    We calculate the magnetic dipole moment of the $\\Delta$ baryon using a background magnetic field on 2+1-flavors of clover fermions on anisotropic lattices. We focus on the finite volume effects that can be significant in background field studies, and thus we use two different spatial volumes in addition to several quark masses.

  4. A High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

    2001-01-01

    A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.

  5. Finite element analysis of laminated plates and shells, volume 1

    NASA Technical Reports Server (NTRS)

    Seide, P.; Chang, P. N. H.

    1978-01-01

    The finite element method is used to investigate the static behavior of laminated composite flat plates and cylindrical shells. The analysis incorporates the effects of transverse shear deformation in each layer through the assumption that the normals to the undeformed layer midsurface remain straight but need not be normal to the mid-surface after deformation. A digital computer program was developed to perform the required computations. The program includes a very efficient equation solution code which permits the analysis of large size problems. The method is applied to the problem of stretching and bending of a perforated curved plate.

  6. One-point functions in finite volume/temperature: a case study

    NASA Astrophysics Data System (ADS)

    Szécsényi, I. M.; Takács, G.; Watts, G. M. T.

    2013-08-01

    We consider finite volume (or equivalently, finite temperature) expectation values of local operators in integrable quantum field theories using a combination of numerical and analytical approaches. It is shown that the truncated conformal space approach, when supplemented with a recently proposed renormalization group, can be sufficiently extended to the low-energy regime that it can be matched with high precision by the low-temperature expansion proposed by Leclair and Mussardo. Besides verifying the consistency of the two descriptions, their combination leads to an evaluation of expectation values which is valid to a very high precision for all volume/temperature scales. As a side result of the investigation, we also discuss some unexpected singularities in the framework recently proposed by Pozsgay and Takács for the description of matrix elements of local operators in finite volume, and show that while some of these singularities are resolved by the inclusion of the class of exponential finite size corrections known as μ-terms, these latter corrections themselves lead to the appearance of new singularities. We point out that a fully consistent description of finite volume matrix elements is expected to be free of singularities, and therefore a more complete and systematic understanding of exponential finite size corrections is necessary.

  7. Numerical Analysis of a Finite Element/Volume Penalty Method

    NASA Astrophysics Data System (ADS)

    Maury, Bertrand

    The penalty method makes it possible to incorporate a large class of constraints in general purpose Finite Element solvers like freeFEM++. We present here some contributions to the numerical analysis of this method. We propose an abstract framework for this approach, together with some general error estimates based on the discretization parameter ɛ and the space discretization parameter h. As this work is motivated by the possibility to handle constraints like rigid motion for fluid-particle flows, we shall pay a special attention to a model problem of this kind, where the constraint is prescribed over a subdomain. We show how the abstract estimate can be applied to this situation, in the case where a non-body-fitted mesh is used. In addition, we describe how this method provides an approximation of the Lagrange multiplier associated to the constraint.

  8. A Finite-Volume "Shaving" Method for Interfacing NASA/DAO''s Physical Space Statistical Analysis System to the Finite-Volume GCM with a Lagrangian Control-Volume Vertical Coordinate

    NASA Technical Reports Server (NTRS)

    Lin, Shian-Jiann; DaSilva, Arlindo; Atlas, Robert (Technical Monitor)

    2001-01-01

    Toward the development of a finite-volume Data Assimilation System (fvDAS), a consistent finite-volume methodology is developed for interfacing the NASA/DAO's Physical Space Statistical Analysis System (PSAS) to the joint NASA/NCAR finite volume CCM3 (fvCCM3). To take advantage of the Lagrangian control-volume vertical coordinate of the fvCCM3, a novel "shaving" method is applied to the lowest few model layers to reflect the surface pressure changes as implied by the final analysis. Analysis increments (from PSAS) to the upper air variables are then consistently put onto the Lagrangian layers as adjustments to the volume-mean quantities during the analysis cycle. This approach is demonstrated to be superior to the conventional method of using independently computed "tendency terms" for surface pressure and upper air prognostic variables.

  9. Finite volume formulation of low-temperature plasma equations and numerical solution in one dimension

    NASA Astrophysics Data System (ADS)

    Vukovic, Mirko

    2008-10-01

    Differential transport equations for plasma are most commonly discretized using the finite difference formalism. More recently, discretizations based on the finite element method have also been used. An alternate method is the finite volume method which discretizes the integral conservation equations.ootnotetextNumerical Heat Transfer and Fluid Flow, Suhas V. Patankar, McGraw-Hill, 1980 This method conserves flux across the grid cell interfaces. In this presentation, we present the discretization of plasma transport equations based on the finite volume formalism. We will discuss the discretization of the drift-diffusion, momentum, and electron kinetic equations based on this formalism. A one-dimensional problem will be solved for several DC and time-dependent cases.

  10. Computation of viscous blast wave solutions with an upwind finite volume method

    NASA Technical Reports Server (NTRS)

    Molvik, Gregory A.

    1987-01-01

    A fully conservative, viscous, implicit, upwind, finite-volume scheme for the thin-layer Navier-Stokes equations is described with application to blast wave flow fields. In this scheme, shocks are captured without the oscillations typical of central differencing techniques and wave speeds are accurately predicted. The finite volume philosophy ensures conservation and since boundary conditions are also treated conservatively, accurate reflections of waves from surfaces are assured. Viscous terms in the governing equations are treated in a manner consistent with the finite volume philosophy, resulting in very accurate prediction of boundary layer quantities. Numerical results are presented for four viscous problems: a steady boundary layer, a shock-induced boundary layer, a blast wave/cylinder interaction and a blast wave/supersonic missile interaction. Comparisons of the results with an established boundary layer code, similarity solution, and experimental data show excellent agreement.

  11. Finite volume method for the Black-Scholes equation transformed on finite interval

    NASA Astrophysics Data System (ADS)

    Valkov, R.

    2012-11-01

    In this paper, we present a fitted FVM for the degenerate at the two ends parabolic equation, derived from the Black-Scholes equation after a transformation to a finite interval. For the case of European options we describe a fully discretization of the vertical method of lines, where the spatial discretization is formulated as a Petrov-Galerkin FEM. We show that the method is O(h) convergent and monotone. Numerical experiments are presented to verify the theoretical results. Experiments on a power-graded mesh demonstrate higher accuracy.

  12. Mathematical model of diffusion-limited gas bubble dynamics in unstirred tissue with finite volume

    NASA Technical Reports Server (NTRS)

    Srinivasan, R. Srini; Gerth, Wayne A.; Powell, Michael R.

    2002-01-01

    Models of gas bubble dynamics for studying decompression sickness have been developed by considering the bubble to be immersed in an extravascular tissue with diffusion-limited gas exchange between the bubble and the surrounding unstirred tissue. In previous versions of this two-region model, the tissue volume must be theoretically infinite, which renders the model inapplicable to analysis of bubble growth in a finite-sized tissue. We herein present a new two-region model that is applicable to problems involving finite tissue volumes. By introducing radial deviations to gas tension in the diffusion region surrounding the bubble, the concentration gradient can be zero at a finite distance from the bubble, thus limiting the tissue volume that participates in bubble-tissue gas exchange. It is shown that these deviations account for the effects of heterogeneous perfusion on gas bubble dynamics, and are required for the tissue volume to be finite. The bubble growth results from a difference between the bubble gas pressure and an average gas tension in the surrounding diffusion region that explicitly depends on gas uptake and release by the bubble. For any given decompression, the diffusion region volume must stay above a certain minimum in order to sustain bubble growth.

  13. Registration of 2D cardiac images to real-time 3D ultrasound volumes for 3D stress echocardiography

    NASA Astrophysics Data System (ADS)

    Leung, K. Y. Esther; van Stralen, Marijn; Voormolen, Marco M.; van Burken, Gerard; Nemes, Attila; ten Cate, Folkert J.; Geleijnse, Marcel L.; de Jong, Nico; van der Steen, Antonius F. W.; Reiber, Johan H. C.; Bosch, Johan G.

    2006-03-01

    Three-dimensional (3D) stress echocardiography is a novel technique for diagnosing cardiac dysfunction, by comparing wall motion of the left ventricle under different stages of stress. For quantitative comparison of this motion, it is essential to register the ultrasound data. We propose an intensity based rigid registration method to retrieve two-dimensional (2D) four-chamber (4C), two-chamber, and short-axis planes from the 3D data set acquired in the stress stage, using manually selected 2D planes in the rest stage as reference. The algorithm uses the Nelder-Mead simplex optimization to find the optimal transformation of one uniform scaling, three rotation, and three translation parameters. We compared registration using the SAD, SSD, and NCC metrics, performed on four resolution levels of a Gaussian pyramid. The registration's effectiveness was assessed by comparing the 3D positions of the registered apex and mitral valve midpoints and 4C direction with the manually selected results. The registration was tested on data from 20 patients. Best results were found using the NCC metric on data downsampled with factor two: mean registration errors were 8.1mm, 5.4mm, and 8.0° in the apex position, mitral valve position, and 4C direction respectively. The errors were close to the interobserver (7.1mm, 3.8mm, 7.4°) and intraobserver variability (5.2mm, 3.3mm, 7.0°), and better than the error before registration (9.4mm, 9.0mm, 9.9°). We demonstrated that the registration algorithm visually and quantitatively improves the alignment of rest and stress data sets, performing similar to manual alignment. This will improve automated analysis in 3D stress echocardiography.

  14. Automatic intensity-based 3D-to-2D registration of CT volume and dual-energy digital radiography for the detection of cardiac calcification

    NASA Astrophysics Data System (ADS)

    Chen, Xiang; Gilkeson, Robert; Fei, Baowei

    2007-03-01

    We are investigating three-dimensional (3D) to two-dimensional (2D) registration methods for computed tomography (CT) and dual-energy digital radiography (DR) for the detection of coronary artery calcification. CT is an established tool for the diagnosis of coronary artery diseases (CADs). Dual-energy digital radiography could be a cost-effective alternative for screening coronary artery calcification. In order to utilize CT as the "gold standard" to evaluate the ability of DR images for the detection and localization of calcium, we developed an automatic intensity-based 3D-to-2D registration method for 3D CT volumes and 2D DR images. To generate digital rendering radiographs (DRR) from the CT volumes, we developed three projection methods, i.e. Gaussian-weighted projection, threshold-based projection, and average-based projection. We tested normalized cross correlation (NCC) and normalized mutual information (NMI) as similarity measurement. We used the Downhill Simplex method as the search strategy. Simulated projection images from CT were fused with the corresponding DR images to evaluate the localization of cardiac calcification. The registration method was evaluated by digital phantoms, physical phantoms, and clinical data sets. The results from the digital phantoms show that the success rate is 100% with mean errors of less 0.8 mm and 0.2 degree for both NCC and NMI. The registration accuracy of the physical phantoms is 0.34 +/- 0.27 mm. Color overlay and 3D visualization of the clinical data show that the two images are registered well. This is consistent with the improvement of the NMI values from 0.20 +/- 0.03 to 0.25 +/- 0.03 after registration. The automatic 3D-to-2D registration method is accurate and robust and may provide a useful tool to evaluate the dual-energy DR images for the detection of coronary artery calcification.

  15. Automatic Intensity-based 3D-to-2D Registration of CT Volume and Dual-energy Digital Radiography for the Detection of Cardiac Calcification

    PubMed Central

    Chen, Xiang; Gilkeson, Robert; Fei, Baowei

    2013-01-01

    We are investigating three-dimensional (3D) to two-dimensional (2D) registration methods for computed tomography (CT) and dual-energy digital radiography (DR) for the detection of coronary artery calcification. CT is an established tool for the diagnosis of coronary artery diseases (CADs). Dual-energy digital radiography could be a cost-effective alternative for screening coronary artery calcification. In order to utilize CT as the “gold standard” to evaluate the ability of DR images for the detection and localization of calcium, we developed an automatic intensity-based 3D-to-2D registration method for 3D CT volumes and 2D DR images. To generate digital rendering radiographs (DRR) from the CT volumes, we developed three projection methods, i.e. Gaussian-weighted projection, threshold-based projection, and average-based projection. We tested normalized cross correlation (NCC) and normalized mutual information (NMI) as similarity measurement. We used the Downhill Simplex method as the search strategy. Simulated projection images from CT were fused with the corresponding DR images to evaluate the localization of cardiac calcification. The registration method was evaluated by digital phantoms, physical phantoms, and clinical data sets. The results from the digital phantoms show that the success rate is 100% with mean errors of less 0.8 mm and 0.2 degree for both NCC and NMI. The registration accuracy of the physical phantoms is 0.34 ± 0.27 mm. Color overlay and 3D visualization of the clinical data show that the two images are registered well. This is consistent with the improvement of the NMI values from 0.20 ± 0.03 to 0.25 ± 0.03 after registration. The automatic 3D-to-2D registration method is accurate and robust and may provide a useful tool to evaluate the dual-energy DR images for the detection of coronary artery calcification. PMID:24386527

  16. Relativistic, model-independent, multichannel 2 →2 transition amplitudes in a finite volume

    NASA Astrophysics Data System (ADS)

    Briceño, Raúl A.; Hansen, Maxwell T.

    2016-07-01

    We derive formalism for determining 2 +J →2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or nonidentical and, in the latter case, can be either degenerate or nondegenerate. We further accommodate any number of strongly coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the ρ -meson form factor, in which the unstable nature of the ρ is rigorously accommodated.

  17. Two-particle multichannel systems in a finite volume with arbitrary spin

    DOE PAGESBeta

    Briceno, Raul A.

    2014-04-08

    The quantization condition for two-particle systems with arbitrary number of two-body open coupled channels, spin and masses in a finite cubic volume with either periodic or twisted boundary conditions is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is relativistic, holds for all momenta below the three- and four-particle thresholds, and is exact up to exponential volume corrections that are governed by L/r, where L is the spatial extent of the volume and r is the range of the interactions between the particles. With hadronic systems the rangemore » of the interaction is set by the inverse of the pion mass, mπ, and as a result the formalism presented is suitable for mπL>>1. Implications of the formalism for the studies of multichannel baryon-baryon systems are discussed.« less

  18. Two-particle multichannel systems in a finite volume with arbitrary spin

    SciTech Connect

    Briceno, Raul A.

    2014-04-08

    The quantization condition for two-particle systems with arbitrary number of two-body open coupled channels, spin and masses in a finite cubic volume with either periodic or twisted boundary conditions is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is relativistic, holds for all momenta below the three- and four-particle thresholds, and is exact up to exponential volume corrections that are governed by L/r, where L is the spatial extent of the volume and r is the range of the interactions between the particles. With hadronic systems the range of the interaction is set by the inverse of the pion mass, mπ, and as a result the formalism presented is suitable for mπL>>1. Implications of the formalism for the studies of multichannel baryon-baryon systems are discussed.

  19. Finite-volume model for chemical vapor infiltration incorporating radiant heat transfer. Interim report

    SciTech Connect

    Smith, A.W.; Starr, T.L.

    1995-05-01

    Most finite-volume thermal models account for the diffusion and convection of heat and may include volume heating. However, for certain simulation geometries, a large percentage of heat flux is due to thermal radiation. In this paper a finite-volume computational procedure for the simulation of heat transfer by conduction, convection and radiation in three dimensional complex enclosures is developed. The radiant heat transfer is included as a source term in each volume element which is derived by Monte Carlo ray tracing from all possible radiating and absorbing faces. The importance of radiative heat transfer is illustrated in the modeling of chemical vapor infiltration (CVI) of tubes. The temperature profile through the tube preform matches experimental measurements only when radiation is included. An alternative, empirical approach using an {open_quotes}effective{close_quotes} thermal conductivity for the gas space can match the initial temperature profile but does not match temperature changes that occur during preform densification.

  20. Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume

    DOE PAGESBeta

    Briceno, Raul A.; Hansen, Maxwell T.

    2016-07-13

    We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of themore » $$\\rho$$-meson form factor, in which the unstable nature of the $$\\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.« less

  1. Finite-volume effects and dynamical chiral symmetry breaking in QED{sub 3}

    SciTech Connect

    Goecke, Tobias; Williams, Richard; Fischer, Christian S.

    2009-02-01

    We investigate the impact of finite-volume effects on the critical number of flavors, N{sub f}{sup c}, for chiral symmetry restoration in QED{sub 3}. To this end we solve a set of coupled Dyson-Schwinger equations on a torus. For order parameters such as the anomalous dimension of the fermion wave function or the chiral condensate, we find substantial evidence for a large dependence on the volume. We observe a shift in N{sub f}{sup c} from values in the range of 3.61{<=}N{sub f}{sup c}{<=}3.84 in the infinite-volume and continuum limit down to values below N{sub f}{<=}1.5 at finite volumes in agreement with earlier results of Gusynin and Reenders in a simpler truncation scheme. These findings explain discrepancies in N{sub f}{sup c} between continuum and lattice studies.

  2. Computation of multi-mode heat transfer using an unstructured finite volume method

    SciTech Connect

    Mathur, S.R.; Murthy, J.Y.

    1999-07-01

    The finite volume method for radiative heat transfer is extended to compute multi-mode heat transfer problems in complex domains. The calculation domain is discretized into unstructured polyhedral control volumes over which the radiative transfer equation (RTE) and the energy equation are integrated. Implicit discretization of volumetric sources and coupling between temperature and radiation at conjugate interfaces and external boundaries is addressed. The scheme is applied to a variety of multi-mode heat transfer problems and shown to perform well.

  3. High spatiotemporal resolution measurement of regional lung air volumes from 2D phase contrast x-ray images

    SciTech Connect

    Leong, Andrew F. T.; Islam, M. Sirajul; Kitchen, Marcus J.; Fouras, Andreas; Wallace, Megan J.; Hooper, Stuart B.

    2013-04-15

    Purpose: Described herein is a new technique for measuring regional lung air volumes from two-dimensional propagation-based phase contrast x-ray (PBI) images at very high spatial and temporal resolution. Phase contrast dramatically increases lung visibility and the outlined volumetric reconstruction technique quantifies dynamic changes in respiratory function. These methods can be used for assessing pulmonary disease and injury and for optimizing mechanical ventilation techniques for preterm infants using animal models. Methods: The volumetric reconstruction combines the algorithms of temporal subtraction and single image phase retrieval (SIPR) to isolate the image of the lungs from the thoracic cage in order to measure regional lung air volumes. The SIPR algorithm was used to recover the change in projected thickness of the lungs on a pixel-by-pixel basis (pixel dimensions {approx}16.2 {mu}m). The technique has been validated using numerical simulation and compared results of measuring regional lung air volumes with and without the use of temporal subtraction for removing the thoracic cage. To test this approach, a series of PBI images of newborn rabbit pups mechanically ventilated at different frequencies was employed. Results: Regional lung air volumes measured from PBI images of newborn rabbit pups showed on average an improvement of at least 20% in 16% of pixels within the lungs in comparison to that measured without the use of temporal subtraction. The majority of pixels that showed an improvement was found to be in regions occupied by bone. Applying the volumetric technique to sequences of PBI images of newborn rabbit pups, it is shown that lung aeration at birth can be highly heterogeneous. Conclusions: This paper presents an image segmentation technique based on temporal subtraction that has successfully been used to isolate the lungs from PBI chest images, allowing the change in lung air volume to be measured over regions as small as the pixel size. Using

  4. Cancellous bone lamellae strongly affect microcrack propagation and apparent mechanical properties: Separation of patients with osteoporotic fracture from normal controls using a 2D nonlinear finite element method (biomechanical stereology)

    PubMed Central

    Wang, Xiang; Zauel, Roger R.; Rao, D. Sudhaker; Fyhrie, David P.

    2009-01-01

    Biomechanical stereology is proposed as a two-dimensional (2D) finite element (FE) method to estimate the ability of bone tissue to sustain damage and to separate patients with osteoporotic fracture from normal controls. Briefly, 2D nonlinear compact tension FE models were created from quantitative back scattered electron images taken of iliac crest bone specimens collected from the individuals with or without osteoporotic fracture history. The effects of bone mineral microstructure on predicted bone fracture toughness and microcrack propagation were examined. The 2D FE models were used as surrogates for the real bone tissues. The calculated microcrack propagation results and bone mechanical properties were examined as surrogates for measurements from mechanical testing of actual specimens. The results for the 2D FE simulation separated patients with osteoporotic fracture from normal controls even though only the variability in tissue mineral microstructure was used to build the models. The models were deliberately created to ignore all differences in mean mineralization. Hence, the current results support the following hypotheses: (1) that material heterogeneity is important to the separation of patients with osteoporotic fracture from normal controls and; and (2) that 2D nonlinear finite element modeling can produce surrogate mechanical parameters that separate patients with fracture from normal controls. PMID:18378204

  5. Survey and development of finite elements for nonlinear structural analysis. Volume 2: Nonlinear shell finite elements

    NASA Technical Reports Server (NTRS)

    1976-01-01

    The development of two new shell finite elements for applications to large deflection problems is considered. The elements in question are doubly curved and of triangular and quadrilateral planform. They are restricted to small strains of elastic materials, and can accommodate large rotations. The elements described, which are based on relatively simple linear elements, make use of a new displacement function approach specifically designed for strongly nonlinear problems. The displacement function development for nonlinear applications is based on certain beam element formulations, and the strain-displacement equations are of a shallow shell type. Additional terms were included in these equations in an attempt to avoid the large errors characteristic of shallow shell elements in certain types of problems. An incremental nonlinear solution procedure specifically adopted to the element formulation was developed. The solution procedure is of combined incremental and total Lagrangian type, and uses a new updating scheme. A computer program was written to evaluate the developed formulations. This program can accommodate small element groups in arbitrary arrangements. Two simple programs were successfully solved. The results indicate that this new type of element has definite promise and should be a fruitful area for further research.

  6. Storm Water Infiltration and Focused Groundwater Recharge in a Rain Garden: Finite Volume Model and Numerical Simulations for Different Configurations and Climates

    NASA Astrophysics Data System (ADS)

    Aravena, J.; Dussaillant, A. R.

    2006-12-01

    Source control is the fundamental principle behind sustainable management of stormwater. Rain gardens are an infiltration practice that provides volume and water quality control, recharge, and multiple landscape, ecological and economic potential benefits. The fulfillment of these objectives requires understanding their behavior during events as well as long term, and tools for their design. We have developed a model based on Richards equation coupled to a surface water balance, solved with a 2D finite volume Fortran code which allows alternating upper boundary conditions, including ponding, which is not present in available 2D models. Also, it can simulate non homogeneous water input, heterogeneous soil (layered or more complex geometries), and surface irregularities -e.g. terracing-, so as to estimate infiltration and recharge. The algorithm is conservative; being an advantage compared to available finite difference and finite element methods. We will present performance comparisons to known models, to experimental data from a bioretention cell, which receives roof water to its surface depression planted with native species in an organic-rich root zone soil layer (underlain by a high conductivity lower layer that, while providing inter-event storage, percolates water readily), as well as long term simulations for different rain garden configurations. Recharge predictions for different climates show significant increases from natural recharge, and that the optimal area ratio (raingarden vs. contributing impervious area) reduces from 20% (humid) to 5% (dry).

  7. Application of the control volume mixed finite element method to a triangular discretization

    USGS Publications Warehouse

    Naff, R.L.

    2012-01-01

    A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.

  8. Local tetrahedron modeling of microelectronics using the finite-volume hybrid-grid technique

    SciTech Connect

    Riley, D.J.; Turner, C.D.

    1995-12-01

    The finite-volume hybrid-grid (FVHG) technique uses both structured and unstructured grid regions in obtaining a solution to the time-domain Maxwell`s equations. The method is based on explicit time differencing and utilizes rectilinear finite-difference time-domain (FDTD) and nonorthogonal finite-volume time-domain (FVTD). The technique directly couples structured FDTD grids with unstructured FVTD grids without the need for spatial interpolation across grid interfaces. In this paper, the FVHG method is applied to simple planar microelectronic devices. Local tetrahedron grids are used to model portions of the device under study, with the remainder of the problem space being modeled with cubical hexahedral cells. The accuracy of propagating microstrip-guided waves from a low-density hexahedron region through a high-density tetrahedron grid is investigated.

  9. Modeling dam-break flows using finite volume method on unstructured grid

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Two-dimensional shallow water models based on unstructured finite volume method and approximate Riemann solvers for computing the intercell fluxes have drawn growing attention because of their robustness, high adaptivity to complicated geometry and ability to simulate flows with mixed regimes and di...

  10. Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

    NASA Technical Reports Server (NTRS)

    Wood, William A.

    1997-01-01

    The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

  11. Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

    NASA Technical Reports Server (NTRS)

    Moore, John; Nicholson, Stephen; Moore, Joan G.

    1986-01-01

    The development of a computational capability to handle viscous flow with an explicit time-marching method based on the finite volume approach is summarized. Emphasis is placed on the extensions to the computational procedure which allow the handling of shock induced separation and large regions of strong backflow. Appendices contain abstracts of papers and whole reports generated during the contract period.

  12. Significant impact of 2D graphene nanosheets on large volume change tin-based anodes in lithium-ion batteries: A review

    NASA Astrophysics Data System (ADS)

    Zhao, Yang; Li, Xifei; Yan, Bo; Li, Dejun; Lawes, Stephen; Sun, Xueliang

    2015-01-01

    Sn-based materials have attracted much attention as anodes in lithium ion batteries (LIBs) due to their low cost, high theoretical capacities, and high energy density. However, their practical applications are limited by the poor cyclability originating from the huge volume changes. Graphene nanosheets (GNSs), a novel two-dimensional carbon sheet with one atom thickness and one of the thinnest materials, significantly address the challenges of Sn-based anodes as excellent buffering materials, showing great research interests in LIBs. In this review, various nanocomposites of GNSs/Sn-based anodes are summarized in detail, including binary and ternary composites. The significant impact of 2D GNSs on the volume change of Sn-based anodes during cycling is discussed, along with with their preparation methods, properties and enhanced LIB performance.

  13. The Three-Dimensional Finite-Volume Non-Hydrostatic Icosahedral Model (NIM)

    NASA Astrophysics Data System (ADS)

    Lee, J. L.; MacDonald, A. E.

    2014-12-01

    A multi-scales Non-hydrostatic Icosahedral Model (NIM) has been developed at Earth System Research Laboratory (ESRL) to meet NOAA's future prediction mission ranging from mesoscale short-range, high-impact weather forecasts to longer-term intra-seasonal climate prediction. NIM formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM is designed to utilize the state-of-art computing architecture such as Graphic Processing Units (GPU) processors to run globally at kilometer scale resolution to explicitly resolve convective storms and complex terrains. The novel features of NIM numerical design include: 1.1. A local coordinate system upon which finite-volume integrations are undertaken. The use of a local Cartesian coordinate greatly simplifies the mathematic formulation of the finite-volume operators and leads to the finite-volume integration along straight lines on the plane, rather than along curved lines on the spherical surface. 1.2. A general indirect addressing scheme developed for modeling on irregular grid. It arranges the icosahedral grid with a one-dimensional vector loop structure, table specified memory order, and an indirect addressing scheme that yields very compact code despite the complexities of this grid. 1.3. Use of three-dimensional finite-volume integration over control volumes constructed on the height coordinates. Three-dimensional finite-volume integration accurately represents the Newton Third Law over terrain and improves pressure gradient force over complex terrain. 1.4. Use of the Runge-Kutta 4th order conservative and positive-definite transport scheme 1.5. NIM dynamical solver has been implemented on CPU as well as GPU. As one of the potential candidates for NWS next generation models, NIM dynamical core has been successfully verified with various benchmark test cases including those proposed by DCMIP

  14. STEALTH: a Lagrange explicit finite difference code for solids, structural, and thermohydraulic analysis. Volume 1A: user's manual - theoretical background and numerical equations. Computer code manual. [PWR; BWR

    SciTech Connect

    Hofmann, R.

    1981-11-01

    A useful computer simulation method based on the explicit finite difference technique can be used to address transient dynamic situations associated with nuclear reactor design and analysis. This volume is divided into two parts. Part A contains the theoretical background (physical and numerical) and the numerical equations for the STEALTH 1D, 2D, and 3D computer codes. Part B contains input instructions for all three codes. The STEALTH codes are based entirely on the published technology of the Lawrence Livermore National Laboratory, Livermore, California, and Sandia National Laboratories, Albuquerque, New Mexico.

  15. STEALTH: a Lagrange explicit finite difference code for solids, structural, and thermohydraulic analysis. Volume 1B: user's manual - input instructions. Computer code manual. [PWR; BWR

    SciTech Connect

    Hofmann, R.

    1981-11-01

    A useful computer simulation method based on the explicit finite difference technique can be used to address transient dynamic situations associated with nuclear reactor design and analysis. This volume is divided into two parts. Part A contains the theoretical background (physical and numerical) and the numerical equations for the STEALTH 1D, 2D, and 3D computer codes. Part B contains input instructions for all three codes. The STEALTH codes are based entirely on the published technology of the Lawrence Livermore National Laboratory, Livermore, California, and Sandia National Laboratories, Albuquerque, New Mexico.

  16. A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)

    NASA Astrophysics Data System (ADS)

    Lee, Jin

    2014-05-01

    The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM dynamic corel innovations include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), *Icosahedral grid optimization (Wang and Lee, 2011), * All differentials evaluated as three-dimensional finite-volume integrals around the control volume. The three-dimensional finite-volume solver in NIM is designed to improve pressure gradient calculation and orographic precipitation over complex terrain. NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as internal gravity wave, and mountain waves in Dynamical Cores Model Inter-comparisons Projects (DCMIP). Physical parameterizations suitable for NWP are incorporated into NIM dynamical core and successfully tested with multimonth aqua-planet simulations. Recently, NIM has started real data simulations using GFS initial conditions. Results from the idealized tests as well as real-data simulations will be shown in the conference.

  17. Coupling mixed and finite volume discretizations of convection-diffusion-reaction equations on non-matching grids

    SciTech Connect

    Lazarov, R; Pasciaic, J; Vassilevski, P

    1999-07-01

    In this paper, we consider approximation of a second order convection- diffusion problem by coupled mixed and finite volume methods. Namely, the domain is partitioned into two subdomains, and in one of them we apply the mixed jinite element method while on the other subdomain we use the finite volume element approximation. We prove the stability of this discretization and derive an error estimate.

  18. A high-resolution finite volume model for shallow water flow on uneven bathymetry using quadrilateral meshes

    Technology Transfer Automated Retrieval System (TEKTRAN)

    A two-dimensional cell-centred finite volume model for quadrilateral grids is presented. The solution methodology of the depth-averaged shallow water equations is based upon a Godunov-type upwind finite volume formulation, whereby the inviscid fluxes of the system of equations are obtained using the...

  19. A preconditioned semi-staggered dilation-free finite volume method for the incompressible Navier-Stokes equations on all-hexahedral elements

    NASA Astrophysics Data System (ADS)

    Sahin, Mehmet

    2005-11-01

    A new semi-staggered finite volume method is presented for the solution of the incompressible Navier-Stokes equations on all-quadrilateral (2D)/hexahedral (3D) meshes. The velocity components are defined at element node points while the pressure term is defined at element centroids. The continuity equation is satisfied exactly within each elements. The checkerboard pressure oscillations are prevented using a special filtering matrix as a preconditioner for the saddle-point problem resulting from second-order discretization of the incompressible Navier-Stokes equations. The preconditioned saddle-point problem is solved using block preconditioners with GMRES solver. In order to achieve higher performance FORTRAN source code is based on highly efficient PETSc and HYPRE libraries. As test cases the 2D/3D lid-driven cavity flow problem and the 3D flow past array of circular cylinders are solved in order to verify the accuracy of the proposed method.

  20. Probability of inducing given-magnitude earthquakes by perturbing finite volumes of rocks

    NASA Astrophysics Data System (ADS)

    Shapiro, Serge A.; Krüger, Oliver S.; Dinske, Carsten

    2013-07-01

    Fluid-induced seismicity results from an activation of finite rock volumes. The finiteness of perturbed volumes influences frequency-magnitude statistics. Previously we observed that induced large-magnitude events at geothermal and hydrocarbon reservoirs are frequently underrepresented in comparison with the Gutenberg-Richter law. This is an indication that the events are more probable on rupture surfaces contained within the stimulated volume. Here we theoretically and numerically analyze this effect. We consider different possible scenarios of event triggering: rupture surfaces located completely within or intersecting only the stimulated volume. We approximate the stimulated volume by an ellipsoid or cuboid and derive the statistics of induced events from the statistics of random thin flat discs modeling rupture surfaces. We derive lower and upper bounds of the probability to induce a given-magnitude event. The bounds depend strongly on the minimum principal axis of the stimulated volume. We compare the bounds with data on seismicity induced by fluid injections in boreholes. Fitting the bounds to the frequency-magnitude distribution provides estimates of a largest expected induced magnitude and a characteristic stress drop, in addition to improved estimates of the Gutenberg-Richter a and b parameters. The observed frequency-magnitude curves seem to follow mainly the lower bound. However, in some case studies there are individual large-magnitude events clearly deviating from this statistic. We propose that such events can be interpreted as triggered ones, in contrast to the absolute majority of the induced events following the lower bound.

  1. A parallel finite-volume finite-element method for transient compressible turbulent flows with heat transfer

    NASA Astrophysics Data System (ADS)

    Ziaei-Rad, Masoud

    2010-12-01

    In this paper, a two-dimensional numerical scheme is presented for the simulation of turbulent, viscous, transient compressible flows in the simultaneously developing hydraulic and thermal boundary layer region. The numerical procedure is a finite-volume-based finite-element method applied to unstructured grids. This combination together with a new method applied for the boundary conditions allows for accurate computation of the variables in the entrance region and for a wide range of flow fields from subsonic to transonic. The Roe-Riemann solver is used for the convective terms, whereas the standard Galerkin technique is applied for the viscous terms. A modified κ-ɛ model with a two-layer equation for the near-wall region combined with a compressibility correction is used to predict the turbulent viscosity. Parallel processing is also employed to divide the computational domain among the different processors to reduce the computational time. The method is applied to some test cases in order to verify the numerical accuracy. The results show significant differences between incompressible and compressible flows in the friction coefficient, Nusselt number, shear stress and the ratio of the compressible turbulent viscosity to the molecular viscosity along the developing region. A transient flow generated after an accidental rupture in a pipeline was also studied as a test case. The results show that the present numerical scheme is stable, accurate and efficient enough to solve the problem of transient wall-bounded flow.

  2. A benchmark study of 2D and 3D finite element calculations simulating dynamic pulse buckling tests of cylindrical shells under axial impact

    SciTech Connect

    Hoffman, E.L.; Ammerman, D.J.

    1993-08-01

    A series of tests investigating dynamic pulse buckling of a cylindrical shell under axial impact is compared to several finite element simulations of the event. The purpose of the study is to compare the performance of the various analysis codes and element types with respect to a problem which is applicable to radioactive material transport packages, and ultimately to develop a benchmark problem to qualify finite element analysis codes for the transport package design industry.

  3. Fast voxel-based 2D/3D registration algorithm using a volume rendering method based on the shear-warp factorization

    NASA Astrophysics Data System (ADS)

    Weese, Juergen; Goecke, Roland; Penney, Graeme P.; Desmedt, Paul; Buzug, Thorsten M.; Schumann, Heidrun

    1999-05-01

    2D/3D registration makes it possible to use pre-operative CT scans for navigation purposes during X-ray fluoroscopy guided interventions. We present a fast voxel-based method for this registration task, which uses a recently introduced similarity measure (pattern intensity). This measure is especially suitable for 2D/3D registration, because it is robust with respect to structures such as a stent visible in the X-ray fluoroscopy image but not in the CT scan. The method uses only a part of the CT scan for the generation of digitally reconstructed radiographs (DRRs) to accelerate their computation. Nevertheless, computation time is crucial for intra-operative application and a further speed-up is required, because numerous DRRs must be computed. For that reason, the suitability of different volume rendering methods for 2D/3D registration has been investigated. A method based on the shear-warp factorization of the viewing transformation turned out to be especially suitable and builds the basis of the registration algorithm. The algorithm has been applied to images of a spine phantom and to clinical images. For comparison, registration results have been calculated using ray-casting. The shear-warp factorization based rendering method accelerates registration by a factor of up to seven compared to ray-casting without degrading registration accuracy. Using a vertebra as feature for registration, computation time is in the range of 3-4s (Sun UltraSparc, 300 MHz) which is acceptable for intra-operative application.

  4. Verification and benchmarking of MAGNUM-2D: a finite element computer code for flow and heat transfer in fractured porous media

    SciTech Connect

    Eyler, L.L.; Budden, M.J.

    1985-03-01

    The objective of this work is to assess prediction capabilities and features of the MAGNUM-2D computer code in relation to its intended use in the Basalt Waste Isolation Project (BWIP). This objective is accomplished through a code verification and benchmarking task. Results are documented which support correctness of prediction capabilities in areas of intended model application. 10 references, 43 figures, 11 tables.

  5. A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation

    SciTech Connect

    Banks, J W; Hittinger, J A

    2009-11-24

    Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.

  6. A finite volume discretization of the pressure gradient force using analytic integration

    NASA Astrophysics Data System (ADS)

    Adcroft, Alistair; Hallberg, Robert; Harrison, Matthew

    Layered ocean models can exhibit spurious thermobaric instability if the compressibility of sea water is not treated accurately enough. We find that previous solutions to this problem are inadequate for simulations of a changing climate. We propose a new discretization of the pressure gradient acceleration using the finite volume method. In this method, the pressure gradient acceleration is exhibited as the difference of the integral "contact" pressure acting on the edges of a finite volume. This integral "contact" pressure can be calculated analytically by choosing a tractable equation of state. The result is a discretization that has zero truncation error for an isothermal and isohaline layer and does not exhibit the spurious thermobaric instability.

  7. Image forces on 3d dislocation structures in crystals of finite volume

    SciTech Connect

    El-Azab, A.

    1999-07-01

    The present work aims at studying the image stress and image Peach-Koehler force fields for three-dimensional dislocation configurations in a single crystal of finite volume. It is shown that the image stress field is significant within the entire crystal volume, and that the image Peach-Koehler force can be of the same order of magnitude as the direct interaction force calculated from the infinite domain solution. The results demonstrate that image stress gives rise to long-range interaction forces that are important in meso-scale dynamics of dislocation structures.

  8. Image Forces on 3-D Dislocation Structures in Crystals of Finite Volume

    SciTech Connect

    El-Azab, Anter ); V.V. Bulatov

    1999-01-01

    The present work aims at studying the image stress and image Peach-Koehler force fields for three-dimensional dislocation configurations in a single crystal of finite volume. It is shown that the image stress field is significant within the entire crystal volume, and that the image Peach-Koehler force can be of the same order of magnitude as the direct interaction force calculated from the infinite domain solution. The results demonstrate that image stress gives rise to long-range interaction forces that are important in meso-scale dynamics of dislocation structures.

  9. A posteriori error estimates for finite volume approximations of elliptic equations on general surfaces

    SciTech Connect

    Ju, Lili; Tian, Li; Wang, Desheng

    2009-01-01

    In this paper, we present a residual-based a posteriori error estimate for the finite volume discretization of steady convection– diffusion–reaction equations defined on surfaces in R3, which are often implicitly represented as level sets of smooth functions. Reliability and efficiency of the proposed a posteriori error estimator are rigorously proved. Numerical experiments are also conducted to verify the theoretical results and demonstrate the robustness of the error estimator.

  10. TRIM: A finite-volume MHD algorithm for an unstructured adaptive mesh

    SciTech Connect

    Schnack, D.D.; Lottati, I.; Mikic, Z.

    1995-07-01

    The authors describe TRIM, a MHD code which uses finite volume discretization of the MHD equations on an unstructured adaptive grid of triangles in the poloidal plane. They apply it to problems related to modeling tokamak toroidal plasmas. The toroidal direction is treated by a pseudospectral method. Care was taken to center variables appropriately on the mesh and to construct a self adjoint diffusion operator for cell centered variables.

  11. Higher-Order, Space-Time Adaptive Finite Volume Methods: Algorithms, Analysis and Applications

    SciTech Connect

    Minion, Michael

    2014-04-29

    The four main goals outlined in the proposal for this project were: 1. Investigate the use of higher-order (in space and time) finite-volume methods for fluid flow problems. 2. Explore the embedding of iterative temporal methods within traditional block-structured AMR algorithms. 3. Develop parallel in time methods for ODEs and PDEs. 4. Work collaboratively with the Center for Computational Sciences and Engineering (CCSE) at Lawrence Berkeley National Lab towards incorporating new algorithms within existing DOE application codes.

  12. Finite volume calculation of three-dimensional potential flow around a propeller

    NASA Technical Reports Server (NTRS)

    Jou, W.-H.

    1982-01-01

    The finite volume scheme of Jameson (1977) is used to calculate potential flow around a propeller rotating at high speed. An H-type mesh is generated and used successfully in the calculations. A test calculation with a thick blade cross section shows that the present code is capable of computing the propeller flow at the advance Mach number 0.8. The possible physical mechanisms which may play an important role in the propeller aerodynamics are discussed.

  13. DAO's Next Generation Physical-Space/Finite-Volume Data Assimilation System: Formulation and Initial Evaluation

    NASA Technical Reports Server (NTRS)

    daSilva, A.; Lin. S.-J.; Dee, D.; Joiner, J.; Atlas, Robert (Technical Monitor)

    2001-01-01

    The Physical-space/Finite-volume Data Assimilation System (fvDAS) is the next generation global atmospheric data assimilation system in development at the Data Assimilation Office at NASA's Goddard Space Flight Center. It is based on a new finite-volume general circulation model jointly developed by NASA and NCAR, and on the Physical-Space Statistical Analysis System (PSAS) developed at the DAO. In this talk we will describe the general system formulation, the adaptive quality control and general aspects of the error covariance modeling. The NASA-NCAR GCM is a completely new model which replaces the CEOs GCM used in the previous GEOS-1/2/3 Data Assimilation systems. A particular configuration of adaptive Statistical Quality Control and the Physical-space Statistical Analysis System (PSAS) are currently implemented in DAO's operational Data Assimilation System. However, the unique finite-volume formulation of the NASA-NCAR GCM, combined with the generality of the observation-space formulation of PSAS, provides for a very simple and accurate model-analysis interface. The system assimilates a variety of conventional and satellite observations. In particular, TOVS Level 1B radiances are assimilated using a 1-D variational scheme, both in clear sky and cloudy conditions. Computationally, the fvDAS runs approximately 10 times faster than the operational GEOS-Terra system. We will show that the next-generation fvDAS has much improved observation-minus-6hr forecast (O-F) statistics, as well as 5-day forecast skills. Top of the atmosphere radiation fields are in closer agreement with CERES measurements, with realistic precipitation and moisture fields. We will also show that the finite-volume formulation of the fvDAS produce assimilated fields which are more suitable for driving constituent transport models.

  14. Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel; Wang, Z. J.; Kwak, Dochan (Technical Monitor)

    2002-01-01

    Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve

  15. An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE

    NASA Technical Reports Server (NTRS)

    Baysal, Oktay; Lessard, Victor R.

    1990-01-01

    The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.

  16. An adaptive mesh finite volume method for the Euler equations of gas dynamics

    NASA Astrophysics Data System (ADS)

    Mungkasi, Sudi

    2016-06-01

    The Euler equations have been used to model gas dynamics for decades. They consist of mathematical equations for the conservation of mass, momentum, and energy of the gas. For a large time value, the solution may contain discontinuities, even when the initial condition is smooth. A standard finite volume numerical method is not able to give accurate solutions to the Euler equations around discontinuities. Therefore we solve the Euler equations using an adaptive mesh finite volume method. In this paper, we present a new construction of the adaptive mesh finite volume method with an efficient computation of the refinement indicator. The adaptive method takes action automatically at around places having inaccurate solutions. Inaccurate solutions are reconstructed to reduce the error by refining the mesh locally up to a certain level. On the other hand, if the solution is already accurate, then the mesh is coarsened up to another certain level to minimize computational efforts. We implement the numerical entropy production as the mesh refinement indicator. As a test problem, we take the Sod shock tube problem. Numerical results show that the adaptive method is more promising than the standard one in solving the Euler equations of gas dynamics.

  17. A time accurate finite volume high resolution scheme for three dimensional Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing; Hsu, Andrew T.

    1989-01-01

    A time accurate, three-dimensional, finite volume, high resolution scheme for solving the compressible full Navier-Stokes equations is presented. The present derivation is based on the upwind split formulas, specifically with the application of Roe's (1981) flux difference splitting. A high-order accurate (up to the third order) upwind interpolation formula for the inviscid terms is derived to account for nonuniform meshes. For the viscous terms, discretizations consistent with the finite volume concept are described. A variant of second-order time accurate method is proposed that utilizes identical procedures in both the predictor and corrector steps. Avoiding the definition of midpoint gives a consistent and easy procedure, in the framework of finite volume discretization, for treating viscous transport terms in the curvilinear coordinates. For the boundary cells, a new treatment is introduced that not only avoids the use of 'ghost cells' and the associated problems, but also satisfies the tangency conditions exactly and allows easy definition of viscous transport terms at the first interface next to the boundary cells. Numerical tests of steady and unsteady high speed flows show that the present scheme gives accurate solutions.

  18. A finite volume method solution for the bidomain equations and their application to modelling cardiac ischaemia.

    PubMed

    Johnston, Peter R

    2010-01-01

    This paper presents an implementation of the finite volume method with the aim of studying subendocardial ischaemia during the ST segment. In this implementation, based on hexahedral finite volumes, each quadrilateral sub-face is split into two triangles to improve the accuracy of the numerical integration in complex geometries and when fibre rotation is included. The numerical method is validated against previously published solutions obtained from slab and cylindrical models of the left ventricle with subendocardial ischaemia and no fibre rotation. Epicardial potential distributions are then obtained for a half-ellipsoid model of the left ventricle. In this case it is shown that for isotropic cardiac tissue the degree of subendocardial ischaemia does not affect the epicardial potential distribution, which is consistent with previous findings from analytical studies in simpler geometries. The paper also considers the behaviour of various preconditioners for solving numerically the resulting system of algebraic equations resulting from the implementation of the finite volume method. It is observed that each geometry considered has its own optimal preconditioner. PMID:19639486

  19. Analysis of acoustic networks including cavities by means of a linear finite volume method

    NASA Astrophysics Data System (ADS)

    Torregrosa, A. J.; Broatch, A.; Gil, A.; Moreno, D.

    2012-09-01

    A procedure allowing for the analysis of complex acoustic networks, including three-dimensional cavities described in terms of zero-dimensional equivalent elements, is presented and validated. The procedure is based on the linearization of the finite volume method often used in gas-dynamics, which is translated into an acoustic network comprising multi-ports accounting for mass exchanges between the finite volumes, and equivalent 2-ports describing momentum exchange across the volume surfaces. The application of the concept to a one-dimensional case shows that it actually converges to the exact analytical solution when a sufficiently large number of volumes are considered. This has allowed the formulation of an objective criterion for the choice of a mesh providing results with a prefixed error up to a certain Helmholtz number, which has been generalized to three-dimensional cases. The procedure is then applied to simple but relevant three-dimensional geometries in the absence of a mean flow, showing good agreement with experimental and other computational results.

  20. On 3-D inelastic analysis methods for hot section components. Volume 1: Special finite element models

    NASA Technical Reports Server (NTRS)

    Nakazawa, S.

    1987-01-01

    This Annual Status Report presents the results of work performed during the third year of the 3-D Inelastic Analysis Methods for Hot Section Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of new computer codes that permit more accurate and efficient three-dimensional analysis of selected hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components. This report is presented in two volumes. Volume 1 describes effort performed under Task 4B, Special Finite Element Special Function Models, while Volume 2 concentrates on Task 4C, Advanced Special Functions Models.

  1. WLS-ENO: Weighted-least-squares based essentially non-oscillatory schemes for finite volume methods on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Liu, Hongxu; Jiao, Xiangmin

    2016-06-01

    ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth solutions. For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities. For unstructured meshes, which are needed for complex geometries, similar schemes are required but they are much more challenging. We propose a new family of non-oscillatory schemes, called WLS-ENO, in the context of solving hyperbolic conservation laws using finite-volume methods over unstructured meshes. WLS-ENO is derived based on Taylor series expansion and solved using a weighted least squares formulation. Unlike other non-oscillatory schemes, the WLS-ENO does not require constructing sub-stencils, and hence it provides a more flexible framework and is less sensitive to mesh quality. We present rigorous analysis of the accuracy and stability of WLS-ENO, and present numerical results in 1-D, 2-D, and 3-D for a number of benchmark problems, and also report some comparisons against WENO.

  2. Solving transient conduction and radiation heat transfer problems using the lattice Boltzmann method and the finite volume method

    SciTech Connect

    Mishra, Subhash C. . E-mail: scm_iitg@yahoo.com; Roy, Hillol K.

    2007-04-10

    The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The finite volume method (FVM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the FVM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 1-D planar and 2-D rectangular geometries were considered. In order to establish the suitability of the LBM, the energy equations of the two problems were also solved using the FVM of the computational fluid dynamics. The FVM used in the radiative heat transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FVM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the FVM for the radiative information, results were analyzed for the effects of various parameters such as the scattering albedo, the conduction-radiation parameter and the boundary emissivity. The results of the LBM-FVM combination were found to be in excellent agreement with the FVM-FVM combination. The number of iterations and CPU times in both the combinations were found comparable.

  3. A finite-volume module for simulating global all-scale atmospheric flows

    NASA Astrophysics Data System (ADS)

    Smolarkiewicz, Piotr K.; Deconinck, Willem; Hamrud, Mats; Kühnlein, Christian; Mozdzynski, George; Szmelter, Joanna; Wedi, Nils P.

    2016-06-01

    The paper documents the development of a global nonhydrostatic finite-volume module designed to enhance an established spectral-transform based numerical weather prediction (NWP) model. The module adheres to NWP standards, with formulation of the governing equations based on the classical meteorological latitude-longitude spherical framework. In the horizontal, a bespoke unstructured mesh with finite-volumes built about the reduced Gaussian grid of the existing NWP model circumvents the notorious stiffness in the polar regions of the spherical framework. All dependent variables are co-located, accommodating both spectral-transform and grid-point solutions at the same physical locations. In the vertical, a uniform finite-difference discretisation facilitates the solution of intricate elliptic problems in thin spherical shells, while the pliancy of the physical vertical coordinate is delegated to generalised continuous transformations between computational and physical space. The newly developed module assumes the compressible Euler equations as default, but includes reduced soundproof PDEs as an option. Furthermore, it employs semi-implicit forward-in-time integrators of the governing PDE systems, akin to but more general than those used in the NWP model. The module shares the equal regions parallelisation scheme with the NWP model, with multiple layers of parallelism hybridising MPI tasks and OpenMP threads. The efficacy of the developed nonhydrostatic module is illustrated with benchmarks of idealised global weather.

  4. Finite Volume Numerical Methods for Aeroheating Rate Calculations from Infrared Thermographic Data

    NASA Technical Reports Server (NTRS)

    Daryabeigi, Kamran; Berry, Scott A.; Horvath, Thomas J.; Nowak, Robert J.

    2003-01-01

    The use of multi-dimensional finite volume numerical techniques with finite thickness models for calculating aeroheating rates from measured global surface temperatures on hypersonic wind tunnel models was investigated. Both direct and inverse finite volume techniques were investigated and compared with the one-dimensional semi -infinite technique. Global transient surface temperatures were measured using an infrared thermographic technique on a 0.333-scale model of the Hyper-X forebody in the Langley Research Center 20-Inch Mach 6 Air tunnel. In these tests the effectiveness of vortices generated via gas injection for initiating hypersonic transition on the Hyper-X forebody were investigated. An array of streamwise orientated heating striations were generated and visualized downstream of the gas injection sites. In regions without significant spatial temperature gradients, one-dimensional techniques provided accurate aeroheating rates. In regions with sharp temperature gradients due to the striation patterns two-dimensional heat transfer techniques were necessary to obtain accurate heating rates. The use of the one-dimensional technique resulted in differences of 20% in the calculated heating rates because it did not account for lateral heat conduction in the model.

  5. An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions

    PubMed Central

    Xia, Guohua; Lin, Ching-Long

    2008-01-01

    A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated. PMID:18496602

  6. AnisWave 2D

    2004-08-01

    AnisWave2D is a 2D finite-difference code for a simulating seismic wave propagation in fully anisotropic materials. The code is implemented to run in parallel over multiple processors and is fully portable. A mesh refinement algorithm has been utilized to allow the grid-spacing to be tailored to the velocity model, avoiding the over-sampling of high-velocity materials that usually occurs in fixed-grid schemes.

  7. Control volume finite element method with multidimensional edge element Scharfetter-Gummel upwinding. Part 1, formulation.

    SciTech Connect

    Bochev, Pavel Blagoveston

    2011-06-01

    We develop a new formulation of the Control Volume Finite Element Method (CVFEM) with a multidimensional Scharfetter-Gummel (SG) upwinding for the drift-diffusion equations. The formulation uses standard nodal elements for the concentrations and expands the flux in terms of the lowest-order Nedelec H(curl; {Omega})-compatible finite element basis. The SG formula is applied to the edges of the elements to express the Nedelec element degree of freedom on this edge in terms of the nodal degrees of freedom associated with the endpoints of the edge. The resulting upwind flux incorporates the upwind effects from all edges and is defined at the interior of the element. This allows for accurate evaluation of integrals on the boundaries of the control volumes for arbitrary quadrilateral elements. The new formulation admits efficient implementation through a standard loop over the elements in the mesh followed by loops over the element nodes (associated with control volume fractions in the element) and element edges (associated with flux degrees of freedom). The quantities required for the SG formula can be precomputed and stored for each edge in the mesh for additional efficiency gains. For clarity the details are presented for two-dimensional quadrilateral grids. Extension to other element shapes and three dimensions is straightforward.

  8. Hurricane Forecasting with the High-resolution NASA Finite-volume General Circulation Model

    NASA Technical Reports Server (NTRS)

    Atlas, R.; Reale, O.; Shen, B.-W.; Lin, S.-J.; Chern, J.-D.; Putman, W.; Lee, T.; Yeh, K.-S.; Bosilovich, M.; Radakovich, J.

    2004-01-01

    A high-resolution finite-volume General Circulation Model (fvGCM), resulting from a development effort of more than ten years, is now being run operationally at the NASA Goddard Space Flight Center and Ames Research Center. The model is based on a finite-volume dynamical core with terrain-following Lagrangian control-volume discretization and performs efficiently on massive parallel architectures. The computational efficiency allows simulations at a resolution of a quarter of a degree, which is double the resolution currently adopted by most global models in operational weather centers. Such fine global resolution brings us closer to overcoming a fundamental barrier in global atmospheric modeling for both weather and climate, because tropical cyclones and even tropical convective clusters can be more realistically represented. In this work, preliminary results of the fvGCM are shown. Fifteen simulations of four Atlantic tropical cyclones in 2002 and 2004 are chosen because of strong and varied difficulties presented to numerical weather forecasting. It is shown that the fvGCM, run at the resolution of a quarter of a degree, can produce very good forecasts of these tropical systems, adequately resolving problems like erratic track, abrupt recurvature, intense extratropical transition, multiple landfall and reintensification, and interaction among vortices.

  9. An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

    NASA Astrophysics Data System (ADS)

    Aguirre, Miquel; Gil, Antonio J.; Bonet, Javier; Lee, Chun Hean

    2015-11-01

    A vertex centred Jameson-Schmidt-Turkel (JST) finite volume algorithm was recently introduced by the authors (Aguirre et al., 2014 [1]) in the context of fast solid isothermal dynamics. The spatial discretisation scheme was constructed upon a Lagrangian two-field mixed (linear momentum and the deformation gradient) formulation presented as a system of conservation laws [2-4]. In this paper, the formulation is further enhanced by introducing a novel upwind vertex centred finite volume algorithm with three key novelties. First, a conservation law for the volume map is incorporated into the existing two-field system to extend the range of applications towards the incompressibility limit (Gil et al., 2014 [5]). Second, the use of a linearised Riemann solver and reconstruction limiters is derived for the stabilisation of the scheme together with an efficient edge-based implementation. Third, the treatment of thermo-mechanical processes through a Mie-Grüneisen equation of state is incorporated in the proposed formulation. For completeness, the study of the eigenvalue structure of the resulting system of conservation laws is carried out to demonstrate hyperbolicity and obtain the correct time step bounds for non-isothermal processes. A series of numerical examples are presented in order to assess the robustness of the proposed methodology. The overall scheme shows excellent behaviour in shock and bending dominated nearly incompressible scenarios without spurious pressure oscillations, yielding second order of convergence for both velocities and stresses.

  10. Effects of finite volume on the KL – KS mass difference

    SciTech Connect

    Christ, N.  H.; Feng, X.; Martinelli, G.; Sachrajda, C.  T.

    2015-06-24

    Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the KL – KS mass difference ΔMK and the CP-violating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.

  11. Justification of the Nonlinear Schrödinger Equation for the Evolution of Gravity Driven 2D Surface Water Waves in a Canal of Finite Depth

    NASA Astrophysics Data System (ADS)

    Düll, Wolf-Patrick; Schneider, Guido; Wayne, C. Eugene

    2016-05-01

    In 1968 V.E. Zakharov derived the Nonlinear Schrödinger equation for the two-dimensional water wave problem in the absence of surface tension, that is, for the evolution of gravity driven surface water waves, in order to describe slow temporal and spatial modulations of a spatially and temporarily oscillating wave packet. In this paper we give a rigorous proof that the wave packets in the two-dimensional water wave problem in a canal of finite depth can be approximated over a physically relevant timespan by solutions of the Nonlinear Schrödinger equation.

  12. Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

    NASA Astrophysics Data System (ADS)

    Pathak, Harshavardhana S.; Shukla, Ratnesh K.

    2016-08-01

    A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of

  13. Modal analysis of delaminated composite plates using the finite element method and damage detection via combined Ritz/2D-wavelet analysis

    NASA Astrophysics Data System (ADS)

    Gallego, A.; Moreno-García, P.; Casanova, Cesar F.

    2013-06-01

    Structural studies to find defects (in particular delaminations) in composite plates have been very prevalent in the Structural Health Monitoring field. The present work develops a new method to detect delaminations in CFRP (Carbon Fiber Reinforced Polymer) plates. In this paper the method is validated with numerical simulations, which come to support its adequacy for use with real acquisition data. This is done firstly through the implementation of a delaminated plate finite element. Using the classical lamination plate theory, delamination is considered in the kinematic equations through jump functions and additional degrees of freedom. The element allows the introduction of nd delaminations through its thickness. Classical QMITC (Quadrilateral Mixed Interpolation Tensorial Components) and DKQ (Discrete Kirchhoff Quadrilateral) elements are used for the membrane and bending FEM (Finite Element Method) formulation. Second, using the vibration modes obtained with the FEM, a damage location technique based on the variational Ritz method and Wavelet Analysis is proposed. The approach has the advantage of requiring only damaged modes and not the healthy ones. Both FEM simulations and Ritz/Wavelet damage detection schemes are applied in an orthotropic CFRP plate with the stacking sequence [0/90]3S. In addition, the influence of delamination thickness position, boundary conditions and added noise (in order to simulate experimental measures) was studied.

  14. Influence of 2D Finite Element Modeling Assumptions on Debonding Prediction for Composite Skin-stiffener Specimens Subjected to Tension and Bending

    NASA Technical Reports Server (NTRS)

    Krueger, Ronald; Minguet, Pierre J.; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane strain elements as well as three different generalized plane strain type approaches were performed. The computed deflections, skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with lamination length. For more accurate predictions, however, a three-dimensional analysis is required.

  15. Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes

    NASA Technical Reports Server (NTRS)

    Jameson, A.; Schmidt, Wolfgang; Turkel, Eli

    1981-01-01

    A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to determine the steady transonic flow past an airfoil using an O mesh. Convergence to a steady state is accelerated by the use of a variable time step determined by the local Courant member, and the introduction of a forcing term proportional to the difference between the local total enthalpy and its free stream value.

  16. High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

    NASA Astrophysics Data System (ADS)

    McCorquodale, P.; Dorr, M. R.; Hittinger, J. A. F.; Colella, P.

    2015-05-01

    We present an approach to solving hyperbolic conservation laws by finite-volume methods on mapped multiblock grids, extending the approach of Colella, Dorr, Hittinger, and Martin (2011) [10] for grids with a single mapping. We consider mapped multiblock domains for mappings that are conforming at inter-block boundaries. By using a smooth continuation of the mapping into ghost cells surrounding a block, we reduce the inter-block communication problem to finding an accurate, robust interpolation into these ghost cells from neighboring blocks. We demonstrate fourth-order accuracy for the advection equation for multiblock coordinate systems in two and three dimensions.

  17. A new nonlinear finite volume scheme preserving positivity for diffusion equations

    NASA Astrophysics Data System (ADS)

    Sheng, Zhiqiang; Yuan, Guangwei

    2016-06-01

    In this paper we present a new nonlinear finite volume scheme preserving positivity for diffusion equations. The main feature of the scheme is the assumption that the values of auxiliary unknowns are nonnegative is avoided. Two nonnegative parameters are introduced to define a new nonlinear two-point flux, in which one point is the cell-center and the other is the midpoint of cell-edge. The final flux on the edge is obtained by the continuity of normal flux. Numerical results show that the accuracy of both solution and flux for our new scheme is superior to that of some existing monotone schemes.

  18. Simulation of viscous flows using a multigrid-control volume finite element method

    SciTech Connect

    Hookey, N.A.

    1994-12-31

    This paper discusses a multigrid control volume finite element method (MG CVFEM) for the simulation of viscous fluid flows. The CVFEM is an equal-order primitive variables formulation that avoids spurious solution fields by incorporating an appropriate pressure gradient in the velocity interpolation functions. The resulting set of discretized equations is solved using a coupled equation line solver (CELS) that solves the discretized momentum and continuity equations simultaneously along lines in the calculation domain. The CVFEM has been implemented in the context of both FMV- and V-cycle multigrid algorithms, and preliminary results indicate a five to ten fold reduction in execution times.

  19. Porous Substrate Effects on Thermal Flows Through a Rev-Scale Finite Volume Lattice Boltzmann Model

    NASA Astrophysics Data System (ADS)

    Zarghami, Ahad; Francesco, Silvia Di; Biscarini, Chiara

    2014-09-01

    In this paper, fluid flows with enhanced heat transfer in porous channels are investigated through a stable finite volume (FV) formulation of the thermal lattice Boltzmann method (LBM). Temperature field is tracked through a double distribution function (DDF) model, while the porous media is modeled using Brinkman-Forchheimer assumptions. The method is tested against flows in channels partially filled with porous media and parametric studies are conducted to evaluate the effects of various parameters, highlighting their influence on the thermo-hydrodynamic behavior.

  20. Explicit multistage finite volume procedure to solve the Euler equations for transonic flow

    NASA Astrophysics Data System (ADS)

    Rizzi, A.; Eriksson, L. E.

    A computational procedure for solving the Euler equations for transonic flow around aircraft upon an O-O mesh generated by transfinite interpolation is presented. An explicit time marching finite volume procedure solves the flow equations and features a nonreflecting far field boundary condition and an internal mechanism for temporal damping together with a model for artificial viscosity. Convergence to a steady state is studied, and results computed on the CYBER 205 vector processor are presented. The Euler equation model is found to predict the existence of a tip vortex created by flow separating from the downstream region of the tip of the M6 wing where the radius of curvature approaches zero.

  1. High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

    SciTech Connect

    McCorquodale, P. W.; Colella, P.; Dorr, M. R.; Hittinger, J. A. F.

    2015-01-13

    We present an approach to solving hyperbolic conservation laws by finite-volume methods on mapped multiblock grids, extending the approach of Colella, Dorr, Hittinger, and Martin (2011) [10] for grids with a single mapping. We consider mapped multiblock domains for mappings that are conforming at inter-block boundaries. By using a smooth continuation of the mapping into ghost cells surrounding a block, we reduce the inter-block communication problem to finding an accurate, robust interpolation into these ghost cells from neighboring blocks. Lastly, we demonstrate fourth-order accuracy for the advection equation for multiblock coordinate systems in two and three dimensions.

  2. Finite Volume Time Domain modelling of microwave breakdown and plasma formation in a metallic aperture

    NASA Astrophysics Data System (ADS)

    Hamiaz, Adnane; Klein, Rudy; Ferrieres, Xavier; Pascal, Olivier; Boeuf, Jean-Pierre; Poirier, Jean-Rene

    2012-08-01

    The modelling of plasma formation during microwave breakdown is a difficult task because of the strong non-linear coupling between Maxwell's equations and plasma equations, and of the large plasma density gradients that form during breakdown. An original Finite Volume Time Domain (FVTD) method has been developed to solve Maxwell's equations coupled with a simplified fluid plasma model and is described in this paper. This method is illustrated with the study of the shielding of a metallic aperture by the plasma generated by an incident high power electromagnetic wave. Typical results obtained with the FVTD method for this shielding problem are shown.

  3. Second order finite volume scheme for Maxwell's equations with discontinuous electromagnetic properties on unstructured meshes

    SciTech Connect

    Ismagilov, Timur Z.

    2015-02-01

    This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.

  4. Finite volume scheme with quadratic reconstruction on unstructured adaptive meshes applied to turbomachinery flows

    SciTech Connect

    Delanaye, M.; Essers, J.A.

    1997-04-01

    This paper presents a new finite volume cell-centered scheme for solving the two-dimensional Euler equations. The technique for computing the advective derivatives is based on a high-order Gauss quadrature and an original quadratic reconstruction of the conservative variables for each control volume. A very sensitive detector identifying discontinuity regions switches the scheme to a TVD scheme, and ensures the monotonicity of the solution. The code uses unstructured meshes whose cells are polygons with any number of edges. A mesh adaptation based on cell division is performed in order to increase the resolution of shocks. The accuracy, insensitivity to grid distortions, and shock capturing properties of the scheme are demonstrated for different cascade flow computations.

  5. Simulation of fatigue crack closure behavior under variable-amplitude loading by a 2D finite element analysis based on the most appropriate mesh size concept

    SciTech Connect

    Park, S.J.; Song, J.H.

    1999-07-01

    A two-dimensional elastic-plastic finite element analysis is performed for plane stress conditions with 4-node isoparametric elements to investigate the closure behavior under various variable-amplitude loading, i.e., single overloading, Hi-Lo block loading, and narrow- and wide-band random loading. The closure behavior under single overloading and Hi-Lo block loading can be well simulated by applying the concept of the most appropriate mesh size that will provide numerical results consistent with experimental data under constant-amplitude loading. It is found that the crack opening load under random loading may be predicted approximately by replacing the complicated random load history with the appropriate equivalent, simplified variable load history.

  6. Form finding and analysis of extensible membranes attached to 2-D and 3-D frames intended for micro air vehicles via experimentally validated finite element methods

    NASA Astrophysics Data System (ADS)

    Abudaram, Yaakov Jack

    This work is concerned with a new method to apply consistent and known pretension to silicone rubber membranes intended for micro air vehicles as well as an understanding in the science of developed pre-tension in membranes constrained by 2- D and 3-D frames and structures. Pre-tension has a marked effect on the static and dynamic response of membrane wings and controls the overall deflections, as such control and measurement of the membrane pre-tension is important. Two different 2-D frame geometries were fabricated to evaluate the technique. For open-cell frames, the pretension was not uniform, whereas it was for closed-cell frames. Results show developed full-field stress and strain fields as a function of membrane attachment temperature and frame geometry along with experimental iterations to prove repeatability. The membranes can be stretched to a specific pretension according to the temperature at which it adheres to frames. Strain fields in membranes attached to 3-D frames at various temperatures are modeled through FEA utilizing Abaqus to be able to predict the developed membrane deformations, stresses, and strains. Rigid frames with various curvatures are built via appropriate molds and then adhered to silicone rubber membranes and elevated to various temperatures to achieve different pre-strains for experimental validation. Additional experiments are conducted for more complex frame geometries involving both convex and concave topologies embedded within frames. Results are then compared with the Abaqus outputs to validate the accuracy of the FEA model. Highly compliant wings have been used for MAV platforms, where the wing structure is determined by some combination of carbon fiber composites and a membrane skin, adhered in between the layers of composite material. Another new technique of attaching membranes firmly on wing structures is introduced, which involves the application of a technology known as corona treatment coupled with another method of

  7. A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

    NASA Technical Reports Server (NTRS)

    Majumdar, Alok

    1998-01-01

    An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

  8. Application of Local Discretization Methods in the NASA Finite-Volume General Circulation Model

    NASA Technical Reports Server (NTRS)

    Yeh, Kao-San; Lin, Shian-Jiann; Rood, Richard B.

    2002-01-01

    We present the basic ideas of the dynamics system of the finite-volume General Circulation Model developed at NASA Goddard Space Flight Center for climate simulations and other applications in meteorology. The dynamics of this model is designed with emphases on conservative and monotonic transport, where the property of Lagrangian conservation is used to maintain the physical consistency of the computational fluid for long-term simulations. As the model benefits from the noise-free solutions of monotonic finite-volume transport schemes, the property of Lagrangian conservation also partly compensates the accuracy of transport for the diffusion effects due to the treatment of monotonicity. By faithfully maintaining the fundamental laws of physics during the computation, this model is able to achieve sufficient accuracy for the global consistency of climate processes. Because the computing algorithms are based on local memory, this model has the advantage of efficiency in parallel computation with distributed memory. Further research is yet desirable to reduce the diffusion effects of monotonic transport for better accuracy, and to mitigate the limitation due to fast-moving gravity waves for better efficiency.

  9. A finite-volume ELLAM for three-dimensional solute-transport modeling

    USGS Publications Warehouse

    Russell, T.F.; Heberton, C.I.; Konikow, L.F.; Hornberger, G.Z.

    2003-01-01

    A three-dimensional finite-volume ELLAM method has been developed, tested, and successfully implemented as part of the U.S. Geological Survey (USGS) MODFLOW-2000 ground water modeling package. It is included as a solver option for the Ground Water Transport process. The FVELLAM uses space-time finite volumes oriented along the streamlines of the flow field to solve an integral form of the solute-transport equation, thus combining local and global mass conservation with the advantages of Eulerian-Lagrangian characteristic methods. The USGS FVELLAM code simulates solute transport in flowing ground water for a single dissolved solute constituent and represents the processes of advective transport, hydrodynamic dispersion, mixing from fluid sources, retardation, and decay. Implicit time discretization of the dispersive and source/sink terms is combined with a Lagrangian treatment of advection, in which forward tracking moves mass to the new time level, distributing mass among destination cells using approximate indicator functions. This allows the use of large transport time increments (large Courant numbers) with accurate results, even for advection-dominated systems (large Peclet numbers). Four test cases, including comparisons with analytical solutions and benchmarking against other numerical codes, are presented that indicate that the FVELLAM can usually yield excellent results, even if relatively few transport time steps are used, although the quality of the results is problem-dependent.

  10. Benchmarking of a New Finite Volume Shallow Water Code for Accurate Tsunami Modelling

    NASA Astrophysics Data System (ADS)

    Reis, Claudia; Clain, Stephane; Figueiredo, Jorge; Baptista, Maria Ana; Miranda, Jorge Miguel

    2015-04-01

    Finite volume methods used to solve the shallow-water equation with source terms receive great attention on the two last decades due to its fundamental properties: the built-in conservation property, the capacity to treat correctly discontinuities and the ability to handle complex bathymetry configurations preserving the some steady-state configuration (well-balanced scheme). Nevertheless, it is still a challenge to build an efficient numerical scheme, with very few numerical artifacts (e.g. numerical diffusion) which can be used in an operational environment, and are able to better capture the dynamics of the wet-dry interface and the physical phenomenon that occur in the inundation area. We present here a new finite volume code and benchmark it against analytical and experimental results, and we test the performance of the code in the complex topographic of the Tagus Estuary, close to Lisbon, Portugal. This work is funded by the Portugal-France research agreement, through the research project FCT-ANR/MAT-NAN/0122/2012.

  11. Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

    NASA Astrophysics Data System (ADS)

    Lucini, B.; Patella, A.; Ramos, A.; Tantalo, N.

    2016-02-01

    In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C⋆ boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C⋆ boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in a fully consistent fashion without relying on gauge fixing and without peculiar complications. This class includes single particle states of most stable hadrons. We also calculate finite-volume corrections to the mass of stable charged particles and show that these are much smaller than in non-local formulations of QED.

  12. Coupled discrete element and finite volume solution of two classical soil mechanics problems

    SciTech Connect

    Chen, Feng; Drumm, Eric; Guiochon, Georges A

    2011-01-01

    One dimensional solutions for the classic critical upward seepage gradient/quick condition and the time rate of consolidation problems are obtained using coupled routines for the finite volume method (FVM) and discrete element method (DEM), and the results compared with the analytical solutions. The two phase flow in a system composed of fluid and solid is simulated with the fluid phase modeled by solving the averaged Navier-Stokes equation using the FVM and the solid phase is modeled using the DEM. A framework is described for the coupling of two open source computer codes: YADE-OpenDEM for the discrete element method and OpenFOAM for the computational fluid dynamics. The particle-fluid interaction is quantified using a semi-empirical relationship proposed by Ergun [12]. The two classical verification problems are used to explore issues encountered when using coupled flow DEM codes, namely, the appropriate time step size for both the fluid and mechanical solution processes, the choice of the viscous damping coefficient, and the number of solid particles per finite fluid volume.

  13. A mass-conservative finite volume predictor-corrector solution of the 1D Richards' equation

    NASA Astrophysics Data System (ADS)

    Lai, Wencong; Ogden, Fred L.

    2015-04-01

    Numerical solution of the Richards' equation (RE) in variably saturated soils continues to be a challenge due to its highly non-linear behavior. This is particularly true as soils approach saturation and the behavior of the fundamental partial differential equation changes from elliptic to parabolic. In this paper, a finite volume predictor-corrector method with adaptive time-stepping was developed to solve the 1D vertical RE. The numerical method was mass-conservative and non-iterative. In the predictor step, the pressure head-based form of the RE was solved using the cell-centered finite volume method and the pressure head was updated. In the corrector step, the soil water content was calculated by solving the mixed form RE. Five different schemes to evaluate the inter-cell hydraulic conductivity were investigated. The robustness and accuracy of the numerical model were demonstrated through simulation of experimental tests, including free drainage, field infiltration into wet and dry soils, and laboratory infiltration with falling water table. Numerical results were compared against laboratory measurements, simulation results from the Hydrus-1D program, or analytical solution when available. Results showed that the developed scheme is robust and accurate in simulating variably saturated flows with various boundary conditions. The arithmetic mean and Szymkiewicz's mean of inter-cell hydraulic conductivity performed better than other methods especially in the case of infiltration into very dry soil.

  14. A time-split finite-volume algorithm for three-dimensional flow-field simulation

    NASA Technical Reports Server (NTRS)

    Hung, C. M.; Kordulla, W.

    1983-01-01

    A general finite-volume algorithm is developed for solving three-dimensional, time-dependent, compressible Navier-Stokes equations for high Reynolds number flows over an arbitrary geometry. This algorithm adapts MacCormack's (1982) explicit-implicit scheme to a time-split, three-dimensional finite-volume concept in a general coordinate system. It is shown that the thin-layer approximation in all three spatial directions significantly reduces the evaluation of viscous terms and allows the algorithm to solve more complicated geometries with all boundaries in two or all three directions. The calculated results using this method are found to be in good agreement with the experimental measurements of a blunt-fin induced shock wave and boundary-layer interaction problems. Observations of the existence of peak pressure, primary horseshoe and secondary vortices, and reversed supersonic zones show that computational fluid dynamics can effectively supplement the wind tunnel tests for aerodynamic design as well as for understanding basic fluid dynamics.

  15. Multiphase flow through porous media: an adaptive control volume finite element formulation

    NASA Astrophysics Data System (ADS)

    Mostaghimi, P.; Tollit, B.; Gorman, G.; Neethling, S.; Pain, C.

    2012-12-01

    Accurate modeling of multiphase flow in porous media is of great importance in a wide range of applications in science and engineering. We have developed a numerical scheme which employs an implicit pressure explicit saturation (IMPES) algorithm for the temporal discretization of the governing equations. The saturation equation is spatially discretized using a node centered control volume method on an unstructured finite element mesh. The face values are determined through an upwind scheme. The pressure equation is spatially discretized using a continuous control volume finite element method (CV-FEM) to achieve consistency with the discrete saturation equation. The numerical simulation is implemented in Fluidity, an open source and general purpose fluid simulator capable of solving a number of different governing equations for fluid flow and accompanying field equations on arbitrary unstructured meshes. The model is verified against the Buckley-Leverett problem where a quasi-analytical solution is available. We discuss the accuracy and the order of convergence of the scheme. We demonstrate the scheme for modeling multiphase flow in a synthetic heterogeneous porous medium along with the use of anisotropic mesh adaptivity to control local solution errors and increase computational efficiency. The adaptive method is also used to simulate two-phase flow in heap leaching, an industrial mining process, where the flow of the leaching solution is gravitationally dominated. Finally we describe the extension of the developed numerical scheme for simulation of flow in multiscale fractured porous media and its capability to model the multiscale characterization of flow in full scale.

  16. Radiative heat transfer in periodic geometries using a finite volume scheme

    SciTech Connect

    Mathur, S.R.; Murthy, J.Y.

    1999-05-01

    Periodic flow and heat transfer occurs in a number of engineering applications. Heat exchangers employ repeating units of fins, dimples, or indentations to increase heat transfer area and improve heat exchanger performance. In many applications, rotational periodicity may be invoked. Burners and combustors, for example, employ swirler vanes and secondary air inlets which destroy axisymmetry. However, it is frequently possible to restrict computations to a single rotationally periodic module and thus to reduce computational time. It would be useful to devise general-purpose calculation procedures for radiative heat transfer in arbitrary geometries with arbitrary rotational and translational periodicity. Here, a procedure for computing radiative heat transfer in translationally and rotationally periodic geometries is presented. The finite volume scheme is applied to meshes composed of arbitrary polyhedral control volumes. The angular domain is discretized into a finite number of control angles over which radiant energy is conserved. At periodic boundaries, control angle overhand occurs because of the misalignment of the arbitrary periodic face with the global angular discretization and due to the arbitrary rotation of adjacent modules with respect to each other. A discretization scheme using control angle pixelation is developed to conservatively transfer radiant energy between adjacent modules. The method is tested for a variety of radiation problems and shown to perform satisfactorily.

  17. The numerical prediction of planar viscoelastic contraction flows using the pom pom model and higher-order finite volume schemes

    NASA Astrophysics Data System (ADS)

    Aguayo, J. P.; Phillips, P. M.; Phillips, T. N.; Tamaddon-Jahromi, H. R.; Snigerev, B. A.; Webster, M. F.

    2007-01-01

    This study investigates the numerical solution of viscoelastic flows using two contrasting high-order finite volume schemes. We extend our earlier work for Poiseuille flow in a planar channel and the single equation form of the extended pom-pom (SXPP) model [M. Aboubacar, J.P. Aguayo, P.M. Phillips, T.N. Phillips, H.R. Tamaddon-Jahromi, B.A. Snigerev, M.F. Webster, Modelling pom-pom type models with high-order finite volume schemes, J. Non-Newtonian Fluid Mech. 126 (2005) 207-220], to determine steady-state solutions for planar 4:1 sharp contraction flows. The numerical techniques employed are time-stepping algorithms: one of hybrid finite element/volume type, the other of pure finite volume form. The pure finite volume scheme is a staggered-grid cell-centred scheme based on area-weighting and a semi-Lagrangian formulation. This may be implemented on structured or unstructured rectangular grids, utilising backtracking along the solution characteristics in time. For the hybrid scheme, we solve the momentum-continuity equations by a fractional-staged Taylor-Galerkin pressure-correction procedure and invoke a cell-vertex finite volume scheme for the constitutive law. A comparison of the two finite volume approaches is presented, concentrating upon the new features posed by the pom-pom class of models in this context of non-smooth flows. Here, the dominant feature of larger shear and extension in the entry zone influences both stress and stretch, so that larger stretch develops around the re-entrant corner zone as Weissenberg number increases, whilst correspondingly stress levels decline.

  18. Regional subsidence modelling in Murcia city (SE Spain) using 1-D vertical finite element analysis and 2-D interpolation of ground surface displacements

    NASA Astrophysics Data System (ADS)

    Tessitore, S.; Fernández-Merodo, J. A.; Herrera, G.; Tomás, R.; Ramondini, M.; Sanabria, M.; Duro, J.; Mulas, J.; Calcaterra, D.

    2015-11-01

    Subsidence is a hazard that may have natural or anthropogenic origin causing important economic losses. The area of Murcia city (SE Spain) has been affected by subsidence due to groundwater overexploitation since the year 1992. The main observed historical piezometric level declines occurred in the periods 1982-1984, 1992-1995 and 2004-2008 and showed a close correlation with the temporal evolution of ground displacements. Since 2008, the pressure recovery in the aquifer has led to an uplift of the ground surface that has been detected by the extensometers. In the present work an elastic hydro-mechanical finite element code has been used to compute the subsidence time series for 24 geotechnical boreholes, prescribing the measured groundwater table evolution. The achieved results have been compared with the displacements estimated through an advanced DInSAR technique and measured by the extensometers. These spatio-temporal comparisons have showed that, in spite of the limited geomechanical data available, the model has turned out to satisfactorily reproduce the subsidence phenomenon affecting Murcia City. The model will allow the prediction of future induced deformations and the consequences of any piezometric level variation in the study area.

  19. Characteristic investigation of 2D photonic crystals with full material anisotropy under out-of-plane propagation and liquid-crystal-filled photonic-band-gap-fiber applications using finite element methods.

    PubMed

    Hsu, Sen-ming; Chang, Hung-chun

    2008-12-22

    To effectively investigate the fundamental characteristics of two-dimensional (2D) photonic crystals (PCs) with arbitrary 3D material anisotropy under the out-of-plane wave propagation, we establish a full-vectorial finite element method based eigenvalue algorithm to perform related analysis correctly. The band edge diagrams can be conveniently constructed from the band structures of varied propagation constants obtained from the algorithm, which is helpful for the analysis and design of photonic ban gap (PBG) fibers. Several PCs are analyzed to demonstrate the correctness of this numerical model. Our analysis results for simple PCs are checked with others' ones using different methods, including the transfer matrix method, the finite-difference frequency-domain (FDFD) method, and the plane-wave expansion method. And the validity of those for the most complex PC with arbitrary 3D anisotropy is supported by related liquid-crystal-filled PBG fiber mode analysis, which demonstrates the dependence of transmission properties on the PBGs, employing a full-vectorial finite element beam propagation method (FE-BPM). PMID:19104565

  20. A 2D magnetic and 3D mechanical coupled finite element model for the study of the dynamic vibrations in the stator of induction motors

    NASA Astrophysics Data System (ADS)

    Martinez, J.; Belahcen, A.; Detoni, J. G.

    2016-01-01

    This paper presents a coupled Finite Element Model in order to study the vibrations in induction motors under steady-state. The model utilizes a weak coupling strategy between both magnetic and elastodynamic fields on the structure. Firstly, the problem solves the magnetic vector potential in an axial cut and secondly the former solution is coupled to a three dimensional model of the stator. The coupling is performed using projection based algorithms between the computed magnetic solution and the three-dimensional mesh. The three-dimensional model of the stator includes both end-windings and end-shields in order to give a realistic picture of the motor. The present model is validated using two steps. Firstly, a modal analysis hammer test is used to validate the material characteristic of this complex structure and secondly an array of accelerometer sensors is used in order to study the rotating waves using multi-dimensional spectral techniques. The analysis of the radial vibrations presented in this paper firstly concludes that slot harmonic components are visible when the motor is loaded. Secondly, the multidimensional spectrum presents the most relevant mechanical waves on the stator such as the ones produced by the space harmonics or the saturation of the iron core. The direct retrieval of the wave-number in a multi-dimensional spectrum is able to show the internal current distribution in a non-intrusive way. Experimental results for healthy induction motors are showing mechanical imbalances in a multi-dimensional spectrum in a more straightforward form.

  1. Solution strategies for finite elements and finite volumes methods applied to flow and heat transfer problem in U-shaped geothermal exchangers

    NASA Astrophysics Data System (ADS)

    Egidi, Nadaniela; Giacomini, Josephin; Maponi, Pierluigi

    2016-06-01

    Matter of this paper is the study of the flow and the corresponding heat transfer in a U-shaped heat exchanger. We propose a mathematical model that is formulated as a forced convection problem for incompressible and Newtonian fluids and results in the unsteady Navier-Stokes problem. In order to get a solution, we discretise the equations with both the Finite Elements Method and the Finite Volumes Method. These procedures give rise to a non-symmetric indefinite quadratic system of equations. Thus, three regularisation techniques are proposed to make approximations effective and ideas to compare their results are provided.

  2. A software implementation for detailed volume conductor modelling in electrophysiology using finite difference method.

    PubMed

    Kauppinen, P; Hyttinen, J; Laarne, P; Malmivuo, J

    1999-02-01

    There is an evolving need for new information available by employing patient tailored anatomically accurate computer models of the electrical properties of the human body. Because construction of a computer model can be difficult and laborious to perform sufficiently well, devised models have varied greatly in the level of anatomical accuracy incorporated in them. This has restricted the validity of conducted simulations. In the present study, a versatile software package was developed to transform anatomic voxel data into accurate finite difference method volume conductor models conveniently and in a short time. The package includes components for model construction, simulation, visualisation and detailed analysis of simulation output based on volume conductor theory. Due to the methods developed, models can comprise more anatomical details than the prior computer models. Several models have been constructed, for example, a highly detailed 3-D anatomically accurate computer model of the human thorax as a volume conductor utilising the US National Library of Medicine's (NLM) Visible Human Man (VHM) digital anatomy data. Based on the validation runs the developed software package is readily applicable in analysis of a wide range of bioelectric field problems. PMID:10092033

  3. JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; Yucca Mountain Site Characterization Project

    SciTech Connect

    Biffle, J.H.; Blanford, M.L.

    1994-05-01

    JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.

  4. Face transformation with harmonic models by the finite-volume method with delaunay triangulation.

    PubMed

    Li, Zi-Cai; Chiang, John Y; Suen, Ching Y

    2010-12-01

    To carry out face transformation, this paper presents new numerical algorithms, which consist of two parts, namely, the harmonic models for changes of face characteristics and the splitting techniques for grayness transition. The main method in this paper is a combination of the finite-volume method (FVM) with Delaunay triangulation to solve the Laplace equations in the harmonic transformation of face images. The advantages of the FVM with Delaunay triangulation are given as follows: 1) easy to formulate the linear algebraic equations; 2) good in retaining the pertinent geometric and physical need; and 3) less central processing unit time needed. Numerical and graphical experiments have been conducted for the face transformation from a female (woman) to a male (man), and vice versa. The computed sequential errors are O(N⁻³/²), where N² is the division number of a pixel into subpixels. These computed errors coincide with the analysis on the splitting-shooting method (SSM) with piecewise constant interpolation in the previous paper of Li and Bai. In computation, the average absolute errors of restored pixel grayness can be smaller than 2 out of 256 grayness levels. The FVM is as simple as the finite-difference method (FDM) and as flexible as the finite-element method (FEM). Hence, the FVM is particularly useful when dealing with large face images with a huge number of pixels in shape distortion. The numerical transformation of face images in this paper can be used not only in pattern recognition but also in resampling, image morphing, and computer animation. PMID:20363682

  5. Long-time behavior of a finite volume discretization for a fourth order diffusion equation

    NASA Astrophysics Data System (ADS)

    Maas, Jan; Matthes, Daniel

    2016-07-01

    We consider a non-standard finite-volume discretization of a strongly non-linear fourth order diffusion equation on the d-dimensional cube, for arbitrary d≥slant 1 . The scheme preserves two important structural properties of the equation: the first is the interpretation as a gradient flow in a mass transportation metric, and the second is an intimate relation to a linear Fokker–Planck equation. Thanks to these structural properties, the scheme possesses two discrete Lyapunov functionals. These functionals approximate the entropy and the Fisher information, respectively, and their dissipation rates converge to the optimal ones in the discrete-to-continuous limit. Using the dissipation, we derive estimates on the long-time asymptotics of the discrete solutions. Finally, we present results from numerical experiments which indicate that our discretization is able to capture significant features of the complex original dynamics, even with a rather coarse spatial resolution.

  6. A scalable implementation of a finite-volume dynamical core in the Community Atmosphere Model

    SciTech Connect

    Mirin, A A; Sawyer, W B

    2004-09-24

    A distributed memory message-passing parallel implementation of a finite-volume discretization of the primitive equations in the Community Atmosphere Model is presented. Due to the data dependencies resulting from the polar singularity of the latitude-longitude coordinate system, we employ two separate domain decompositions within the dynamical core--one in latitude/level space, and the other in longitude/latitude space. This requires that the data be periodically redistributed between these two decompositions. In addition, the domains contain halo regions that cover the nearest neighbor data dependencies. A combination of several techniques, such as one-sided communication and multithreading, are presented to optimize data movements. The resulting algorithm is shown to scale to very large machine configurations, even for relatively coarse resolutions.

  7. Hybrid, explicit-implicit, finite-volume schemes on unstructured grids for unsteady compressible flows

    NASA Astrophysics Data System (ADS)

    Timofeev, Evgeny; Norouzi, Farhang

    2016-06-01

    The motivation for using hybrid, explicit-implicit, schemes rather than fully implicit or explicit methods for some unsteady high-speed compressible flows with shocks is firstly discussed. A number of such schemes proposed in the past are briefly overviewed. A recently proposed hybridization approach is then introduced and used for the development of a hybrid, explicit-implicit, TVD (Total Variation Diminishing) scheme of the second order in space and time on smooth solutions in both, explicit and implicit, modes for the linear advection equation. Further generalizations of this finite-volume method for the Burgers, Euler and Navier-Stokes equations discretized on unstructured grids are mentioned in the concluding remarks.

  8. A vertex-based finite-volume algorithm for the Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Chakrabartty, S. K.; Dhanalakshmi, K.

    1993-07-01

    A vertex-based, finite-volume algorithm has been developed to solve the Reynolds-averaged Navier-Stokes equations without thin-layer approximation. An explicit, five-stage Runge-Kutta, time-stepping scheme has been used for time integration along with different acceleration techniques to reach the steady state. A code employing multi-block grid structure has been developed. This code can accept any type of grid topology. As test cases, the turbulent flow past RAE-2822 and NACA-0012 airfoils, and the laminar flow past a cropped delta wing at ten degrees angle of attack have been computed and the results compared with available numerical and experimental results. The Baldwin-Lomax turbulence model has been used in the case of turbulent flows.

  9. Application of a finite volume based method of lines to turbulent forced convection in circular tubes

    SciTech Connect

    Campo, A.; Tebeest, K.; Lacoa, U.; Morales, J.C.

    1996-10-01

    A semianalytic analysis of in-tube turbulent forced convection is performed whose special computational feature is the combination of the method of lines, the finite volume technique, and a radial coordinate transformation. First, a numerical solution of the momentum equation was obtained by a simple Runge-Kutta integration scheme. Second, the energy equation was reformulated into a system of ordinary differential equations of first order. Each equation in the system controls the temperature along a line in a mesh consisting of concentric lines. Reliable analytic solutions for the temperature distribution of fluids in the region of thermal development can be determined for combinations of Reynolds and Prandtl numbers. Predicted results for the distributions of mean bulk temperature and local Nusselt numbers for air, water, and oils compare satisfactorily with the available experimental data.

  10. Finite volume methods for submarine debris flow with Herschel-Bulkley rheology

    NASA Astrophysics Data System (ADS)

    Kim, Jihwan; Issler, Dieter

    2015-04-01

    Submarine landslides can impose great danger to the underwater structures and generate destructive waves. The Herschel-Bulkley rheological model is known to be appropriate for describing the nonlinear viscoplastic behavior of the debris flow. The numerical implementation of the depth-averaged Herschel-Bulkley models such as BING has so-far been limited to the 1-dimensional Lagrangian coordinate system. In this work, we develop numerical schemes with the finite volume methods in the Eulerian coordinates. We provide parameter sensitivity analysis and demonstrate how common ad-hoc assumptions such as including a minimum shear layer depth influence the modeling of the landslide dynamics. The possibility of adding hydrodynamic resistance forces, hydroplaning, and remolding into this Eulerian framework is also discussed. Finally, the possible extension to a two-dimensional operational model for coupling towards operational tsunami models is discussed.

  11. Second-order accurate finite volume method for well-driven flows

    NASA Astrophysics Data System (ADS)

    Dotlić, M.; Vidović, D.; Pokorni, B.; Pušić, M.; Dimkić, M.

    2016-02-01

    We consider a finite volume method for a well-driven fluid flow in a porous medium. Due to the singularity of the well, modeling in the near-well region with standard numerical schemes results in a completely wrong total well flux and an inaccurate hydraulic head. Local grid refinement can help, but it comes at computational cost. In this article we propose two methods to address the well singularity. In the first method the flux through well faces is corrected using a logarithmic function, in a way related to the Peaceman model. Coupling this correction with a non-linear second-order accurate two-point scheme gives a greatly improved total well flux, but the resulting scheme is still inconsistent. In the second method fluxes in the near-well region are corrected by representing the hydraulic head as a sum of a logarithmic and a linear function. This scheme is second-order accurate.

  12. A High-Order Finite-Volume Algorithm for Fokker-Planck Collisions in Magnetized Plasmas

    SciTech Connect

    Xiong, Z; Cohen, R H; Rognlien, T D; Xu, X Q

    2007-04-18

    A high-order finite volume algorithm is developed for the Fokker-Planck Operator (FPO) describing Coulomb collisions in strongly magnetized plasmas. The algorithm is based on a general fourth-order reconstruction scheme for an unstructured grid in the velocity space spanned by parallel velocity and magnetic moment. The method provides density conservation and high-order-accurate evaluation of the FPO independent of the choice of the velocity coordinates. As an example, a linearized FPO in constant-of-motion coordinates, i.e. the total energy and the magnetic moment, is developed using the present algorithm combined with a cut-cell merging procedure. Numerical tests include the Spitzer thermalization problem and the return to isotropy for distributions initialized with velocity space loss cones. Utilization of the method for a nonlinear FPO is straightforward but requires evaluation of the Rosenbluth potentials.

  13. A finite-volume numerical method to calculate fluid forces and rotordynamic coefficients in seals

    NASA Technical Reports Server (NTRS)

    Athavale, M. M.; Przekwas, A. J.; Hendricks, R. C.

    1992-01-01

    A numerical method to calculate rotordynamic coefficients of seals is presented. The flow in a seal is solved by using a finite-volume formulation of the full Navier-Stokes equations with appropriate turbulence models. The seal rotor is perturbed along a diameter such that the position of the rotor is a sinusoidal function of time. The resulting flow domain changes with time, and the time-dependent flow in the seal is solved using a space conserving moving grid formulation. The time-varying fluid pressure reaction forces are then linked with the rotor center displacement, velocity and acceleration to yield the rotordynamic coefficients. Results for an annular seal are presented, and compared with experimental data and other more simplified numerical methods.

  14. A finite volume Euler calculation of the aerodynamics of transonic airfoil-vortex interaction

    NASA Technical Reports Server (NTRS)

    Damodaran, Murali; Caughey, David A.

    1987-01-01

    Unsteady inviscid transonic airfoil-vortex interaction is numerically analyzed by solving the two-dimensional unsteady Euler equations in integral form using a finite volume scheme. The solution procedure is based on an explicit Runge-Kutta time-stepping scheme wherein the spatial terms are central-differenced and a combination of second- and fourth-differences in the flow variables is used to form the numerical dissipation terms to stabilize the scheme. A velocity decomposition technique is applied to alleviate the problem of vortex diffusion by the numerical dissipation terms and to treat the interaction of a Rankine vortex with an airfoil accurately. Results obtained are compared with available numerical data.

  15. Finite volume computation of unsteady inviscid rotational transonic flows past airfoils in rigid body motion

    NASA Technical Reports Server (NTRS)

    Damodaran, Murali

    1988-01-01

    Unsteady inviscid transonic flow over airfoils in arbitrary rigid body motion is analyzed numerically by solving the two-dimensional unsteady Euler equations in integral form using a finite volume scheme. The solution procedure is based on an explicit Runge-Kutta time-stepping scheme wherein the spatial terms are central-differenced and a combination of second- and fourth-differences in the flow variables are used to form the numerical dissipation terms to stabilize the scheme. Unsteady calculations are started from converged steady-state solutions as initial conditions. Nonreflective boundary conditions are imposed on the far-field boundaries. Results are presented and, where possible, validated against available numerical and experimental data for airfoils subjected to a step change in angle of attack, airfoils oscillating and plunging in transonic flow, and airfoils immersed in a time-varying free stream.

  16. A high resolution finite volume method for efficient parallel simulation of casting processes on unstructured meshes

    SciTech Connect

    Kothe, D.B.; Turner, J.A.; Mosso, S.J.; Ferrell, R.C.

    1997-03-01

    We discuss selected aspects of a new parallel three-dimensional (3-D) computational tool for the unstructured mesh simulation of Los Alamos National Laboratory (LANL) casting processes. This tool, known as {bold Telluride}, draws upon on robust, high resolution finite volume solutions of metal alloy mass, momentum, and enthalpy conservation equations to model the filling, cooling, and solidification of LANL castings. We briefly describe the current {bold Telluride} physical models and solution methods, then detail our parallelization strategy as implemented with Fortran 90 (F90). This strategy has yielded straightforward and efficient parallelization on distributed and shared memory architectures, aided in large part by new parallel libraries {bold JTpack9O} for Krylov-subspace iterative solution methods and {bold PGSLib} for efficient gather/scatter operations. We illustrate our methodology and current capabilities with source code examples and parallel efficiency results for a LANL casting simulation.

  17. Modeling electron dynamics coupled to continuum states in finite volumes with absorbing boundaries

    NASA Astrophysics Data System (ADS)

    De Giovannini, Umberto; Larsen, Ask Hjorth; Rubio, Angel

    2015-03-01

    Absorbing boundaries are frequently employed in real-time propagation of the Schrödinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for the calculation of observables involving infinitely extended continuum states in finite volumes. In the literature, several boundary absorbers have been proposed. They mostly fall into three main families: mask function absorbers, complex absorbing potentials, and exterior complex-scaled potentials. To date none of the proposed absorbers is perfect, and all present a certain degree of reflections. Characterization of such reflections is thus a critical task with strong implications for time-dependent simulations of atoms and molecules. We introduce a method to evaluate the reflection properties of a given absorber and present a comparison of selected samples for each family of absorbers. Further, we discuss the connections between members of each family and show how the same reflection curves can be obtained with very different absorption schemes.

  18. On 3-D inelastic analysis methods for hot section components. Volume 1: Special finite element models

    NASA Technical Reports Server (NTRS)

    Nakazawa, S.

    1988-01-01

    This annual status report presents the results of work performed during the fourth year of the 3-D Inelastic Analysis Methods for Hot Section Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of new computer codes permitting more accurate and efficient 3-D analysis of selected hot section components, i.e., combustor liners, turbine blades and turbine vanes. The computer codes embody a progression of math models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components. Volume 1 of this report discusses the special finite element models developed during the fourth year of the contract.

  19. Finite volume approach for the instationary Cosserat rod model describing the spinning of viscous jets

    NASA Astrophysics Data System (ADS)

    Arne, Walter; Marheineke, Nicole; Meister, Andreas; Schiessl, Stefan; Wegener, Raimund

    2015-08-01

    The spinning of slender viscous jets can be asymptotically described by one-dimensional models that consist of systems of partial and ordinary differential equations. Whereas well-established string models only possess solutions for certain choices of parameters and configurations, the more sophisticated rod model is not limited by restrictions. It can be considered as an ɛ-regularized string model, but containing the slenderness ratio ɛ in the equations complicates its numerical treatment. We develop numerical schemes for fixed or enlarging (time-dependent) domains, using a finite volume approach in space with mixed central, up- and down-winded differences and stiffly accurate Radau methods for the time integration. For the first time, results of instationary simulations for a fixed or growing jet in a rotational spinning process are presented for arbitrary parameter ranges.

  20. Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes

    SciTech Connect

    Montecinos, Gino I.; Müller, Lucas O.; Toro, Eleuterio F.

    2014-06-01

    The applicability of ADER finite volume methods to solve hyperbolic balance laws with stiff source terms in the context of well-balanced and non-conservative schemes is extended to solve a one-dimensional blood flow model for viscoelastic vessels, reformulated as a hyperbolic system, via a relaxation time. A criterion for selecting relaxation times is found and an empirical convergence rate assessment is carried out to support this result. The proposed methodology is validated by applying it to a network of viscoelastic vessels for which experimental and numerical results are available. The agreement between the results obtained in the present paper and those available in the literature is satisfactory. Key features of the present formulation and numerical methodologies, such as accuracy, efficiency and robustness, are fully discussed in the paper.

  1. Finite volume - space-time discontinuous Galerkin method for the solution of compressible turbulent flow

    NASA Astrophysics Data System (ADS)

    Česenek, Jan

    2016-03-01

    In this article we deal with numerical simulation of the non-stationary compressible turbulent flow. Compressible turbulent flow is described by the Reynolds-Averaged Navier-Stokes (RANS) equations. This RANS system is equipped with two-equation k-omega turbulence model. These two systems of equations are solved separately. Discretization of the RANS system is carried out by the space-time discontinuous Galerkin method which is based on piecewise polynomial discontinuous approximation of the sought solution in space and in time. Discretization of the two-equation k-omega turbulence model is carried out by the implicit finite volume method, which is based on piecewise constant approximation of the sought solution. We present some numerical experiments to demonstrate the applicability of the method using own-developed code.

  2. Adaptive finite volume methods for time-dependent P.D.E.S.

    SciTech Connect

    Ware, J.; Berzins, M.

    1995-12-31

    The aim of adaptive methods for time-dependent p.d.e.s is to control the numerical error so that it is less than a user-specified tolerance. This error depends on the spatial discretization method, the spatial mesh, the method of time integration and the timestep. The spatial discretization method and positioning of the spatial mesh points should attempt to ensure that the spatial error is controlled to meet the user`s requirements. It is then desirable to integrate the o.d.e. system in time with sufficient accuracy so that the temporal error does not corrupt the spatial accuracy or the reliability of the spatial error estimates. This paper is concerned with the development of a prototype algorithm of this type, based on a cell-centered triangular finite volume scheme, for two space dimensional convection-dominated problems.

  3. Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

    NASA Technical Reports Server (NTRS)

    Schallhorn, Paul; Majumdar, Alok

    2012-01-01

    This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

  4. A parallel finite-volume MHD code for plasma thrusters with an applied magnetic field

    NASA Astrophysics Data System (ADS)

    Norgaard, Peter; Choueiri, Edgar; Jardin, Stephen

    2006-10-01

    The Princeton Code for Advanced Plasma Propulsion Simulation (PCAPPS) is a recently developed parallel finite volume code that solves the resistive MHD equations in axisymmetric form. It is intended for simulating complex plasma flows, especially those in plasma thrusters. The code uses a flux function to represent the poloidal field. It allows for externally applied magnetic fields, necessary for efficient operation of magnetoplasmadynamic thrusters (MPDT) at low power. Separate electron and heavy species energy equations are employed, and model closure is achieved by a multi-level equilibrium ionization equation of state. We provide results from various validation tests, along with solver accuracy and parallel efficiency studies. Preliminary numerical studies of a lithium-fed MPDT are also presented.

  5. Notes on Accuracy of Finite-Volume Discretization Schemes on Irregular Grids

    NASA Technical Reports Server (NTRS)

    Diskin, Boris; Thomas, James L.

    2011-01-01

    Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finite-volume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a certain degree of geometric regularity. Such degradation of truncation-error convergence does not necessarily imply a lower-order convergence of discretization errors. In these notes, irregular-grid computations demonstrate that the design-order discretization-error convergence can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all.

  6. Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver

    NASA Technical Reports Server (NTRS)

    Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

    2013-01-01

    This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.

  7. Control theory based airfoil design for potential flow and a finite volume discretization

    NASA Technical Reports Server (NTRS)

    Reuther, J.; Jameson, A.

    1994-01-01

    This paper describes the implementation of optimization techniques based on control theory for airfoil design. In previous studies it was shown that control theory could be used to devise an effective optimization procedure for two-dimensional profiles in which the shape is determined by a conformal transformation from a unit circle, and the control is the mapping function. The goal of our present work is to develop a method which does not depend on conformal mapping, so that it can be extended to treat three-dimensional problems. Therefore, we have developed a method which can address arbitrary geometric shapes through the use of a finite volume method to discretize the potential flow equation. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented, where both target speed distributions and minimum drag are used as objective functions.

  8. The Implementation of the Finite-Volume Dynamical Core in the Community Atmosphere Model

    SciTech Connect

    Sawyer, W B; Mirin, A A

    2005-07-26

    A distributed memory message-passing parallel implementation of a finite-volume discretization of the primitive equations in the Community Atmosphere Model 3.0 is presented. These three-dimensional equations can be decoupled into a set of two-dimensional equations by the introduction of a floating vertical coordinate, resulting in considerable potential parallelism. Subsequent analysis of the data dependencies --in particular those arising from the polar singularity of the latitude-longitude coordinate system--suggests that two separate domain decompositions should be employed, each tailored for a different part of the model. The implementation requires that data be periodically redistributed between these two decompositions. Furthermore, data from nearest neighbors are kept in halo regions, which are updated between iterations. These data movements are optimized through one-sided communication primitives and multithreading. The resulting algorithm is shown to scale to very large machine configurations, even for relatively coarse resolutions.

  9. The Implementation of the Finite-Volume Dynamical Core in the Community Atmosphere Model

    SciTech Connect

    Sawyer, W B; Mirin, A A

    2004-11-30

    A distributed memory message-passing parallel implementation of a finite-volume discretization of the primitive equations in the Community Atmosphere Model is presented. These three-dimensional equations can be decoupled into a set of two-dimensional equations by the introduction of a floating vertical coordinate, resulting in considerable potential parallelism. Subsequent analysis of the data dependencies--in particular those arising from the polar singularity of the latitude-longitude coordinate system--suggests that two separate domain decompositions should be employed, each tailored for a different part of the model. The implementation requires that data be periodically redistributed between these two decompositions. Furthermore, data from nearest neighbors are kept in halo regions, which are updated between iterations. These data movements are optimized through one-sided communication primitives and multithreading. The resulting algorithm is shown to scale to very large machine configurations, even for relatively coarse resolutions.

  10. A Scalable Implementation of a Finite-Volume Dynamical Core in the Community Atmosphere Model

    SciTech Connect

    Sawyer, W; Mirin, A

    2004-06-25

    A distributed memory message-passing parallel implementation of a finite-volume discretization of the primitive equations in the Community Atmosphere Model is presented. Due to the data dependencies resulting from the polar singularity of the latitude-longitude coordinate system, it is necessary to employ two separate domain decompositions within the dynamical core. Data must be periodically redistributed between these two decompositions. In addition, the domains contain halo regions that cover the nearest neighbor data dependencies. A combination of several techniques, such as one-sided communication and multithreading, are presented to optimize data movements. The resulting algorithm is shown to scale to very large machine configurations, even for relatively coarse resolutions.

  11. Dust Emissions, Transport, and Deposition Simulated with the NASA Finite-Volume General Circulation Model

    NASA Technical Reports Server (NTRS)

    Colarco, Peter; daSilva, Arlindo; Ginoux, Paul; Chin, Mian; Lin, S.-J.

    2003-01-01

    Mineral dust aerosols have radiative impacts on Earth's atmosphere, have been implicated in local and regional air quality issues, and have been identified as vectors for transporting disease pathogens and bringing mineral nutrients to terrestrial and oceanic ecosystems. We present for the first time dust simulations using online transport and meteorological analysis in the NASA Finite-Volume General Circulation Model (FVGCM). Our dust formulation follows the formulation in the offline Georgia Institute of Technology-Goddard Global Ozone Chemistry Aerosol Radiation and Transport Model (GOCART) using a topographical source for dust emissions. We compare results of the FVGCM simulations with GOCART, as well as with in situ and remotely sensed observations. Additionally, we estimate budgets of dust emission and transport into various regions.

  12. Mimetic Theory for Cell-Centered Lagrangian Finite Volume Formulation on General Unstructured Grids

    SciTech Connect

    Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.; Christon, Mark A.

    2012-07-19

    A finite volume cell-centered Lagrangian scheme for solving large deformation problems is constructed based on the hypo-elastic model and using the mimetic theory. Rigorous analysis in the context of gas and solid dynamics, and arbitrary polygonal meshes, is presented to demonstrate the ability of cell-centered schemes in mimicking the continuum properties and principles at the discrete level. A new mimetic formulation based gradient evaluation technique and physics-based, frame independent and symmetry preserving slope limiters are proposed. Furthermore, a physically consistent dissipation model is employed which is both robust and inexpensive to implement. The cell-centered scheme along with these additional new features are applied to solve solids undergoing elasto-plastic deformation.

  13. Coupling of Smoothed Particle Hydrodynamics with Finite Volume method for free-surface flows

    NASA Astrophysics Data System (ADS)

    Marrone, S.; Di Mascio, A.; Le Touzé, D.

    2016-04-01

    A new algorithm for the solution of free surface flows with large front deformation and fragmentation is presented. The algorithm is obtained by coupling a classical Finite Volume (FV) approach, that discretizes the Navier-Stokes equations on a block structured Eulerian grid, with an approach based on the Smoothed Particle Hydrodynamics (SPH) method, implemented in a Lagrangian framework. The coupling procedure is formulated in such a way that each solver is applied in the region where its intrinsic characteristics can be exploited in the most efficient and accurate way: the FV solver is used to resolve the bulk flow and the wall regions, whereas the SPH solver is implemented in the free surface region to capture details of the front evolution. The reported results clearly prove that the combined use of the two solvers is convenient from the point of view of both accuracy and computing time.

  14. Finite volume and asymptotic methods for stochastic neuron models with correlated inputs.

    PubMed

    Rosenbaum, Robert; Marpeau, Fabien; Ma, Jianfu; Barua, Aditya; Josić, Krešimir

    2012-07-01

    We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker-Planck equation with non-trivial boundary conditions resulting from the refractory period and firing threshold. We propose a finite volume method that is orders of magnitude faster than the Monte Carlo methods traditionally used to model such systems. The resulting numerical approximations are proved to be accurate, nonnegative and integrate to 1. We also approximate the transient evolution of the system using an Ornstein-Uhlenbeck process, and use the result to examine the properties of the joint output of cell pairs. The results suggests that the joint output of a cell pair is most sensitive to changes in input variance, and less sensitive to changes in input mean and correlation. PMID:21717104

  15. DAO's Finite-volume/Physical-space Data Assimilation System: Stratospheric Applications

    NASA Technical Reports Server (NTRS)

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

    2000-01-01

    In this talk we describe the next-generation data assimilation system being developed at NASA's Data Assimilation Office (DAO), with emphasis on the applications to stratospheric forecasts and stratospheric constituent transport. This data assimilation system includes the General Circulation Model jointly developed by the DAO and the Climate and Global Dynamics Division (CGDD) at NCAR. This model is based on the finite-volume dynamical core) developed at DAO with physical parameterizations from the NCAR Climate Community Model. The Physical-space Statistical Analysis System (PSAS) is used to combine a first guess from the NASA-NCAR GCM with observational data to provide an updated estimate of the state of the atmosphere. Case studies for the (northern) Winter of 2000 will be discussed.

  16. Discontinuous finite volume element discretization for coupled flow-transport problems arising in models of sedimentation

    NASA Astrophysics Data System (ADS)

    Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo

    2015-10-01

    The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.

  17. A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

    NASA Technical Reports Server (NTRS)

    Bui, Trong T.

    1999-01-01

    A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

  18. Towards registration of temporal mammograms by finite element simulation of MR breast volumes

    NASA Astrophysics Data System (ADS)

    Qiu, Yan; Sun, Xuejun; Manohar, Vasant; Goldgof, Dmitry

    2008-03-01

    Performing regular mammographic screening and comparing corresponding mammograms taken from multiple views or at different times are necessary for early detection and treatment evaluation of breast cancer, which is key to successful treatment. However, mammograms taken at different times are often obtained under different compression, orientation, or body position. A temporal pair of mammograms may vary significantly due to the spatial disparities caused by the variety in acquisition environments, including 3D position of the breast, the amount of pressure applied, etc. Such disparities can be corrected through the process of temporal registration. We propose to use a 3D finite element model for temporal registration of digital mammography. In this paper, we apply patient specific 3D breast model constructed from MRI data of the patient, for cases where lesions are detectable in multiple mammographic views across time. The 3D location of the lesion in the breast model is computed through a breast deformation simulation step presented in our earlier work. Lesion correspondence is established by using a nearest neighbor approach in the uncompressed breast volume. Our experiments show that the use of a 3D finite element model for simulating and analyzing breast deformation contributes to good accuracy when matching suspicious regions in temporal mammograms.

  19. High order finite volume WENO schemes for the Euler equations under gravitational fields

    NASA Astrophysics Data System (ADS)

    Li, Gang; Xing, Yulong

    2016-07-01

    Euler equations with gravitational source terms are used to model many astrophysical and atmospheric phenomena. This system admits hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term, and two commonly seen equilibria are the isothermal and polytropic hydrostatic solutions. Exact preservation of these equilibria is desirable as many practical problems are small perturbations of such balance. High order finite difference weighted essentially non-oscillatory (WENO) schemes have been proposed in [22], but only for the isothermal equilibrium state. In this paper, we design high order well-balanced finite volume WENO schemes, which can preserve not only the isothermal equilibrium but also the polytropic hydrostatic balance state exactly, and maintain genuine high order accuracy for general solutions. The well-balanced property is obtained by novel source term reformulation and discretization, combined with well-balanced numerical fluxes. Extensive one- and two-dimensional simulations are performed to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.

  20. A finite volume scheme for radiative heat transfer in semi-transparent media

    SciTech Connect

    Murthy, J.Y.; Mathur, S.R.

    1999-07-01

    Radiation in semi-transparent media occurs in a variety of industrial applications. In the HVAC area, the selective transmission of thermal radiation through windows governs the heat load of rooms. In fiber drawing applications, the rate of quenching of the semi-transparent glass fiber is critically dependent on the radiant exchange with the hot furnace. In ceramics processing, the high index of refraction leads to strong internal reflection effects, and greatly influences the thermal field. It would be useful to develop numerical methods for computing this type of radiation heat transfer in the complex geometries encountered in most industrial applications. Here, a procedure for computing radiation in semi-transparent media is presented. A conservative cell-based finite volume method is developed for unstructured meshes composed of arbitrary polyhedra. The angular domain is discretized into a finite number of control angles over which radiant energy is conserved. At Fresnel interfaces, numerical procedures are developed to conservatively transfer radiant energy from one angular direction to another as a result of reflection and refraction, while accounting for control angle overhang. Similar procedures are also employed at specular surfaces and symmetry boundaries. The method is tested against analytical solutions and shown to perform satisfactorily.

  1. Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

    NASA Technical Reports Server (NTRS)

    Nicholson, S.; Moore, J.

    1986-01-01

    A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is now needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes. A special discretization technique is also used to stabilize these calculations. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in a adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a

  2. Finite-volume modelling of geophysical electromagnetic data on unstructured grids using potentials

    NASA Astrophysics Data System (ADS)

    Jahandari, H.; Farquharson, C. G.

    2015-09-01

    The solution of the geophysical electromagnetic (EM) modelling problem on unstructured tetrahedral-Voronoï grids using EM potentials is investigated. Unstructured grids enable accurate representation of geological structures and interfaces and allow local refinements that can be beneficial in the mesh, for example, at the observation points and at the source. The time-harmonic Helmholtz equation in terms of EM potentials together with the equation of conservation of charge are discretized on staggered tetrahedral-Voronoï grids using a finite-volume method and solved in a total-field approach. The solutions are the total-field quantities of vector and scalar potentials along the edges and at the nodes of the tetrahedral elements, respectively. Two benchmark models with electric and magnetic sources are employed for verification. Also, to illustrate the versatility of the scheme, data for a model of the Ovoid ore body at Voisey's Bay, Labrador, Canada, are synthesized and compared with real helicopter-borne data. The finite-volume results show good agreement with those from the literature and with the real data. The Coulomb gauge is used for ensuring the uniqueness of the potentials in order to study the galvanic and inductive components of the solutions. The results indicate an agreement between the relative importance of these two components and the anticipated coupling of the source with the conductivity model. The solution of the gauged and ungauged schemes using iterative and direct solvers is studied and compared with the solution of a direct EM-field scheme. The results demonstrate that the potential-based schemes can be solved by iterative solvers unlike the corresponding EM-field scheme. An accuracy study is also conducted which showed the higher accuracy of the solutions from the potential method compared to those from the direct EM-field method.

  3. A new tracer technique for monitoring groundwater fluxes: the Finite Volume Point Dilution Method.

    PubMed

    Brouyère, Serge; Batlle-Aguilar, Jordi; Goderniaux, Pascal; Dassargues, Alain

    2008-01-28

    Quantification of pollutant mass fluxes is essential for assessing the impact of contaminated sites on their surrounding environment, particularly on adjacent surface water bodies. In this context, it is essential to quantify but also to be able to monitor the variations with time of Darcy fluxes in relation with changes in hydrogeological conditions and groundwater - surface water interactions. A new tracer technique is proposed that generalizes the single-well point dilution method to the case of finite volumes of tracer fluid and water flush. It is called the Finite Volume Point Dilution Method (FVPDM). It is based on an analytical solution derived from a mathematical model proposed recently to accurately model tracer injection into a well. Using a non-dimensional formulation of the analytical solution, a sensitivity analysis is performed on the concentration evolution in the injection well, according to tracer injection conditions and well-aquifer interactions. Based on this analysis, optimised field techniques and interpretation methods are proposed. The new tracer technique is easier to implement in the field than the classical point dilution method while it further allows monitoring temporal changes of the magnitude of estimated Darcy fluxes, which is not the case for the former technique. The new technique was applied to two experimental sites with contrasting objectives, geological and hydrogeological conditions, and field equipment facilities. In both cases, field tracer concentrations monitored in the injection wells were used to fit the calculated modelled concentrations by adjusting the apparent Darcy flux crossing the well screens. Modelling results are very satisfactory and indicate that the methodology is efficient and accurate, with a wide range of potential applications in different environments and experimental conditions, including the monitoring with time of changes in Darcy fluxes. PMID:17949849

  4. Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids

    SciTech Connect

    Burton, D.E.

    1994-10-17

    We consider the conservation properties of a staggered-grid Lagrange formulation of the hydrodynamics equations (SGH). Hydrodynamics algorithms are often formulated in a relatively ad hoc manner in which independent discretizations are proposed for mass, momentum, energy, and so forth. We show that, once discretizations for mass and momentum are stated, the remaining discretizations are very nearly uniquely determined, so there is very little latitude for variation. As has been known for some time, the kinetic energy discretization must follow directly from the momentum equation; and the internal energy must follow directly from the energy currents affecting the kinetic energy. A fundamental requirement (termed isentropicity) for numerical hydrodynamics algorithms is the ability to remain on an isentrope in the absence of heating or viscous forces and in the limit of small timesteps. We show that the requirements of energy conservation and isentropicity lead to the replacement of the usual volume calculation with a conservation integral. They further forbid the use of higher order functional representations for either velocity or stress within zones or control volumes, forcing the use of a constant stress element and a constant velocity control volume. This, in turn, causes the point and zone coordinates to formally disappear from the Cartesian formulation. The form of the work equations and the requirement for dissipation by viscous forces strongly limits the possible algebraic forms for artificial viscosity. The momentum equation and a center-of-mass definition lead directly to an angular momentum conservation law that is satisfied by the system. With a few straightforward substitutions, the Cartesian formulation can be converted to a multidimensional curvilinear one. The formulation in 2D symmetric geometry preserves rotational symmetry.

  5. Study of the deconfinement phase transition in a finite volume with massive particles: Hydrodynamics of the system near the transition

    SciTech Connect

    Ghenam, L.; Djoudi, A. Ait El

    2012-06-27

    We study the finite size and finite mass effects for the thermal deconfinement phase transition in Quantum Chromodynamics (QCD), using a simple model of coexistence of hadronic (H) gas and quark-gluon plasma (QGP) phases in a finite volume. We consider the equations of state of the two phases with the QGP containing two massless u and d quarks and massive s quarks, and a hadronic gas of massive pions, and we probe the system near the transition. For this, we examine the behavior of the most important hydrodynamical quantities describing the system, at a vanishing chemical potential ({mu}= 0), with temperature and energy density.

  6. Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws

    NASA Astrophysics Data System (ADS)

    Boscheri, Walter; Loubère, Raphaël; Dumbser, Michael

    2015-07-01

    In this paper we present a new family of efficient high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-MOOD finite volume schemes for the solution of nonlinear hyperbolic systems of conservation laws for moving unstructured triangular and tetrahedral meshes. This family is the next generation of the ALE ADER-WENO schemes presented in [16,20]. Here, we use again an element-local space-time Galerkin finite element predictor method to achieve a high order accurate one-step time discretization, while the somewhat expensive WENO approach on moving meshes, used to obtain high order of accuracy in space, is replaced by an a posteriori MOOD loop which is shown to be less expensive but still as accurate. This a posteriori MOOD loop ensures the numerical solution in each cell at any discrete time level to fulfill a set of user-defined detection criteria. If a cell average does not satisfy the detection criteria, then the solution is locally re-computed by progressively decrementing the order of the polynomial reconstruction, following a so-called cascade of predefined schemes with decreasing approximation order. A so-called parachute scheme, typically a very robust first order Godunov-type finite volume method, is employed as a last resort for highly problematic cells. The cascade of schemes defines how the decrementing process is carried out, i.e. how many schemes are tried and which orders are adopted for the polynomial reconstructions. The cascade and the parachute scheme are choices of the user or the code developer. Consequently the iterative MOOD loop allows the numerical solution to maintain some interesting properties such as positivity, mesh validity, etc., which are otherwise difficult to ensure. We have applied our new high order unstructured direct ALE ADER-MOOD schemes to the multi-dimensional Euler equations of compressible gas dynamics. A large set of test problems has been simulated and analyzed to assess the validity of our approach

  7. Multi-channel 1-to-2 transition amplitudes in a finite volume

    SciTech Connect

    Briceno, Raul; Hansen, Maxwell; Walker-Loud, Andre P

    2015-04-01

    We derive a model-independent expression for finite-volume matrix elements. Specifically, we present a relativistic, non-perturbative analysis of the matrix element of an external current between a one-scalar in-state and a two-scalar out-state. Our result, which is valid for energies below higher-particle inelastic thresholds, generalizes the Lellouch-Luscher formula in two ways: we allow the external current to inject arbitrary momentum into the system and we allow for the final state to be composed an arbitrary number of strongly coupled two-particle states with arbitrary partial waves (including partial-wave mixing induced by the volume). We also illustrate how our general result can be applied to some key examples, such as heavy meson decays and meson photo production. Finally, we point out complications that arise involving unstable resonance states, such as B to K*+l+l when staggered or mixed-action/partially-quenched calculations are performed.

  8. Ash3d: A finite-volume, conservative numerical model for ash transport and tephra deposition

    USGS Publications Warehouse

    Schwaiger, Hans F.; Denlinger, Roger P.; Mastin, Larry G.

    2012-01-01

    We develop a transient, 3-D Eulerian model (Ash3d) to predict airborne volcanic ash concentration and tephra deposition during volcanic eruptions. This model simulates downwind advection, turbulent diffusion, and settling of ash injected into the atmosphere by a volcanic eruption column. Ash advection is calculated using time-varying pre-existing wind data and a robust, high-order, finite-volume method. Our routine is mass-conservative and uses the coordinate system of the wind data, either a Cartesian system local to the volcano or a global spherical system for the Earth. Volcanic ash is specified with an arbitrary number of grain sizes, which affects the fall velocity, distribution and duration of transport. Above the source volcano, the vertical mass distribution with elevation is calculated using a Suzuki distribution for a given plume height, eruptive volume, and eruption duration. Multiple eruptions separated in time may be included in a single simulation. We test the model using analytical solutions for transport. Comparisons of the predicted and observed ash distributions for the 18 August 1992 eruption of Mt. Spurr in Alaska demonstrate to the efficacy and efficiency of the routine.

  9. Equilibrium and non-equilibrium properties of finite-volume crystallites

    NASA Astrophysics Data System (ADS)

    Degawa, Masashi

    Finite volume effects on equilibrium and non-equilibrium properties of nano-crystallites are studied theoretically and compared to both experiment and simulation. When a system is isolated or its size is small compared to the correlation length, all equilibrium and close-to-equilibrium properties will depend on the system boundary condition. Specifically for solid nano-crystallites, their finite size introduces global curvature to the system, which alters its equilibrium properties compared to the thermodynamic limit. Also such global curvature leads to capillary-induced morphology changes of the surface. Interesting dynamics can arise when the crystallite is supported on a substrate, with crossovers of the dominant driving force from the capillary force and crystallite-substrate interactions. To address these questions, we introduce thermodynamic functions for the boundary conditions, which can be derived from microscopic models. For nano-crystallites, the boundary is the surface (including interfaces), the thermodynamic description is based on the steps that define the shape of the surface, and the underlying microscopic model includes kinks. The global curvature of the surface introduces metastable states with different shapes governed by a constant of integration of the extra boundary condition, which we call the shape parameter c. The discrete height of the steps introduces transition states in between the metastable states, and the lowest energy accessible structure (energy barrier less 10k BT) as a function of the volume has been determined. The dynamics of nano-crystallites as they relax from a non-equilibrium structure is described quantitatively in terms of the motion of steps in both capillary-induced and interface-boundary-induced regimes. The step-edge fluctuations of the top facet are also influenced by global curvature and volume conservation and the effect yields different dynamic scaling exponents from a pure 1D system. Theoretical results are

  10. Accurate, finite-volume methods for 3D MHD on unstructured Lagrangian meshes

    SciTech Connect

    Barnes, D.C.; Rousculp, C.L.

    1998-10-01

    Previous 2D methods for magnetohydrodynamics (MHD) have contributed both to development of core code capability and to physics applications relevant to AGEX pulsed-power experiments. This strategy is being extended to 3D by development of a modular extension of an ASCI code. Extension to 3D not only increases complexity by problem size, but also introduces new physics, such as magnetic helicity transport. The authors have developed a method which incorporates all known conservation properties into the difference scheme on a Lagrangian unstructured mesh. Because the method does not depend on the mesh structure, mesh refinement is possible during a calculation to prevent the well known problem of mesh tangling. Arbitrary polyhedral cells are decomposed into tetrahedrons. The action of the magnetic vector potential, A {center_dot} {delta}l, is centered on the edges of this extended mesh. For ideal flow, this maintains {del} {center_dot} B = 0 to round-off error. Vertex forces are derived by the variation of magnetic energy with respect to vertex positions, F = {minus}{partial_derivative}W{sub B}/{partial_derivative}r. This assures symmetry as well as magnetic flux, momentum, and energy conservation. The method is local so that parallelization by domain decomposition is natural for large meshes. In addition, a simple, ideal-gas, finite pressure term has been included. The resistive diffusion part is calculated using the support operator method, to obtain an energy conservative, symmetric method on an arbitrary mesh. Implicit time difference equations are solved by preconditioned, conjugate gradient methods. Results of convergence tests are presented. Initial results of an annular Z-pinch implosion problem illustrate the application of these methods to multi-material problems.

  11. Realizable high-order finite-volume schemes for quadrature-based moment methods applied to diffusion population balance equations

    NASA Astrophysics Data System (ADS)

    Vikas, V.; Wang, Z. J.; Fox, R. O.

    2013-09-01

    Population balance equations with advection and diffusion terms can be solved using quadrature-based moment methods. Recently, high-order realizable finite-volume schemes with appropriate realizability criteria have been derived for the advection term. However, hitherto no work has been reported with respect to realizability problems for the diffusion term. The current work focuses on developing high-order realizable finite-volume schemes for diffusion. The pitfalls of existing finite-volume schemes for the diffusion term based on the reconstruction of moments are discussed, and it is shown that realizability can be guaranteed only with the 2nd-order scheme and that the realizability criterion for the 2nd-order scheme is the same as the stability criterion. However, realizability of moments cannot be guaranteed when higher-order moment-based reconstruction schemes are used. To overcome this problem, realizable high-order finite-volume schemes based on the reconstruction of weights and abscissas are proposed and suitable realizability criteria are derived. The realizable schemes can achieve higher than 2nd-order accuracy for problems with smoothly varying abscissas. In the worst-case scenario of highly nonlinear abscissas, the realizable schemes are 2nd-order accurate but have lower error magnitudes compared to existing schemes. The results obtained using the realizable high-order schemes are shown to be consistent with those obtained using the 2nd-order moment-based reconstruction scheme.

  12. A study on the optimization of finite volume effects of B K in lattice QCD by using the CUDA

    NASA Astrophysics Data System (ADS)

    Kim, Jangho; Cho, Kihyeon

    2015-07-01

    Lattice quantum chromodynamics (QCD) is the non-perturbative implementation of field theory to solve the QCD theory of quarks and gluons by using the Feynman path integral approach. We calculate the kaon CP (charge-parity) violation parameter B K generally arising in theories of physics beyond the Standard Model. Because lattice simulations are performed on finite volume lattices, the finite volume effects must be considered to exactly estimate the systematic error. The computational cost of numerical simulations may increase dramatically as the lattice spacing is decreased. Therefore, lattice QCD calculations must be optimized to account for the finite volume effects. The methodology used in this study was to develop an algorithm to parallelize the code by using a graphic processing unit (GPU) and to optimize the code to achieve as close to the theoretical peak performance as possible. The results revealed that the calculation speed of the newly-developed algorithm is significantly improved compared with that of the current algorithm for the finite volume effects.

  13. A finite-volume Eulerian-Lagrangian localized adjoint method for solution of the advection-dispersion equation

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1993-01-01

    Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods for solute transport problems that are dominated by advection. FVELLAM systematically conserves mass globally with all types of boundary conditions. Integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking of characteristic lines intersecting inflow boundaries. FVELLAM extends previous results by obtaining mass conservation locally on Lagrangian space-time elements. -from Authors

  14. Modeling of photon migration in the human lung using a finite volume solver

    NASA Astrophysics Data System (ADS)

    Sikorski, Zbigniew; Furmanczyk, Michal; Przekwas, Andrzej J.

    2006-02-01

    The application of the frequency domain and steady-state diffusive optical spectroscopy (DOS) and steady-state near infrared spectroscopy (NIRS) to diagnosis of the human lung injury challenges many elements of these techniques. These include the DOS/NIRS instrument performance and accurate models of light transport in heterogeneous thorax tissue. The thorax tissue not only consists of different media (e.g. chest wall with ribs, lungs) but its optical properties also vary with time due to respiration and changes in thorax geometry with contusion (e.g. pneumothorax or hemothorax). This paper presents a finite volume solver developed to model photon migration in the diffusion approximation in heterogeneous complex 3D tissues. The code applies boundary conditions that account for Fresnel reflections. We propose an effective diffusion coefficient for the void volumes (pneumothorax) based on the assumption of the Lambertian diffusion of photons entering the pleural cavity and accounting for the local pleural cavity thickness. The code has been validated using the MCML Monte Carlo code as a benchmark. The code environment enables a semi-automatic preparation of 3D computational geometry from medical images and its rapid automatic meshing. We present the application of the code to analysis/optimization of the hybrid DOS/NIRS/ultrasound technique in which ultrasound provides data on the localization of thorax tissue boundaries. The code effectiveness (3D complex case computation takes 1 second) enables its use to quantitatively relate detected light signal to absorption and reduced scattering coefficients that are indicators of the pulmonary physiologic state (hemoglobin concentration and oxygenation).

  15. Simulation studies of vestibular macular afferent-discharge patterns using a new, quasi-3-D finite volume method

    NASA Technical Reports Server (NTRS)

    Ross, M. D.; Linton, S. W.; Parnas, B. R.

    2000-01-01

    A quasi-three-dimensional finite-volume numerical simulator was developed to study passive voltage spread in vestibular macular afferents. The method, borrowed from computational fluid dynamics, discretizes events transpiring in small volumes over time. The afferent simulated had three calyces with processes. The number of processes and synapses, and direction and timing of synapse activation, were varied. Simultaneous synapse activation resulted in shortest latency, while directional activation (proximal to distal and distal to proximal) yielded most regular discharges. Color-coded visualizations showed that the simulator discretized events and demonstrated that discharge produced a distal spread of voltage from the spike initiator into the ending. The simulations indicate that directional input, morphology, and timing of synapse activation can affect discharge properties, as must also distal spread of voltage from the spike initiator. The finite volume method has generality and can be applied to more complex neurons to explore discrete synaptic effects in four dimensions.

  16. Axial coupling constant of the nucleon for two flavors of dynamical quarks in finite and infinite volume

    SciTech Connect

    Khan, A. Ali; Goeckeler, M.; Schaefer, A.; Haegler, Ph.; Hemmert, T. R.; Wollenweber, T.; Horsley, R.; Zanotti, J. M.; Pleiter, D.; Rakow, P. E. L.; Schierholz, G.

    2006-11-01

    We present data for the axial coupling constant g{sub A} of the nucleon obtained in lattice QCD with two degenerate flavors of dynamical nonperturbatively improved Wilson quarks. The renormalization is also performed nonperturbatively. For the analysis we give a chiral extrapolation formula for g{sub A} based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavors. Applying this formalism in a finite volume, we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattice data in finite volume, we are able to determine the axial coupling of the nucleon in the chiral limit without imposing the known value at the physical point.

  17. High Order Finite Volume Nonlinear Schemes for the Boltzmann Transport Equation

    SciTech Connect

    Bihari, B L; Brown, P N

    2005-03-29

    The authors apply the nonlinear WENO (Weighted Essentially Nonoscillatory) scheme to the spatial discretization of the Boltzmann Transport Equation modeling linear particle transport. The method is a finite volume scheme which ensures not only conservation, but also provides for a more natural handling of boundary conditions, material properties and source terms, as well as an easier parallel implementation and post processing. It is nonlinear in the sense that the stencil depends on the solution at each time step or iteration level. By biasing the gradient calculation towards the stencil with smaller derivatives, the scheme eliminates the Gibb's phenomenon with oscillations of size O(1) and reduces them to O(h{sup r}), where h is the mesh size and r is the order of accuracy. The current implementation is three-dimensional, generalized for unequally spaced meshes, fully parallelized, and up to fifth order accurate (WENO5) in space. For unsteady problems, the resulting nonlinear spatial discretization yields a set of ODE's in time, which in turn is solved via high order implicit time-stepping with error control. For the steady-state case, they need to solve the non-linear system, typically by Newton-Krylov iterations. There are several numerical examples presented to demonstrate the accuracy, non-oscillatory nature and efficiency of these high order methods, in comparison with other fixed-stencil schemes.

  18. Tetrahedral finite-volume solutions to the Navier-Stokes equations on complex configurations

    NASA Astrophysics Data System (ADS)

    Frink, N. T.; Pirzadeh, S. Z.

    1999-09-01

    A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the USA for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

  19. A conservative Dirichlet boundary treatment for the finite volume lattice Boltzmann method

    NASA Astrophysics Data System (ADS)

    Chen, Leitao; Schaefer, Laura

    2014-11-01

    The finite volume lattice Boltzmann method (FVLBM) enables the model to use the exact body-fitting mesh in the flow problems that involve the complex boundaries. However, the development of proper boundary treatment for the FVLBM has been outpaced. The boundary treatments designed for the conventional lattice Boltzmann method (LBM) framework are still heavily applied to the FVLBM. The largest defect of using the old boundary treatment is that, on the Dirichlet boundaries, the macroscopic variables cannot be conserved. In another word, there exist nontrivial discrepancies between the macroscopic variables defined by the boundary conditions and those yield by the numerical solutions. The errors on the boundaries will contaminate the internal solutions and even cause instability, especially on the complex boundaries. To overcome such a shortcoming, a conservative boundary treatment for the Dirichlet hydrodynamic boundary conditions is developed for the FVLBM. Through the benchmark tests, it is shown that the macroscopic conservations on the Direchlet boundaries are up to machine accuracy and completely independent of the size of relaxation time, the type of lattice model, the level of mesh resolution, the shape of boundaries and the type of internal scheme.

  20. Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes

    NASA Technical Reports Server (NTRS)

    Diskin, Boris; Thomas, James L.

    2012-01-01

    The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.

  1. Analysis of triangular C-grid finite volume scheme for shallow water flows

    NASA Astrophysics Data System (ADS)

    Shirkhani, Hamidreza; Mohammadian, Abdolmajid; Seidou, Ousmane; Qiblawey, Hazim

    2015-08-01

    In this paper, a dispersion relation analysis is employed to investigate the finite volume triangular C-grid formulation for two-dimensional shallow-water equations. In addition, two proposed combinations of time-stepping methods with the C-grid spatial discretization are investigated. In the first part of this study, the C-grid spatial discretization scheme is assessed, and in the second part, fully discrete schemes are analyzed. Analysis of the semi-discretized scheme (i.e. only spatial discretization) shows that there is no damping associated with the spatial C-grid scheme, and its phase speed behavior is also acceptable for long and intermediate waves. The analytical dispersion analysis after considering the effect of time discretization shows that the Leap-Frog time stepping technique can improve the phase speed behavior of the numerical method; however it could not damp the shorter decelerated waves. The Adams-Bashforth technique leads to slower propagation of short and intermediate waves and it damps those waves with a slower propagating speed. The numerical solutions of various test problems also conform and are in good agreement with the analytical dispersion analysis. They also indicate that the Adams-Bashforth scheme exhibits faster convergence and more accurate results, respectively, when the spatial and temporal step size decreases. However, the Leap-Frog scheme is more stable with higher CFL numbers.

  2. Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

    NASA Technical Reports Server (NTRS)

    Frink, Neal T.; Pirzadeh, Shahyar Z.

    1998-01-01

    A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

  3. Accuracy analysis of mimetic finite volume operators on geodesic grids and a consistent alternative

    NASA Astrophysics Data System (ADS)

    Peixoto, Pedro S.

    2016-04-01

    Many newly developed climate, weather and ocean global models are based on quasi-uniform spherical polygonal grids, aiming for high resolution and better scalability. Thuburn et al. (2009) and Ringler et al. (2010) developed a C staggered finite volume/difference method for arbitrary polygonal spherical grids suitable for these next generation dynamical cores. This method has many desirable mimetic properties and became popular, being adopted in some recent models, in spite of being known to possess low order of accuracy. In this work, we show that, for the nonlinear shallow water equations on non-uniform grids, the method has potentially 3 main sources of inconsistencies (local truncation errors not converging to zero as the grid is refined): (i) the divergence term of the continuity equation, (ii) the perpendicular velocity and (iii) the kinetic energy terms of the vector invariant form of the momentum equations. Although some of these inconsistencies have not impacted the convergence on some standard shallow water test cases up until now, they may constitute a potential problem for high resolution 3D models. Based on our analysis, we propose modifications for the method that will make it first order accurate in the maximum norm. It preserves many of the mimetic properties, albeit having non-steady geostrophic modes on the f-sphere. Experimental results show that the resulting model is a more accurate alternative to the existing formulations and should provide means of having a consistent, computationally cheap and scalable atmospheric or ocean model on C staggered Voronoi grids.

  4. Simulating the Flow Dynamics in the Southern Everglades using a Finite Volume Model

    NASA Astrophysics Data System (ADS)

    Senarath, S. U.; Novoa, R. J.; Barnes, J. A.; Brion, L. M.

    2001-12-01

    The Regional Simulation Model (RSM) is a weighted, implicit, finite-volume, rainfall-runoff model and is capable of simulating two-dimensional flow in arbitrarily shaped areas using a variable mesh structure. In this study the RSM is used to investigate the effect of structural and operational water management alternatives on flow-dynamics in South Florida's southern Everglades and Big Cypress National Preserve. The model domain encompasses some of the areas earmarked for restoration under the Comprehensive Everglades Restoration Plan (CERP). The RSM will be used to assess the effect/sensitivity of flow barriers and man-made structures on flow dynamics. The RSM has the capability of simulating overland and ground water interactions, evapotranspiration, infiltration, levee seepage, and canal flow. One-dimensional canal flow and two-dimensional overland flow are simulated in the model using the diffusive wave approximation to the Saint Venant equation. The Darcy equation is used for one-dimensional canal seepage and two-dimensional groundwater flow calculations. Overland and groundwater flow components are fully coupled for a more realistic representation of runoff generation making the RSM ideally suited for simulating the high water table, highly permeable soils and relatively flat terrain, associated with the southern Everglades region of Florida.

  5. Micro Blowing Simulations Using a Coupled Finite-Volume Lattice-Boltzman n L ES Approach

    NASA Technical Reports Server (NTRS)

    Menon, S.; Feiz, H.

    1990-01-01

    Three dimensional large-eddy simulations (LES) of single and multiple jet-in-cross-flow (JICF) are conducted using the 19-bit Lattice Boltzmann Equation (LBE) method coupled with a conventional finite-volume (FV) scheme. In this coupled LBE-FV approach, the LBE-LES is employed to simulate the flow inside the jet nozzles while the FV-LES is used to simulate the crossflow. The key application area is the use of this technique is to study the micro blowing technique (MBT) for drag control similar to the recent experiments at NASA/GRC. It is necessary to resolve the flow inside the micro-blowing and suction holes with high resolution without being restricted by the FV time-step restriction. The coupled LBE-FV-LES approach achieves this objectives in a computationally efficient manner. A single jet in crossflow case is used for validation purpose and the results are compared with experimental data and full LBE-LES simulation. Good agreement with data is obtained. Subsequently, MBT over a flat plate with porosity of 25% is simulated using 9 jets in a compressible cross flow at a Mach number of 0.4. It is shown that MBT suppresses the near-wall vortices and reduces the skin friction by up to 50 percent. This is in good agreement with experimental data.

  6. Some recent finite volume schemes to compute Euler equations using real gas EOS

    NASA Astrophysics Data System (ADS)

    Gallouët, T.; Hérard, J.-M.; Seguin, N.

    2002-08-01

    This paper deals with the resolution by finite volume methods of Euler equations in one space dimension, with real gas state laws (namely, perfect gas EOS, Tammann EOS and Van Der Waals EOS). All tests are of unsteady shock tube type, in order to examine a wide class of solutions, involving Sod shock tube, stationary shock wave, simple contact discontinuity, occurrence of vacuum by double rarefaction wave, propagation of a one-rarefaction wave over vacuum, Most of the methods computed herein are approximate Godunov solvers: VFRoe, VFFC, VFRoe ncv (, u, p) and PVRS. The energy relaxation method with VFRoe ncv (, u, p) and Rusanov scheme have been investigated too. Qualitative results are presented or commented for all test cases and numerical rates of convergence on some test cases have been measured for first- and second-order (Runge-Kutta 2 with MUSCL reconstruction) approximations. Note that rates are measured on solutions involving discontinuities, in order to estimate the loss of accuracy due to these discontinuities. Copyright

  7. Finite Element Surface Registration Incorporating Curvature, Volume Preservation, and Statistical Model Information

    PubMed Central

    Lüthi, Marcel; Vetter, Thomas

    2013-01-01

    We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models. PMID:24187581

  8. A finite volume Fokker-Planck collision operator in constants-of-motion coordinates

    NASA Astrophysics Data System (ADS)

    Xiong, Z.; Xu, X. Q.; Cohen, B. I.; Cohen, R.; Dorr, M. R.; Hittinger, J. A.; Kerbel, G.; Nevins, W. M.; Rognlien, T.

    2006-04-01

    TEMPEST is a 5D gyrokinetic continuum code for edge plasmas. Constants of motion, namely, the total energy E and the magnetic moment μ, are chosen as coordinate s because of their advantage in minimizing numerical diffusion in advection operato rs. Most existing collision operators are written in other coordinates; using them by interpolating is shown to be less satisfactory in maintaining overall numerical accuracy and conservation. Here we develop a Fokker-Planck collision operator directly in (E,μ) space usin g a finite volume approach. The (E, μ) grid is Cartesian, and the turning point boundary represents a straight line cutting through the grid that separates the ph ysical and non-physical zones. The resulting cut-cells are treated by a cell-mergin g technique to ensure a complete particle conservation. A two dimensional fourth or der reconstruction scheme is devised to achieve good numerical accuracy with modest number of grid points. The new collision operator will be benchmarked by numerical examples.

  9. An unstructured-grid finite-volume surface wave model (FVCOM-SWAVE): Implementation, validations and applications

    NASA Astrophysics Data System (ADS)

    Qi, Jianhua; Chen, Changsheng; Beardsley, Robert C.; Perrie, Will; Cowles, Geoffrey W.; Lai, Zhigang

    The structured-grid surface wave model SWAN (Simulating Waves Nearshore) has been converted into an unstructured-grid finite-volume version (hereafter referred to as FVCOM-SWAVE) for use in coastal ocean regions with complex irregular geometry. The implementation is made using the Flux-Corrected Transport (FCT) algorithm in frequency space, the implicit Crank-Nicolson method in directional space and options of explicit or implicit second-order upwind finite-volume schemes in geographic space. FVCOM-SWAVE is validated using four idealized benchmark test problems with emphasis on numerical dispersion, wave-current interactions, wave propagation over a varying-bathymetry shallow water region, and the basic wave grow curves. Results demonstrate that in the rectangular geometric domain, the second-order finite-volume method used in FVCOM-SWAVE has the same accuracy as the third-order finite-difference method used in SWAN. FVCOM-SWAVE was then applied to simulate wind-induced surface waves on the US northeast shelf with a central focus in the Gulf of Maine and New England Shelf. Through improved geometric fitting of the complex irregular coastline, FVCOM-SWAVE was able to robustly capture the spatial and temporal variation of surface waves in both deep and shallow regions along the US northeast coast.

  10. Survey and development of finite elements for nonlinear structural analysis. Volume 1: Handbook for nonlinear finite elements

    NASA Technical Reports Server (NTRS)

    1976-01-01

    A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity.

  11. Computer-aided structural engineering (CASE) project: Application of finite-element, grid generation, and scientific visualization techniques to 2-D and 3-d seepage and ground-water modeling. Final report

    SciTech Connect

    Tracy, F.T.

    1991-09-01

    This report describes new advances in the computational modeling of ground water and seepage using the finite element method (FEM) in conjunction with tools and techniques typically used by the aerospace engineers. The unsolved environmental issues regarding our hazardous and toxic waste problems must be resolved, and significant resources must be placed on this effort. Some military bases are contaminated with hazardous waste that has entered the groundwater domain. A groundwater model that takes into account contaminant flow is therefore critical. First, an extension of the technique of generating an orthogonal structured grid (using the Cauchy-Riemann equations) to automatically generate a flow net for two-dimensional (2-D) steady-state seepage problems is presented for various boundary conditions. Second, a complete implementation of a three-dimensional (3-D) seepage package is described where (1) grid generation is accomplished using the EAGLE program, (2) the seepage and groundwater analysis for either confined or unconfined steady-state flow, homogeneous or inhomogeneous media, and isotropic or anisotropic soil is accomplished with no restriction on the FE grid or requirement of an initial guess of the free surface for unconfined flow problems, and (3) scientific visualization is accomplished using the program FAST developed by NASA.

  12. Curvilinear finite-volume schemes using high-order compact interpolation

    SciTech Connect

    Fosso P, Arnaud Deniau, Hugues; Sicot, Frederic; Sagaut, Pierre

    2010-07-01

    During the last years, the need of high fidelity simulations on complex geometries for aeroacoustics predictions has grown. Most of high fidelity numerical schemes, in terms of low dissipative and low dispersive effects, lie on finite-difference (FD) approach. But for industrial applications, FD schemes are less robust compared to finite-volume (FV) ones. Thus the present study focuses on the development of a new compact FV scheme for two- and three-dimensional applications. The proposed schemes are formulated in the physical space and not in the computational space as it is the case in most of the known works. Therefore, they are more appropriate for general grids. They are based on compact interpolation to approximate interface-averaged field values using known cell-averaged values. For each interface, the interpolation coefficients are determined by matching Taylor series expansions around the interface center. Two types of schemes can be distinguished. The first one uses only the curvilinear abscissa along a mesh line to derive a sixth-order compact interpolation formulae while the second, more general, uses coordinates in a spatial three-dimensional frame well chosen. This latter is formally sixth-order accurate in a preferred direction almost orthogonal to the interface and at most fourth-order accurate in transversal directions. For non-linear problems, different approaches can be used to keep the high-order scheme. However, in the present paper, a MUSCL-like formulation was sufficient to address the presented test cases. All schemes have been modified to treat multiblock and periodic interfaces in such a way that high-order accuracy, stability, good spectral resolution, conservativeness and low computational costs are guaranteed. This is a first step to insure good scalability of the schemes although parallel performances issues are not addressed. As high frequency waves, badly resolved, could be amplified and then destabilize the scheme, compact filtering

  13. Interface control volume finite element method for modelling multi-phase fluid flow in highly heterogeneous and fractured reservoirs

    NASA Astrophysics Data System (ADS)

    Abushaikha, Ahmad S.; Blunt, Martin J.; Gosselin, Olivier R.; Pain, Christopher C.; Jackson, Matthew D.

    2015-10-01

    We present a new control volume finite element method that improves the modelling of multi-phase fluid flow in highly heterogeneous and fractured reservoirs, called the Interface Control Volume Finite Element (ICVFE) method. The method drastically decreases the smearing effects in other CVFE methods, while being mass conservative and numerically consistent. The pressure is computed at the interfaces of elements, and the control volumes are constructed around them, instead of at the elements' vertices. This assures that a control volume straddles, at most, two elements, which decreases the fluid smearing between neighbouring elements when large variations in their material properties are present. Lowest order Raviart-Thomas vectorial basis functions are used for the pressure calculation and first-order Courant basis functions are used to compute fluxes. The method is a combination of Mixed Hybrid Finite Element (MHFE) and CVFE methods. Its accuracy and convergence are tested using three dimensional tetrahedron elements to represent heterogeneous reservoirs. Our new approach is shown to be more accurate than current CVFE methods.

  14. Glacial isostatic adjustment on 3-D Earth models: a finite-volume formulation

    NASA Astrophysics Data System (ADS)

    Latychev, Konstantin; Mitrovica, Jerry X.; Tromp, Jeroen; Tamisiea, Mark E.; Komatitsch, Dimitri; Christara, Christina C.

    2005-05-01

    We describe and present results from a finite-volume (FV) parallel computer code for forward modelling the Maxwell viscoelastic response of a 3-D, self-gravitating, elastically compressible Earth to an arbitrary surface load. We implement a conservative, control volume discretization of the governing equations using a tetrahedral grid in Cartesian geometry and a low-order, linear interpolation. The basic starting grid honours all major radial discontinuities in the Preliminary Reference Earth Model (PREM), and the models are permitted arbitrary spatial variations in viscosity and elastic parameters. These variations may be either continuous or discontinuous at a set of grid nodes forming a 3-D surface within the (regional or global) modelling domain. In the second part of the paper, we adopt the FV methodology and a spherically symmetric Earth model to generate a suite of predictions sampling a broad class of glacial isostatic adjustment (GIA) data types (3-D crustal motions, long-wavelength gravity anomalies). These calculations, based on either a simple disc load history or a global Late Pleistocene ice load reconstruction (ICE-3G), are benchmarked against predictions generated using the traditional normal-mode approach to GIA. The detailed comparison provides a guide for future analyses (e.g. what grid resolution is required to obtain a specific accuracy?) and it indicates that discrepancies in predictions of 3-D crustal velocities less than 0.1 mm yr-1 are generally obtainable for global grids with ~3 × 106 nodes; however, grids of higher resolution are required to predict large-amplitude (>1 cm yr-1) radial velocities in zones of peak post-glacial uplift (e.g. James bay) to the same level of absolute accuracy. We conclude the paper with a first application of the new formulation to a 3-D problem. Specifically, we consider the impact of mantle viscosity heterogeneity on predictions of present-day 3-D crustal motions in North America. In these tests, the

  15. A finite volume solver for three dimensional debris flow simulations based on a single calibration parameter

    NASA Astrophysics Data System (ADS)

    von Boetticher, Albrecht; Turowski, Jens M.; McArdell, Brian; Rickenmann, Dieter

    2016-04-01

    Debris flows are frequent natural hazards that cause massive damage. A wide range of debris flow models try to cover the complex flow behavior that arises from the inhomogeneous material mixture of water with clay, silt, sand, and gravel. The energy dissipation between moving grains depends on grain collisions and tangential friction, and the viscosity of the interstitial fine material suspension depends on the shear gradient. Thus a rheology description needs to be sensitive to the local pressure and shear rate, making the three-dimensional flow structure a key issue for flows in complex terrain. Furthermore, the momentum exchange between the granular and fluid phases should account for the presence of larger particles. We model the fine material suspension with a Herschel-Bulkley rheology law, and represent the gravel with the Coulomb-viscoplastic rheology of Domnik & Pudasaini (Domnik et al. 2013). Both composites are described by two phases that can mix; a third phase accounting for the air is kept separate to account for the free surface. The fluid dynamics are solved in three dimensions using the finite volume open-source code OpenFOAM. Computational costs are kept reasonable by using the Volume of Fluid method to solve only one phase-averaged system of Navier-Stokes equations. The Herschel-Bulkley parameters are modeled as a function of water content, volumetric solid concentration of the mixture, clay content and its mineral composition (Coussot et al. 1989, Yu et al. 2013). The gravel phase properties needed for the Coulomb-viscoplastic rheology are defined by the angle of repose of the gravel. In addition to this basic setup, larger grains and the corresponding grain collisions can be introduced by a coupled Lagrangian particle simulation. Based on the local Savage number a diffusive term in the gravel phase can activate phase separation. The resulting model can reproduce the sensitivity of the debris flow to water content and channel bed roughness, as

  16. Using Finite Volume Element Definitions to Compute the Gravitation of Irregular Small Bodies

    NASA Astrophysics Data System (ADS)

    Zhao, Y. H.; Hu, S. C.; Wang, S.; Ji, J. H.

    2015-03-01

    In the orbit design procedure of the small bodies exploration missions, it's important to take the effect of the gravitation of the small bodies into account. However, a majority of the small bodies in the solar system are irregularly shaped with non-uniform density distribution which makes it difficult to precisely calculate the gravitation of these bodies. This paper proposes a method to model the gravitational field of an irregularly shaped small body and calculate the corresponding spherical harmonic coefficients. This method is based on the shape of the small bodies resulted from the light curve data via observation, and uses finite volume element to approximate the body shape. The spherical harmonic parameters could be derived numerically by computing the integrals according to their definition. Comparison with the polyhedral method is shown in our works. We take the asteroid (433) Eros as an example. Spherical harmonic coefficients resulted from this method are compared with the results derived from the track data obtained by NEAR (Near-Earth Asteroid Rendezvous) detector. The comparison shows that the error of C_{20} is less than 2%. The spherical harmonic coefficients of (1996) FG3 which is a selected target in our future exploration mission are computed. Taking (4179) Toutatis, the target body in Chang'e 2's flyby mission, for example, the gravitational field is calculated combined with the shape model from radar data, which provides theoretical basis for analyzing the soil distribution and flow from the optical image obtained in the mission. This method is applied to uneven density distribution objects, and could be used to provide reliable gravity field data of small bodies for orbit design and landing in the future exploration missions.

  17. High-order central ENO finite-volume scheme for ideal MHD

    NASA Astrophysics Data System (ADS)

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

    2013-10-01

    A high-order accurate finite-volume scheme for the compressible ideal magnetohydrodynamics (MHD) equations is proposed. The high-order MHD scheme is based on a central essentially non-oscillatory (CENO) method combined with the generalized Lagrange multiplier divergence cleaning method for MHD. The CENO method uses k-exact multidimensional reconstruction together with a monotonicity procedure that switches from a high-order reconstruction to a limited low-order reconstruction in regions of discontinuous or under-resolved solution content. Both reconstructions are performed on central stencils, and the switching procedure is based on a smoothness indicator. The proposed high-order accurate MHD scheme can be used on general polygonal grids. A highly sophisticated parallel implementation of the scheme is described that is fourth-order accurate on two-dimensional dynamically-adaptive body-fitted structured grids. The hierarchical multi-block body-fitted grid permits grid lines to conform to curved boundaries. High-order accuracy is maintained at curved domain boundaries by employing high-order spline representations and constraints at the Gauss quadrature points for flux integration. Detailed numerical results demonstrate high-order convergence for smooth flows and robustness against oscillations for problems with shocks. A new MHD extension of the well-known Shu-Osher test problem is proposed to test the ability of the high-order MHD scheme to resolve small-scale flow features in the presence of shocks. The dynamic mesh adaptation capabilities of the approach are demonstrated using adaptive time-dependent simulations of the Orszag-Tang vortex problem with high-order accuracy and unprecedented effective resolution.

  18. Finite volume numerical scheme for high-resolution gravity field modelling and its parallel implementation

    NASA Astrophysics Data System (ADS)

    Fašková, Z.; Macák, M.; Čunderlík, R.; Mikula, K.

    2012-04-01

    The paper discusses a numerical solution of the geodetic boundary value problem (GBVP) by the finite volume method (FVM). The FVM is a numerical method where numerical flux is conserved from one discretization cell to its neighbour, so it's very appropriate for solving GBVP with the Neumann and the Dirichlet BCs. Our numerical scheme is developed for 3D computational domain above an ellipsoid. It is shown that a refinement of the discretization in height's direction leads to more precise numerical results. In order to achieve high-resolution numerical results, parallel implementations of algorithms using the MPI procedures were developed and computations on parallel computers were successfully performed. This basis includes the splitting of all arrays in meridian's direction, usage of an implementation of the Bi-CGSTAB non-stationary iterative solver instead of the standard SOR and an optimization of communications on parallel computers with the NUMA architecture. This gives us higher speed up in comparison to standard approaches and enables us to develop an efficient tool for high-resolution global or regional gravity field modelling in huge areas. Numerical experiments present global modelling with the resolution comparable with EGM2008 and detailed regional modelling in the Pacific Ocean with the resolution 2x2 arc min. Input gravity disturbances are generated from the DTU10-GRAV gravity field model and the disturbing potential is computed from the GOCE_DIR2 satellite geopotential model up to degree 240. Finally, the obtained disturbing potential is used to evaluate the geopotential on the DTU10 mean sea surface and the achieved mean dynamic topography is compared with the ECCO oceanographic model.

  19. Hybrid finite-volume/transported PDF method for the simulation of turbulent reactive flows

    NASA Astrophysics Data System (ADS)

    Raman, Venkatramanan

    A novel computational scheme is formulated for simulating turbulent reactive flows in complex geometries with detailed chemical kinetics. A Probability Density Function (PDF) based method that handles the scalar transport equation is coupled with an existing Finite Volume (FV) Reynolds-Averaged Navier-Stokes (RANS) flow solver. The PDF formulation leads to closed chemical source terms and facilitates the use of detailed chemical mechanisms without approximations. The particle-based PDF scheme is modified to handle complex geometries and grid structures. Grid-independent particle evolution schemes that scale linearly with the problem size are implemented in the Monte-Carlo PDF solver. A novel algorithm, in situ adaptive tabulation (ISAT) is employed to ensure tractability of complex chemistry involving a multitude of species. Several non-reacting test cases are performed to ascertain the efficiency and accuracy of the method. Simulation results from a turbulent jet-diffusion flame case are compared against experimental data. The effect of micromixing model, turbulence model and reaction scheme on flame predictions are discussed extensively. Finally, the method is used to analyze the Dow Chlorination Reactor. Detailed kinetics involving 37 species and 158 reactions as well as a reduced form with 16 species and 21 reactions are used. The effect of inlet configuration on reactor behavior and product distribution is analyzed. Plant-scale reactors exhibit quenching phenomena that cannot be reproduced by conventional simulation methods. The FV-PDF method predicts quenching accurately and provides insight into the dynamics of the reactor near extinction. The accuracy of the fractional time-stepping technique in discussed in the context of apparent multiple-steady states observed in a non-premixed feed configuration of the chlorination reactor.

  20. A 3-D implicit finite-volume model of shallow water flows

    NASA Astrophysics Data System (ADS)

    Wu, Weiming; Lin, Qianru

    2015-09-01

    A three-dimensional (3-D) model has been developed to simulate shallow water flows in large water bodies, such as coastal and estuarine waters. The eddy viscosity is determined using a newly modified mixing length model that uses different mixing length functions for the horizontal and vertical shear strain rates. The 3-D shallow water flow equations with the hydrostatic pressure assumption are solved using an implicit finite-volume method based on a quadtree (telescoping) rectangular mesh on the horizontal plane and the sigma coordinate in the vertical direction. The quadtree technique can locally refine the mesh around structures or in high-gradient regions by splitting a coarse cell into four child cells. The grid nodes are numbered with a one-dimensional index system that has unstructured grid feature for better grid flexibility. All the primary variables are arranged in a non-staggered grid system. Fluxes at cell faces are determined using a Rhie and Chow-type momentum interpolation, to avoid the possible spurious checkerboard oscillations caused by linear interpolation. Each of the discretized governing equations is solved iteratively using the flexible GMRES method with ILUT preconditioning, and coupling of water level and velocity among these equations is achieved by using the SIMPLEC algorithm with under-relaxation. The model has been tested in four cases, including steady flow near a spur-dyke, tidal flows in San Francisco Bay and Gironde Estuary, and wind-induced current in a flume. The calculated water levels and velocities are in good agreement with the measured values.

  1. One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

    NASA Technical Reports Server (NTRS)

    Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

    2007-01-01

    The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

  2. Time-accurate analysis of nonequilibrium gas-particle mixtures using upwind/implicit finite-volume methodology

    SciTech Connect

    Hosangadi, A.; Sinha, N.; Dash, S.M. )

    1992-01-01

    A new Eulerian particulate solver whose numerical formulation is compatible with the numerics in state-of-the-art finite-volume upwind/implicit gas dynamic computer codes is presented. The heat transfer, drag, thermodynamic, and phase-change procedures in this code are derived from earlier, well established data fits and procedures. Performance for numerous flow problems with one- and two-way coupling is quite good. The solutions are nonoscillatory and robust and conserve flux balances very well. 18 refs.

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

    NASA Technical Reports Server (NTRS)

    Diskin, Boris; Thomas, James L.

    2010-01-01

    Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC

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

    NASA Technical Reports Server (NTRS)

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

    2010-01-01

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

  5. Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

    NASA Technical Reports Server (NTRS)

    Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

    2002-01-01

    The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

  6. A new numerical framework to simulate viscoelastic free-surface flows with the finite-volume method

    NASA Astrophysics Data System (ADS)

    Comminal, R.; Spangenberg, J.; Hattel, J. H.

    2015-04-01

    A new method for the simulation of 2D viscoelastic flow is presented. Numerical stability is obtained by the logarithmic-conformation change of variable, and a fully-implicit pure-streamfunction flow formulation, without use of any artificial diffusion. As opposed to other simulation results, our calculations predict a hydrodynamic instability in the 4:1 contraction geometry at a Weissenberg number of order 4. This new result is in qualitative agreement with the prediction of a non-linear subcritical elastic instability in Poiseuille flow. Our viscoelastic flow solver is coupled with a volume-of-fluid solver in order to predict free- surfaces in extrusion.

  7. Image fusion of Ultrasound Computer Tomography volumes with X-ray mammograms using a biomechanical model based 2D/3D registration.

    PubMed

    Hopp, T; Duric, N; Ruiter, N V

    2015-03-01

    Ultrasound Computer Tomography (USCT) is a promising breast imaging modality under development. Comparison to a standard method like mammography is essential for further development. Due to significant differences in image dimensionality and compression state of the breast, correlating USCT images and X-ray mammograms is challenging. In this paper we present a 2D/3D registration method to improve the spatial correspondence and allow direct comparison of the images. It is based on biomechanical modeling of the breast and simulation of the mammographic compression. We investigate the effect of including patient-specific material parameters estimated automatically from USCT images. The method was systematically evaluated using numerical phantoms and in-vivo data. The average registration accuracy using the automated registration was 11.9mm. Based on the registered images a method for analysis of the diagnostic value of the USCT images was developed and initially applied to analyze sound speed and attenuation images based on X-ray mammograms as ground truth. Combining sound speed and attenuation allows differentiating lesions from surrounding tissue. Overlaying this information on mammograms, combines quantitative and morphological information for multimodal diagnosis. PMID:25456144

  8. Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale.

    PubMed

    Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

    2016-02-01

    Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions. PMID:26986440

  9. Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale

    NASA Astrophysics Data System (ADS)

    Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

    2016-02-01

    Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

  10. A multi-moment finite volume method for incompressible Navier-Stokes equations on unstructured grids: Volume-average/point-value formulation

    NASA Astrophysics Data System (ADS)

    Xie, Bin; , Satoshi, Ii; Ikebata, Akio; Xiao, Feng

    2014-11-01

    A robust and accurate finite volume method (FVM) is proposed for incompressible viscous fluid dynamics on triangular and tetrahedral unstructured grids. Differently from conventional FVM where the volume integrated average (VIA) value is the only computational variable, the present formulation treats both VIA and the point value (PV) as the computational variables which are updated separately at each time step. The VIA is computed from a finite volume scheme of flux form, and is thus numerically conservative. The PV is updated from the differential form of the governing equation that does not have to be conservative but can be solved in a very efficient way. Including PV as the additional variable enables us to make higher-order reconstructions over compact mesh stencil to improve the accuracy, and moreover, the resulting numerical model is more robust for unstructured grids. We present the numerical formulations in both two and three dimensions on triangular and tetrahedral mesh elements. Numerical results of several benchmark tests are also presented to verify the proposed numerical method as an accurate and robust solver for incompressible flows on unstructured grids.

  11. Multiscale simulation of 2D elastic wave propagation

    NASA Astrophysics Data System (ADS)

    Zhang, Wensheng; Zheng, Hui

    2016-06-01

    In this paper, we develop the multiscale method for simulation of elastic wave propagation. Based on the first-order velocity-stress hyperbolic form of 2D elastic wave equation, the particle velocities are solved first ona coarse grid by the finite volume method. Then the stress tensor is solved by using the multiscale basis functions which can represent the fine-scale variation of the wavefield on the coarse grid. The basis functions are computed by solving a local problem with the finite element method. The theoretical formulae and description of the multiscale method for elastic wave equation are given in more detail. The numerical computations for an inhomogeneous model with random scatter are completed. The results show the effectiveness of the multiscale method.

  12. A Godunov-type Finite Volume Scheme for Meso- and Micro-scale Flows in Three Dimensions

    NASA Astrophysics Data System (ADS)

    Ahmad, Nash'at; Lindeman, John

    2008-10-01

    This short note reports the extension of the f-waves approximate Riemann solver (A hmad and L indeman, 2007; L eV eque, 2002; B ale et al., 2002) for three-dimensional meso- and micro-scale atmospheric flows. The Riemann solver employs flux-based wave decomposition for the calculation of Godunov fluxes and does not require the explicit definition of the Roe matrix to enforce conservation. The other important feature of the Riemann solver is its ability to incorporate source term due to gravity without introducing discretization errors. The resulting finite volume scheme is second-order accurate in space and time. The finite-difference schemes currently used in atmospheric flow models are neither conservative nor able to resolve regions of sharp gradients. The finite volume scheme described in this paper is fully conservative and has the ability to resolve regions of sharp gradients without introducing spurious oscillations in the solution. The scheme shows promise in accurately resolving flows on the meso- and micro-scales and should be considered for implementation in the dynamical cores of next generation meso- and micro-scale atmospheric flow models.

  13. Compact high order finite volume method on unstructured grids I: Basic formulations and one-dimensional schemes

    NASA Astrophysics Data System (ADS)

    Wang, Qian; Ren, Yu-Xin; Li, Wanai

    2016-06-01

    The large reconstruction stencil has been the major bottleneck problem in developing high order finite volume schemes on unstructured grids. This paper presents a compact reconstruction procedure for arbitrarily high order finite volume method on unstructured grids to overcome this shortcoming. In this procedure, a set of constitutive relations are constructed by requiring the reconstruction polynomial and its derivatives on the control volume of interest to conserve their averages on face-neighboring cells. These relations result in an over-determined linear equation system, which, in the sense of least-squares, can be reduced to a block-tridiagonal system in the one-dimensional case. The one-dimensional formulations of the reconstruction are discussed in detail and a Fourier analysis is presented to study the dispersion/dissipation and stability properties. The WBAP limiter based on the secondary reconstruction is used to suppress the non-physical oscillations near discontinuities while achieve high order accuracy in smooth regions of the solution. Numerical results demonstrate the method's high order accuracy, robustness and shock capturing capability.

  14. Very Large Data Volumes Analysis of Collaborative Systems with Finite Number of States

    ERIC Educational Resources Information Center

    Ivan, Ion; Ciurea, Cristian; Pavel, Sorin

    2010-01-01

    The collaborative system with finite number of states is defined. A very large database is structured. Operations on large databases are identified. Repetitive procedures for collaborative systems operations are derived. The efficiency of such procedures is analyzed. (Contains 6 tables, 5 footnotes and 3 figures.)

  15. A numerically efficient finite element hydroelastic analysis. Volume 1: Theory and results

    NASA Technical Reports Server (NTRS)

    Coppolino, R. N.

    1976-01-01

    Symmetric finite element matrix formulations for compressible and incompressible hydroelasticity are developed on the basis of Toupin's complementary formulation of classical mechanics. Results of implementation of the new technique in the NASTRAN structural analysis program are presented which demonstrate accuracy and efficiency.

  16. A preconditioned fast finite volume scheme for a fractional differential equation discretized on a locally refined composite mesh

    NASA Astrophysics Data System (ADS)

    Jia, Jinhong; Wang, Hong

    2015-10-01

    Numerical methods for fractional differential equations generate full stiffness matrices, which were traditionally solved via Gaussian type direct solvers that require O (N3) of computational work and O (N2) of memory to store where N is the number of spatial grid points in the discretization. We develop a preconditioned fast Krylov subspace iterative method for the efficient and faithful solution of finite volume schemes defined on a locally refined composite mesh for fractional differential equations to resolve boundary layers of the solutions. Numerical results are presented to show the utility of the method.

  17. A Freestream-Preserving High-Order Finite-Volume Method for Mapped Grids with Adaptive-Mesh Refinement

    SciTech Connect

    Guzik, S; McCorquodale, P; Colella, P

    2011-12-16

    A fourth-order accurate finite-volume method is presented for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Novel considerations for formulating the semi-discrete system of equations in computational space combined with detailed mechanisms for accommodating the adapting grids ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). Advancement in time is achieved with a fourth-order Runge-Kutta method.

  18. Finite-volume scheme for transonic potential flow about airfoils and bodies in an arbitrarily-shaped channel

    NASA Technical Reports Server (NTRS)

    South, J. C., Jr.; Green, L. L.; Doria, M. L.

    1985-01-01

    A conservative finite-volume difference scheme is developed for the potential equation to solve transonic flow about airfoils and bodies in an arbitrary channel. The scheme employs a mesh which is a nearly-conformal 'O' mesh about the airfoil and nearly orthogonal at the channel walls. The mesh extends to infinity upstream and downstream, where the mapping is singular. Special procedures are required to treat the singularities at infinity, including computation of the metrics near those points. Channels with exit areas different from inlet areas are solved; a body with a sting mount is an example of such a case.

  19. Finite-volume scheme for transonic potential flow about airfoils and bodies in an arbitrarily shaped channel

    NASA Technical Reports Server (NTRS)

    South, Jerry C., Jr.; Doria, Michael L.; Green, Lawrence L.

    1986-01-01

    A conservative finite-volume difference scheme is developed for the potential equation to solve transonic flow about airfoils and bodies in an arbitrarily shaped channel. The scheme employs a mesh which is a nearly conformal O mesh about the airfoil and nearly orthogonal at the channel walls. The mesh extends to infinity upstream and downstream, where the mapping is singular. Special procedures are required to treat the singularities at infinity, including computation of the metrics near those points. Channels with exit areas different from inlet areas are solved; a body with a sting mount is an example of such a case.

  20. An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

    SciTech Connect

    McCorquodale, Peter; Ullrich, Paul; Johansen, Hans; Colella, Phillip

    2015-09-04

    We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed-sphere. This approach combines a Runge--Kutta time discretization with a fourth-order accurate spatial discretization, and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy, but with many fewer operations.

  1. Incorporation of modified dynamic inverse Jiles-Atherton model in finite volume time domain for nonlinear electromagnetic field computation

    NASA Astrophysics Data System (ADS)

    Hamimid, M.; Mimoune, S. M.; Feliachi, M.

    2013-01-01

    In this paper, a time stepping finite volume method (FVM) associated with the modified inverse Jiles-Atherton model for the nonlinear electromagnetic field computation is presented. To describe the dynamic behavior in the conducting media, the effective field is modified by adding two counter-fields associated respectively to the eddy current and excess losses. The hysteresis loss can be estimated by the integration over the obtained hysteresis loop at each frequency. To examine the validity of the proposed dynamic model coupled with FVM, the computed total losses and hysteresis loops are compared to experiments.

  2. Relationship between sample volumes and modulus of human vertebral trabecular bone in micro-finite element analysis.

    PubMed

    Wen, Xin-Xin; Xu, Chao; Zong, Chun-Lin; Feng, Ya-Fei; Ma, Xiang-Yu; Wang, Fa-Qi; Yan, Ya-Bo; Lei, Wei

    2016-07-01

    Micro-finite element (μFE) models have been widely used to assess the biomechanical properties of trabecular bone. How to choose a proper sample volume of trabecular bone, which could predict the real bone biomechanical properties and reduce the calculation time, was an interesting problem. Therefore, the purpose of this study was to investigate the relationship between different sample volumes and apparent elastic modulus (E) calculated from μFE model. 5 Human lumbar vertebral bodies (L1-L5) were scanned by micro-CT. Cubic concentric samples of different lengths were constructed as the experimental groups and the largest possible volumes of interest (VOI) were constructed as the control group. A direct voxel-to-element approach was used to generate μFE models and steel layers were added to the superior and inferior surface to mimic axial compression tests. A 1% axial strain was prescribed to the top surface of the model to obtain the E values. ANOVA tests were performed to compare the E values from the different VOIs against that of the control group. Nonlinear function curve fitting was performed to study the relationship between volumes and E values. The larger cubic VOI included more nodes and elements, and more CPU times were needed for calculations. E values showed a descending tendency as the length of cubic VOI decreased. When the volume of VOI was smaller than (7.34mm(3)), E values were significantly different from the control group. The fit function showed that E values approached an asymptotic values with increasing length of VOI. Our study demonstrated that apparent elastic modulus calculated from μFE models were affected by the sample volumes. There was a descending tendency of E values as the length of cubic VOI decreased. Sample volume which was not smaller than (7.34mm(3)) was efficient enough and timesaving for the calculation of E. PMID:26999702

  3. Modelling capillary trapping using finite-volume simulation of two-phase flow directly on micro-CT images

    NASA Astrophysics Data System (ADS)

    Raeini, Ali Q.; Bijeljic, Branko; Blunt, Martin J.

    2015-09-01

    We study capillary trapping in porous media using direct pore-scale simulation of two-phase flow on micro-CT images of a Berea sandstone and a sandpack. The trapped non-wetting phase saturations are predicted by solving the full Navier-Stokes equations using a volume-of-fluid based finite-volume framework to simulate primary drainage followed by water injection. Using these simulations, we analyse the effects of initial non-wetting-phase saturation, capillary number and flow direction on the residual saturation. The predictions from our numerical method are in agreement with published experimental measurements of capillary trapping curves. This shows that our direct simulation method can be used to elucidate the effect of pore structure and flow pattern of capillary trapping and provides a platform to study the physics of multiphase flow at the pore scale.

  4. PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual

    NASA Technical Reports Server (NTRS)

    Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.

    1977-01-01

    The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.

  5. MAZE96. Generates 2D Input for DYNA NIKE & TOPAZ

    SciTech Connect

    Sanford, L.; Hallquist, J.O.

    1992-02-24

    MAZE is an interactive program that serves as an input and two-dimensional mesh generator for DYNA2D, NIKE2D, TOPAZ2D, and CHEMICAL TOPAZ2D. MAZE also generates a basic template for ISLAND input. MAZE has been applied to the generation of input data to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.

  6. Generates 2D Input for DYNA NIKE & TOPAZ

    1996-07-15

    MAZE is an interactive program that serves as an input and two-dimensional mesh generator for DYNA2D, NIKE2D, TOPAZ2D, and CHEMICAL TOPAZ2D. MAZE also generates a basic template for ISLAND input. MAZE has been applied to the generation of input data to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.

  7. Conventional versus pre-balanced forms of the shallow-water equations solved using finite-volume method

    NASA Astrophysics Data System (ADS)

    Lu, Xinhua; Xie, Shengbai

    2016-05-01

    In the existing literature, various forms of governing equations have been proposed to solve the shallow-water equations (SWEs). Recently, attention has been dedicated to the so-called "pre-balanced" form, because finite-volume schemes that are designed on this basis satisfy the well-balanced property. In this study, we theoretically investigate the relationship between numerical schemes devised using approximate Riemann solvers in the framework of finite-volume methods for solving the conventional form of the SWEs and its "pre-balanced" variant. We find that the numerical schemes for solving these two forms of the SWEs turn out to be identical when some widely employed upwind or centered approximate Riemann solvers are adopted for the numerical flux evaluations, such as the HLL (Harten, Lax, and van Leer), HLLC (HLL solver with restoring the contact surface), FORCE (first-order centered), and SLIC (slope limited centered) schemes. Some numerical experiments are performed, which verify the validity of the result of our theoretical analysis. The theoretical and numerical results suggest that the "pre-balanced" SWEs variant is not superior to the conventional one for solving the SWEs using approximate Riemann solvers.

  8. Multichannel 0→2 and 1→2 transition amplitudes for arbitrary spin particles in a finite volume

    DOE PAGESBeta

    Hansen, Maxwell; Briceno, Raul

    2015-10-01

    We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volumemore » $$\\textbf{0}\\rightarrow\\textbf{2}$$ and $$\\textbf{1}\\rightarrow\\textbf{2}$$ transition amplitudes. Our result accommodates theories in which the final two-particle state is coupled to any number of other two-body channels, with all angular momentum states included. The derivation uses generic, fully relativistic field theory, and is exact up to exponentially suppressed corrections in the lightest particle mass times the box size. This work distinguishes itself from previous studies by accommodating particles with any intrinsic spin. To illustrate the utility of our general result, we discuss how it can be implemented for studies of $$N+\\mathcal{J}~\\rightarrow~(N\\pi,N\\eta,N\\eta',\\Sigma K,\\Lambda K)$$ transitions, where $$\\mathcal{J}$$ is a generic external current. The reduction of rotational symmetry, due to the cubic finite volume, manifests in this example through the mixing of S- and P-waves when the system has nonzero total momentum.« less

  9. Generalization of the CCLADS method for modeling anisotropic diffusion tensors on three-dimensional finite-volume grids

    NASA Astrophysics Data System (ADS)

    Provost, A.; Langevin, C.

    2012-12-01

    A number of numerical methods exist for incorporating anisotropic diffusion tensors, such as hydraulic or thermal conductivity, into two- and three-dimensional numerical models. The methods vary in mathematical approach, complexity, performance, and applicability to different types of model grids. The CCLADS variant of the CCLAD (Cell-Centered LAgrangian Diffusion) method of Maire & Breil (2011) is applicable to two-dimensional, unstructured, cell-centered finite-volume grids. It has a local stencil and exhibits nearly second-order accuracy on smooth distorted grids. As originally derived, CCLADS is not directly generalizable to three dimensions, and the derivation breaks down when adjacent cell edges meet at 180 degrees. Here, we rederive CCLADS to overcome these limitations and investigate the performance of the generalized method in a suite of three-dimensional test problems on structured, rectangular grids. As in two dimensions, the generalized method should be applicable to unstructured grids. Maire, P.-H., and Breil J., 2012, A nominally second-order accurate finite volume cell-centered scheme for anisotropic diffusion on two-dimensional unstructured grids, J. Comput. Phys., 231 (5), 2259-2299.

  10. Coupled numerical approach combining finite volume and lattice Boltzmann methods for multi-scale multi-physicochemical processes

    SciTech Connect

    Chen, Li; He, Ya-Ling; Kang, Qinjun; Tao, Wen-Quan

    2013-12-15

    A coupled (hybrid) simulation strategy spatially combining the finite volume method (FVM) and the lattice Boltzmann method (LBM), called CFVLBM, is developed to simulate coupled multi-scale multi-physicochemical processes. In the CFVLBM, computational domain of multi-scale problems is divided into two sub-domains, i.e., an open, free fluid region and a region filled with porous materials. The FVM and LBM are used for these two regions, respectively, with information exchanged at the interface between the two sub-domains. A general reconstruction operator (RO) is proposed to derive the distribution functions in the LBM from the corresponding macro scalar, the governing equation of which obeys the convection–diffusion equation. The CFVLBM and the RO are validated in several typical physicochemical problems and then are applied to simulate complex multi-scale coupled fluid flow, heat transfer, mass transport, and chemical reaction in a wall-coated micro reactor. The maximum ratio of the grid size between the FVM and LBM regions is explored and discussed. -- Highlights: •A coupled simulation strategy for simulating multi-scale phenomena is developed. •Finite volume method and lattice Boltzmann method are coupled. •A reconstruction operator is derived to transfer information at the sub-domains interface. •Coupled multi-scale multiple physicochemical processes in micro reactor are simulated. •Techniques to save computational resources and improve the efficiency are discussed.

  11. HipMatch: an object-oriented cross-platform program for accurate determination of cup orientation using 2D-3D registration of single standard X-ray radiograph and a CT volume.

    PubMed

    Zheng, Guoyan; Zhang, Xuan; Steppacher, Simon D; Murphy, Stephen B; Siebenrock, Klaus A; Tannast, Moritz

    2009-09-01

    The widely used procedure of evaluation of cup orientation following total hip arthroplasty using single standard anteroposterior (AP) radiograph is known inaccurate, largely due to the wide variability in individual pelvic orientation relative to X-ray plate. 2D-3D image registration methods have been introduced for an accurate determination of the post-operative cup alignment with respect to an anatomical reference extracted from the CT data. Although encouraging results have been reported, their extensive usage in clinical routine is still limited. This may be explained by their requirement of a CAD model of the prosthesis, which is often difficult to be organized from the manufacturer due to the proprietary issue, and by their requirement of either multiple radiographs or a radiograph-specific calibration, both of which are not available for most retrospective studies. To address these issues, we developed and validated an object-oriented cross-platform program called "HipMatch" where a hybrid 2D-3D registration scheme combining an iterative landmark-to-ray registration with a 2D-3D intensity-based registration was implemented to estimate a rigid transformation between a pre-operative CT volume and the post-operative X-ray radiograph for a precise estimation of cup alignment. No CAD model of the prosthesis is required. Quantitative and qualitative results evaluated on cadaveric and clinical datasets are given, which indicate the robustness and the accuracy of the program. HipMatch is written in object-oriented programming language C++ using cross-platform software Qt (TrollTech, Oslo, Norway), VTK, and Coin3D and is transportable to any platform. PMID:19328585

  12. Aniso2D

    2005-07-01

    Aniso2d is a two-dimensional seismic forward modeling code. The earth is parameterized by an X-Z plane in which the seismic properties Can have monoclinic with x-z plane symmetry. The program uses a user define time-domain wavelet to produce synthetic seismograms anrwhere within the two-dimensional media.

  13. Brittle damage models in DYNA2D

    SciTech Connect

    Faux, D.R.

    1997-09-01

    DYNA2D is an explicit Lagrangian finite element code used to model dynamic events where stress wave interactions influence the overall response of the system. DYNA2D is often used to model penetration problems involving ductile-to-ductile impacts; however, with the advent of the use of ceramics in the armor-anti-armor community and the need to model damage to laser optics components, good brittle damage models are now needed in DYNA2D. This report will detail the implementation of four brittle damage models in DYNA2D, three scalar damage models and one tensor damage model. These new brittle damage models are then used to predict experimental results from three distinctly different glass damage problems.

  14. Test functions for three-dimensional control-volume mixed finite-element methods on irregular grids

    USGS Publications Warehouse

    Naff, R.L.; Russell, T.F.; Wilson, J.D.

    2000-01-01

    Numerical methods based on unstructured grids, with irregular cells, usually require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element methods, vector shape functions are used to approximate the distribution of velocities across cells and vector test functions are used to minimize the error associated with the numerical approximation scheme. For a logically cubic mesh, the lowest-order shape functions are chosen in a natural way to conserve intercell fluxes that vary linearly in logical space. Vector test functions, while somewhat restricted by the mapping into the logical reference cube, admit a wider class of possibilities. Ideally, an error minimization procedure to select the test function from an acceptable class of candidates would be the best procedure. Lacking such a procedure, we first investigate the effect of possible test functions on the pressure distribution over the control volume; specifically, we look for test functions that allow for the elimination of intermediate pressures on cell faces. From these results, we select three forms for the test function for use in a control-volume mixed method code and subject them to an error analysis for different forms of grid irregularity; errors are reported in terms of the discrete L2 norm of the velocity error. Of these three forms, one appears to produce optimal results for most forms of grid irregularity.

  15. Finite volume method for radiative heat transfer in an unstructured flow solver for emitting, absorbing and scattering media

    NASA Astrophysics Data System (ADS)

    Gazdallah, Moncef; Feldheim, Véronique; Claramunt, Kilian; Hirsch, Charles

    2012-06-01

    This paper presents the implementation of the finite volume method to solve the radiative transfer equation in a commercial code. The particularity of this work is that the method applied on unstructured hexahedral meshes does not need a pre-processing step establishing a particular marching order to visit all the control volumes. The solver simply visits the faces of the control volumes as numbered in the hexahedral unstructured mesh. A cell centred mesh and a spatial differencing step scheme to relate facial radiative intensities to nodal intensities is used. The developed computer code based on FVM has been integrated in the CFD solver FINE™/Open from NUMECA Int. Radiative heat transfer can be evaluated within systems containing uniform, grey, emitting, absorbing and/or isotropically or linear anisotropically scattering medium bounded by diffuse grey walls. This code has been validated for three test cases. The first one is a three dimensional rectangular enclosure filled with emitting, absorbing and anisotropically scattering media. The second is the differentially heated cubic cavity. The third one is the L-shaped enclosure. For these three test cases a good agreement has been observed when temperature and heat fluxes predictions are compared with references taken, from literature.

  16. Crystal plasticity finite element analysis for René88DT statistical volume element generation

    NASA Astrophysics Data System (ADS)

    Tucker, Joseph C.; Cerrone, Albert R., III; Ingraffea, Anthony R.; Rollett, Anthony D.

    2015-04-01

    This work focuses on the major cause of life limiting behavior in Ni-based superalloys for high pressure and temperature turbine disks applications in low cycle fatigue. Specific ideas of local microstructure features, such as the role of as large as (ALA) grains, in promoting slip localization in directly measured 3D microstructures were tested with finite element method (FEM) simulations with crystal plasticity. Synthetic microstructures with experimentally determined microstructurally small fatigue crack weakest link features of ALA grains comprise the test cases. A René88 damage tolerant (R88DT) dataset, from electron backscatter diffraction, was used to instantiate approximately 1.5 million elements and 200 grains from FEM sensitivity studies. Changing mesh resolution minimally impacted global damage response, but local convergence required the maximum resolution. The present results help to quantify the deleterious impact of ALA grains in Ni-based superalloys to extend service life.

  17. Mesh2d

    SciTech Connect

    Greg Flach, Frank Smith

    2011-12-31

    Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.

  18. Mesh2d

    2011-12-31

    Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assignsmore » an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.« less

  19. Multiphase flow modelling using non orthogonal collocated finite volumes : application to fluid catalytical cracking and large scale geophysical flows.

    NASA Astrophysics Data System (ADS)

    Martin, R. M.; Nicolas, A. N.

    2003-04-01

    A modeling approach of gas solid flow, taking into account different physical phenomena such as gas turbulence and inter-particle interactions is presented. Moment transport equations are derived for the second order fluctuating velocity tensor which allow to involve practical closures based on single phase turbulence modeling on one hand and kinetic theory of granular media on the other hand. The model is applied to fluid catalytic cracking processes and explosive volcanism. In the industry as well as in the geophysical community, multiphase flows are modeled using a finite volume approach and a multicorrector algorithm in time in order to determine implicitly the pressures, velocities and volume fractions for each phase. Pressures, and velocities are generally determined at mid-half mesh step from each other following the staggered grid approach. This ensures stability and prevents oscillations in pressure. It allows to treat almost all the Reynolds number ranges for all speeds and viscosities. The disadvantages appear when we want to treat more complex geometries or if a generalized curvilinear formulation of the conservation equations is considered. Too many interpolations have to be done and accuracy is then lost. In order to overcome these problems, we use here a similar algorithm in time and a Rhie and Chow interpolation (1983) of the collocated variables and essentially the velocities at the interface. The Rhie and Chow interpolation of the velocities at the finite volume interfaces allows to have no oscillations of the pressure without checkerboard effects and to stabilize all the algorithm. In a first predictor step, fluxes at the interfaces of the finite volumes are then computed using 2nd and 3rd order shock capturing schemes of MUSCL/TVD or Van Leer type, and the orthogonal stress components are treated implicitly while cross viscous/diffusion terms are treated explicitly. Pentadiagonal linear systems are solved in each geometrical direction (the so

  20. Vertical 2D Heterostructures

    NASA Astrophysics Data System (ADS)

    Lotsch, Bettina V.

    2015-07-01

    Graphene's legacy has become an integral part of today's condensed matter science and has equipped a whole generation of scientists with an armory of concepts and techniques that open up new perspectives for the postgraphene area. In particular, the judicious combination of 2D building blocks into vertical heterostructures has recently been identified as a promising route to rationally engineer complex multilayer systems and artificial solids with intriguing properties. The present review highlights recent developments in the rapidly emerging field of 2D nanoarchitectonics from a materials chemistry perspective, with a focus on the types of heterostructures available, their assembly strategies, and their emerging properties. This overview is intended to bridge the gap between two major—yet largely disjunct—developments in 2D heterostructures, which are firmly rooted in solid-state chemistry or physics. Although the underlying types of heterostructures differ with respect to their dimensions, layer alignment, and interfacial quality, there is common ground, and future synergies between the various assembly strategies are to be expected.

  1. Unstructured Finite Volume Computational Thermo-Fluid Dynamic Method for Multi-Disciplinary Analysis and Design Optimization

    NASA Technical Reports Server (NTRS)

    Majumdar, Alok; Schallhorn, Paul

    1998-01-01

    This paper describes a finite volume computational thermo-fluid dynamics method to solve for Navier-Stokes equations in conjunction with energy equation and thermodynamic equation of state in an unstructured coordinate system. The system of equations have been solved by a simultaneous Newton-Raphson method and compared with several benchmark solutions. Excellent agreements have been obtained in each case and the method has been found to be significantly faster than conventional Computational Fluid Dynamic(CFD) methods and therefore has the potential for implementation in Multi-Disciplinary analysis and design optimization in fluid and thermal systems. The paper also describes an algorithm of design optimization based on Newton-Raphson method which has been recently tested in a turbomachinery application.

  2. Amplitude flux, probability flux, and gauge invariance in the finite volume scheme for the Schrödinger equation

    SciTech Connect

    Gordon, D.F.; Hafizi, B.; Landsman, A.S.

    2015-01-01

    The time-dependent Schrödinger equation can be put in a probability conserving, gauge invariant form, on arbitrary structured grids via finite volume discretization. The gauge terms in the discrete system cancel with a portion of the amplitude flux to produce abbreviated flux functions. The resulting time translation operator is strictly unitary, and is compatible with an efficient operator splitting scheme that allows for multi-dimensional simulation with complex grid geometries. Moreover, the abbreviated amplitude flux is necessary to the construction of a conservative probability current. This construction turns out to be important when computing Bohmian trajectories in multi-dimensions. Bohmian trajectories are useful in the interpretation of quantum mechanical phenomena such as tunneling ionization, and provide a bridge between quantum and classical regimes.

  3. Calculation of Magnetospheric Equilibria and Evolution of Plasma Bubbles with a New Finite-Volume MHD/Magnetofriction Code

    NASA Astrophysics Data System (ADS)

    Silin, I.; Toffoletto, F.; Wolf, R.; Sazykin, S. Y.

    2013-12-01

    We present a finite-volume MHD code for simulations of magnetospheric dynamics of the plasma sheet and the inner magnetosphere. The code uses staggered non-uniform Cartesian grids to preserve the divergence-free magnetic fields, along with various numerical approximations and flux limiters for the plasma variables. The code can be initialized with empirical magnetic field models, such as the Tsyganenko models along with pressure information from either the Tsyganenko-Mukai models, or observational data, such as DMSP pressure maps. Artificial "friction term" can be added to the momentum equation, which turns the MHD code into "magnetofriction" code which can be used to construct approximate equilibrium solutions. We demonstrate some applications for our code, in both the "magnetofriction" and MHD mode, including relaxation of the empirical models to equilibrium and the evolution of a plasma bubble in the near magnetotail. The latter MHD simulation results exhibit oscillations about their equilibrium position in agreement with recent observations.

  4. Finite-volume application of high-order ENO schemes to two-dimensional boundary-value problems

    NASA Technical Reports Server (NTRS)

    Casper, Jay

    1991-01-01

    Finite-volume applications of high-order accurate ENO schemes to two-dimensional boundary-value problems are studied. These schemes achieve high-order spatial accuracy, in smooth regions, by a piecewise polynomial approximation of the solution from cell averages. In addition, this spatial operation involves an adaptive stencil algorithm in order to avoid the oscillatory behavior that is associated with interpolation across steep gradients. High-order TVD Runge-Kutta methods are employed for time integration, thus making these schemes best suited for unsteady problems. Fifth- and sixth-order accurate applications are validated through a grid refinement study involving the solutions of scalar hyperbolic equations. A previously proposed extension for the Euler equations of gas dynamics is tested, including its application to solutions of boundary-value problems involving solid walls and curvilinear coordinates.

  5. SIMULATING WAVES IN THE UPPER SOLAR ATMOSPHERE WITH SURYA: A WELL-BALANCED HIGH-ORDER FINITE-VOLUME CODE

    SciTech Connect

    Fuchs, F. G.; McMurry, A. D.; Mishra, S.; Waagan, K. E-mail: a.d.mcmurry@ifi.uio.no E-mail: kwaagan@cscamm.umd.edu

    2011-05-10

    We consider the propagation of waves in a stratified non-isothermal magnetic atmosphere. The situation of interest corresponds to waves in the outer solar (chromosphere and corona) and other stellar atmospheres. The waves are simulated by using a high-resolution, well-balanced finite-volume-based massively parallel code named SURYA. Numerical experiments in both two and three space dimensions involving realistic temperature distributions, driving forces, and magnetic field configurations are described. Diverse phenomena such as mode conversion, wave acceleration at the transition layer, and driving-dependent wave dynamics are observed. We obtain evidence for the presence of coronal Alfven waves in some three-dimensional configurations. Although some of the incident wave energy is transmitted into the corona, a large proportion of it is accumulated in the chromosphere, providing a possible mechanism for chromospheric heating.

  6. A QR accelerated volume-to-surface boundary condition for finite element solution of eddy current problems

    SciTech Connect

    White, D; Fasenfest, B; Rieben, R; Stowell, M

    2006-09-08

    We are concerned with the solution of time-dependent electromagnetic eddy current problems using a finite element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. We propose a Biot-Savart law based volume-to-surface boundary condition to meet this requirement. This Biot-Savart approach is demonstrated to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart law.

  7. A finite volume method and experimental study of a stator of a piezoelectric traveling wave rotary ultrasonic motor.

    PubMed

    Bolborici, V; Dawson, F P; Pugh, M C

    2014-03-01

    Piezoelectric traveling wave rotary ultrasonic motors are motors that generate torque by using the friction force between a piezoelectric composite ring (or disk-shaped stator) and a metallic ring (or disk-shaped rotor) when a traveling wave is excited in the stator. The motor speed is proportional to the amplitude of the traveling wave and, in order to obtain large amplitudes, the stator is excited at frequencies close to its resonance frequency. This paper presents a non-empirical partial differential equations model for the stator, which is discretized using the finite volume method. The fundamental frequency of the discretized model is computed and compared to the experimentally-measured operating frequency of the stator of Shinsei USR60 piezoelectric motor. PMID:24210273

  8. A vertex centred Finite Volume Jameson-Schmidt-Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics

    NASA Astrophysics Data System (ADS)

    Aguirre, Miquel; Gil, Antonio J.; Bonet, Javier; Arranz Carreño, Aurelio

    2014-02-01

    A vertex centred Finite Volume algorithm is presented for the numerical simulation of fast transient dynamics problems involving large deformations. A mixed formulation based upon the use of the linear momentum, the deformation gradient tensor and the total energy as conservation variables is discretised in space using linear triangles and tetrahedra in two-dimensional and three-dimensional computations, respectively. The scheme is implemented using central differences for the evaluation of the interface fluxes in conjunction with the Jameson-Schmidt-Turkel (JST) artificial dissipation term. The discretisation in time is performed by using a Total Variational Diminishing (TVD) two-stage Runge-Kutta time integrator. The JST algorithm is adapted in order to ensure the preservation of linear and angular momenta. The framework results in a low order computationally efficient solver for solid dynamics, which proves to be very competitive in nearly incompressible scenarios and bending dominated applications.

  9. Finite Volume schemes on unstructured grids for non-local models: Application to the simulation of heat transport in plasmas

    SciTech Connect

    Goudon, Thierry; Parisot, Martin

    2012-10-15

    In the so-called Spitzer-Haerm regime, equations of plasma physics reduce to a nonlinear parabolic equation for the electronic temperature. Coming back to the derivation of this limiting equation through hydrodynamic regime arguments, one is led to construct a hierarchy of models where the heat fluxes are defined through a non-local relation which can be reinterpreted as well by introducing coupled diffusion equations. We address the question of designing numerical methods to simulate these equations. The basic requirement for the scheme is to be asymptotically consistent with the Spitzer-Haerm regime. Furthermore, the constraints of physically realistic simulations make the use of unstructured meshes unavoidable. We develop a Finite Volume scheme, based on Vertex-Based discretization, which reaches these objectives. We discuss on numerical grounds the efficiency of the method, and the ability of the generalized models in capturing relevant phenomena missed by the asymptotic problem.

  10. Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium

    NASA Astrophysics Data System (ADS)

    Mishra, S.; Schwab, Ch.; Šukys, J.

    2016-05-01

    We consider the very challenging problem of efficient uncertainty quantification for acoustic wave propagation in a highly heterogeneous, possibly layered, random medium, characterized by possibly anisotropic, piecewise log-exponentially distributed Gaussian random fields. A multi-level Monte Carlo finite volume method is proposed, along with a novel, bias-free upscaling technique that allows to represent the input random fields, generated using spectral FFT methods, efficiently. Combined together with a recently developed dynamic load balancing algorithm that scales to massively parallel computing architectures, the proposed method is able to robustly compute uncertainty for highly realistic random subsurface formations that can contain a very high number (millions) of sources of uncertainty. Numerical experiments, in both two and three space dimensions, illustrating the efficiency of the method are presented.

  11. An Incompressible 2D Didactic Model with Singularity and Explicit Solutions of the 2D Boussinesq Equations

    NASA Astrophysics Data System (ADS)

    Chae, Dongho; Constantin, Peter; Wu, Jiahong

    2014-09-01

    We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time for all time. In addition, we introduce a variant of the 2D Boussinesq equations which is perhaps a more faithful companion of the 3D axisymmetric Euler equations than the usual 2D Boussinesq equations.

  12. Women with Anorexia Nervosa: Finite Element and Trabecular Structure Analysis by Using Flat-Panel Volume CT

    PubMed Central

    Phan, Catherine M.; Misra, Madhusmita; Bredella, Miriam A.; Miller, Karen K.; Fazeli, Pouneh K.; Bayraktar, Harun H.; Klibanski, Anne; Gupta, Rajiv

    2010-01-01

    Purpose: To use finite element modeling based on flat-panel volume computed tomography (CT) and bone mineral density (BMD) provided by dual-energy x-ray absorptiometry (DXA) to compare bone failure load, stiffness, and trabecular structure in women with anorexia nervosa (AN) and age-matched normal-weight control subjects. Materials and Methods: The study was approved by the institutional review board and complied with HIPAA guidelines. Informed consent was obtained. Fourteen women, eight with AN (mean age, 26.6 years) and six control subjects (mean age, 26.3 years), underwent flat-panel volume CT of the distal radius to determine apparent trabecular bone volume fraction (BV/TV), apparent trabecular number (TbN), apparent trabecular thickness (TbTh), and apparent trabecular separation (TbSp). Bone strength and stiffness were calculated from uniaxial compression tests by using finite element models created from flat-panel volume CT. DXA was used to determine BMD of the radius, lumbar spine, and hip. Means ± standard deviations of all variables were calculated for both groups and compared (Student t test). Univariate regression analysis and stepwise regression modeling were performed. Results: Patients with AN had lower values for stiffness (284.77 kN/mm ± 76.14 vs 389.97 kN/mm ± 84.90, P = .04), failure load (4.98 kN ± 1.23 vs 7.01 kN ± 1.52, P = .02), BV/TV (0.32% ± 0.09 vs 0.44% ± 0.02, P = .007), and TbN (1.15 mm−3 ± 0.20 vs 1.43 mm−3 ± 0.13, P = .008) and higher values for TbSp (0.62 mm ± 0.20 vs 0.40 mm ± 0.04, P = .02) compared with normal-weight control subjects. TbTh was lower in women with AN (P = .1). BMD measurements were significantly lower for the AN group. BMD measurements and trabecular parameters (except TbTh) correlated with stiffness and failure load (r = 0.58 to 0.83). Conclusion: Failure load and stiffness are abnormal in women with AN compared with those in normal-weight control subjects and correlate with BMD and trabecular

  13. Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1992-01-01

    A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

  14. The role of computational fluid dynamics in aeronautical engineering (5). Improvements and applications of implicit TVD finite volume code

    NASA Astrophysics Data System (ADS)

    Shima, Eiji; Yoshida, Kenji; Amano, Kanichi

    1987-11-01

    An automatic grid generator for multiple element airfoils was developed and the existing implicit Total Variation Diminishing (TVD) finite volume code was improved in both accuracy and efficiency, in order to make the Navier-Stokes solver a practical design tool for high lift devices. Utilizing these codes, Navier-Stokes analysis of the single slotted flap was carried out. The automatic grid generator utilizes the elliptic equation solver using the finite difference method combined with the panel method. The flow field is divided into subregions by the dividing stream lines which are calculated by the panel method and the computational grid in each subregion is generated by solving the elliptic equations (Thompson's method). Since the panel method can solve the potential flow around any number of arbitrary shaped bodies, this grid generator can generate a H-type computational grid around such bodies automatically. To obtain a high accuracy on a rapidly stretching grid, the flow solver uses the TVD formulation containing an explicit treatment of nonuniform grid spacing. Converging rate and numerical stability of the flow solver is augmented by the relaxation approach using Symmetric Point Gauss Seidel method in matrix inversion process which is necessary for an implicit scheme.

  15. A new high-resolution unstructured grid finite volume Arctic Ocean model (AO-FVCOM): An application for tidal studies

    NASA Astrophysics Data System (ADS)

    Chen, Changsheng; Gao, Guoping; Qi, Jianhua; Proshutinsky, Andrey; Beardsley, Robert C.; Kowalik, Zygmunt; Lin, Huichan; Cowles, Geoffrey

    2009-08-01

    A spherical coordinate version of the unstructured grid 3-D FVCOM (finite volume coastal ocean model) has been applied to the Arctic Ocean to simulate tides with a horizontal resolution ranging from 1 km in the near-coastal areas to 15 km in the deep ocean. By accurately resolving the irregular coastlines and bathymetry in the Arctic Ocean coastal regions, this model reproduces the diurnal (K1 and O1) and semidiurnal (M2 and S2) tidal wave dynamics and captures the complex tidal structure along the coast, particularly in the narrow straits of the Canadian Archipelago. The simulated tidal parameters (harmonic constituents of sea surface elevation and currents) agree well with the available observational data. High-resolution meshes over the continental shelf and slope capture the detailed spatial structure of topographic trapped shelf waves, which are quite energetic along the Greenland, Siberia, and Spitsbergen continental slope and shelf break areas. Water stratification influences the vertical distribution of tidal currents but not the water transport and thus tidal elevation. The comparison with previous finite difference models suggests that horizontal resolution and geometric fitting are two prerequisites to simulate realistically the tidal energy flux in the Arctic Ocean, particularly in the Canadian Archipelago.

  16. Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction

    NASA Astrophysics Data System (ADS)

    Kidanemariam, Aman G.; Chan-Braun, Clemens; Doychev, Todor; Uhlmann, Markus

    2013-02-01

    We have performed direct numerical simulation of turbulent open channel flow over a smooth horizontal wall in the presence of finite-size, heavy particles. The spherical particles have a diameter of approximately 7 wall units, a density of 1.7 times the fluid density and a solid volume fraction of 5 × 10-4. The value of the Galileo number is set to 16.5, while the Shields parameter measures approximately 0.2. Under these conditions, the particles are predominantly located in the vicinity of the bottom wall, where they exhibit strong preferential concentration which we quantify by means of Voronoi analysis and by computing the particle-conditioned concentration field. As observed in previous studies with similar parameter values, the mean streamwise particle velocity is smaller than that of the fluid. We propose a new definition of the fluid velocity ‘seen’ by finite-size particles based on an average over a spherical surface segment, from which we deduce in the present case that the particles are instantaneously lagging the fluid only by a small amount. The particle-conditioned fluid velocity field shows that the particles preferentially reside in the low-speed streaks, leading to the observed apparent lag. Finally, a vortex eduction study reveals that spanwise particle motion is significantly correlated with the presence of vortices with the corresponding sense of rotation which are located in the immediate vicinity of the near-wall particles.

  17. Contribution of the finite volume point dilution method for measurement of groundwater fluxes in a fractured aquifer.

    PubMed

    Jamin, P; Goderniaux, P; Bour, O; Le Borgne, T; Englert, A; Longuevergne, L; Brouyère, S

    2015-11-01

    Measurement of groundwater fluxes is the basis of all hydrogeological study, from hydraulic characterization to the most advanced reactive transport modeling. Usual groundwater flux estimation with Darcy's law may lead to cumulated errors on spatial variability, especially in fractured aquifers where local direct measurement of groundwater fluxes becomes necessary. In the present study, both classical point dilution method (PDM) and finite volume point dilution method (FVPDM) are compared on the fractured crystalline aquifer of Ploemeur, France. The manipulation includes the first use of the FVPDM in a fractured aquifer using a double packer. This configuration limits the vertical extent of the tested zone to target a precise fracture zone of the aquifer. The result of this experiment is a continuous monitoring of groundwater fluxes that lasted for more than 4 days. Measurements of groundwater flow rate in the fracture (Q(t)) by PDM provide good estimates only if the mixing volume (V(w)) (volume of water in which the tracer is mixed) is precisely known. Conversely, the FVPDM allows for an independent estimation of V(w) and Q(t), leading to better precision in case of complex experimental setup such as the one used. The precision of a PDM does not rely on the duration of the experiment while a FVPDM may require long experimental duration to guarantees a good precision. Classical PDM should then be used for rapid estimation of groundwater flux using simple experimental setup. On the other hand, the FVPDM is a more precise method that has a great potential for development but may require longer duration experiment to achieve a good precision if the groundwater fluxes investigated are low and/or the mixing volume is large. PMID:26519822

  18. Contribution of the finite volume point dilution method for measurement of groundwater fluxes in a fractured aquifer

    NASA Astrophysics Data System (ADS)

    Jamin, P.; Goderniaux, P.; Bour, O.; Le Borgne, T.; Englert, A.; Longuevergne, L.; Brouyère, S.

    2015-11-01

    Measurement of groundwater fluxes is the basis of all hydrogeological study, from hydraulic characterization to the most advanced reactive transport modeling. Usual groundwater flux estimation with Darcy's law may lead to cumulated errors on spatial variability, especially in fractured aquifers where local direct measurement of groundwater fluxes becomes necessary. In the present study, both classical point dilution method (PDM) and finite volume point dilution method (FVPDM) are compared on the fractured crystalline aquifer of Ploemeur, France. The manipulation includes the first use of the FVPDM in a fractured aquifer using a double packer. This configuration limits the vertical extent of the tested zone to target a precise fracture zone of the aquifer. The result of this experiment is a continuous monitoring of groundwater fluxes that lasted for more than 4 days. Measurements of groundwater flow rate in the fracture (Qt) by PDM provide good estimates only if the mixing volume (Vw) (volume of water in which the tracer is mixed) is precisely known. Conversely, the FVPDM allows for an independent estimation of Vw and Qt, leading to better precision in case of complex experimental setup such as the one used. The precision of a PDM does not rely on the duration of the experiment while a FVPDM may require long experimental duration to guarantees a good precision. Classical PDM should then be used for rapid estimation of groundwater flux using simple experimental setup. On the other hand, the FVPDM is a more precise method that has a great potential for development but may require longer duration experiment to achieve a good precision if the groundwater fluxes investigated are low and/or the mixing volume is large.

  19. Accuracy Analysis for Finite-Volume Discretization Schemes on Irregular Grids

    NASA Technical Reports Server (NTRS)

    Diskin, Boris; Thomas, James L.

    2010-01-01

    A new computational analysis tool, downscaling test, is introduced and applied for studying the convergence rates of truncation and discretization errors of nite-volume discretization schemes on general irregular (e.g., unstructured) grids. The study shows that the design-order convergence of discretization errors can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all. The downscaling test is a general, efficient, accurate, and practical tool, enabling straightforward extension of verification and validation to general unstructured grid formulations. It also allows separate analysis of the interior, boundaries, and singularities that could be useful even in structured-grid settings. There are several new findings arising from the use of the downscaling test analysis. It is shown that the discretization accuracy of a common node-centered nite-volume scheme, known to be second-order accurate for inviscid equations on triangular grids, degenerates to first order for mixed grids. Alternative node-centered schemes are presented and demonstrated to provide second and third order accuracies on general mixed grids. The local accuracy deterioration at intersections of tangency and in flow/outflow boundaries is demonstrated using the DS tests tailored to examining the local behavior of the boundary conditions. The discretization-error order reduction within inviscid stagnation regions is demonstrated. The accuracy deterioration is local, affecting mainly the velocity components, but applies to any order scheme.

  20. PLANS: A finite element program for nonlinear analysis of structures. Volume 1: Theoretical manual

    NASA Technical Reports Server (NTRS)

    Pifko, A.; Levine, H. S.; Armen, H., Jr.

    1975-01-01

    The PLANS system is described which is a finite element program for nonlinear analysis. The system represents a collection of special purpose computer programs each associated with a distinct physical problem class. Modules of PLANS specifically referenced and described in detail include: (1) REVBY, for the plastic analysis of bodies of revolution; (2) OUT-OF-PLANE, for the plastic analysis of 3-D built-up structures where membrane effects are predominant; (3) BEND, for the plastic analysis of built-up structures where bending and membrane effects are significant; (4) HEX, for the 3-D elastic-plastic analysis of general solids; and (5) OUT-OF-PLANE-MG, for material and geometrically nonlinear analysis of built-up structures. The SATELLITE program for data debugging and plotting of input geometries is also described. The theoretical foundations upon which the analysis is based are presented. Discussed are the form of the governing equations, the methods of solution, plasticity theories available, a general system description and flow of the programs, and the elements available for use.

  1. Accurate, finite-volume methods for three dimensional magneto-hydrodynamics on Lagrangian meshes

    SciTech Connect

    Rousculp, C.L.; Barnes, D.C.

    1999-07-01

    Recently developed algorithms for ideal and resistive, 3D MHD calculations on Lagrangian hexahedral meshes have been generalized to work with a lagrangian mesh composed of arbitrary polyhedral cells. this allows for mesh refinement during a calculation to prevent the well known problem of tangling in a Lagrangian mesh. Arbitrary polyhedral cells are decomposed into tetrahedrons. The action of the magnetic vector potential, A {sm_bullet} {delta}1, is centered on all faces edges of this extended mesh. Thus, {triangledown} {sm_bullet} B = 0 is maintained to round-off error. For ideal flow, (E = v x B), vertex forces are derived by the variation of magnetic energy with respect to vertex positions, F = {minus}{partial_derivative}W{sub B}/{partial_derivative}r. This assures symmetry as well as magnetic flux, momentum, and energy conservation. The method is local so that parallelization by domain decomposition is natural for large meshes. In addition, a simple, ideal-gas, finite pressure term has been included. The resistive diffusion, (E = {minus}{eta}J), is treated with a support operator method, to obtain an energy conservative, symmetric method on an arbitrary polyhedral mesh. The equation of motion is time-step-split. First, the ideal term is treated explicitly. Next, the diffusion is solved implicitly with a preconditioned conjugate gradient method. Results of convergence tests are presented. Initial results of an annular Z-pinch implosion problem illustrate the application of these methods to multi-material problems.

  2. WFR-2D: an analytical model for PWAS-generated 2D ultrasonic guided wave propagation

    NASA Astrophysics Data System (ADS)

    Shen, Yanfeng; Giurgiutiu, Victor

    2014-03-01

    This paper presents WaveFormRevealer 2-D (WFR-2D), an analytical predictive tool for the simulation of 2-D ultrasonic guided wave propagation and interaction with damage. The design of structural health monitoring (SHM) systems and self-aware smart structures requires the exploration of a wide range of parameters to achieve best detection and quantification of certain types of damage. Such need for parameter exploration on sensor dimension, location, guided wave characteristics (mode type, frequency, wavelength, etc.) can be best satisfied with analytical models which are fast and efficient. The analytical model was constructed based on the exact 2-D Lamb wave solution using Bessel and Hankel functions. Damage effects were inserted in the model by considering the damage as a secondary wave source with complex-valued directivity scattering coefficients containing both amplitude and phase information from wave-damage interaction. The analytical procedure was coded with MATLAB, and a predictive simulation tool called WaveFormRevealer 2-D was developed. The wave-damage interaction coefficients (WDICs) were extracted from harmonic analysis of local finite element model (FEM) with artificial non-reflective boundaries (NRB). The WFR-2D analytical simulation results were compared and verified with full scale multiphysics finite element models and experiments with scanning laser vibrometer. First, Lamb wave propagation in a pristine aluminum plate was simulated with WFR-2D, compared with finite element results, and verified by experiments. Then, an inhomogeneity was machined into the plate to represent damage. Analytical modeling was carried out, and verified by finite element simulation and experiments. This paper finishes with conclusions and suggestions for future work.

  3. Compact high order finite volume method on unstructured grids II: Extension to two-dimensional Euler equations

    NASA Astrophysics Data System (ADS)

    Wang, Qian; Ren, Yu-Xin; Li, Wanai

    2016-06-01

    In this paper, the compact least-squares finite volume method on unstructured grids proposed in our previous paper is extended to multi-dimensional systems, namely the two-dimensional Euler equations. The key element of this scheme is the compact least-squares reconstruction in which a set of constitutive relations are constructed by requiring the reconstruction polynomial and its spatial derivatives on the control volume of interest to conserve their averages on the face-neighboring cells. These relations result in an over-determined linear equation system. A large sparse system of linear equations is resulted by using the least-squares technique. An efficient solution strategy is of crucial importance for the application of the proposed scheme in multi-dimensional problems since both direct and iterative solvers for this system are computationally very expensive. In the present paper, it is found that in the cases of steady flow simulation and unsteady flow simulation using dual time stepping technique, the present reconstruction method can be coupled with temporal discretization scheme to achieve high computational efficiency. The WBAP limiter and a problem-independent shock detector are used in the simulation of flow with discontinuities. Numerical results demonstrate the high order accuracy, high computational efficiency and capability of handling both complex physics and geometries of the proposed schemes.

  4. Static & Dynamic Response of 2D Solids

    1996-07-15

    NIKE2D is an implicit finite-element code for analyzing the finite deformation, static and dynamic response of two-dimensional, axisymmetric, plane strain, and plane stress solids. The code is fully vectorized and available on several computing platforms. A number of material models are incorporated to simulate a wide range of material behavior including elasto-placicity, anisotropy, creep, thermal effects, and rate dependence. Slideline algorithms model gaps and sliding along material interfaces, including interface friction, penetration and single surfacemore » contact. Interactive-graphics and rezoning is included for analyses with large mesh distortions. In addition to quasi-Newton and arc-length procedures, adaptive algorithms can be defined to solve the implicit equations using the solution language ISLAND. Each of these capabilities and more make NIKE2D a robust analysis tool.« less

  5. Onset of Time-Dependent 3-D spherical Mantle Convection using a Radial Basis Function-Pseudospectral Method ; Spectral-Finite Volume ; Spectral Higher-Order Finite- Difference Methods

    NASA Astrophysics Data System (ADS)

    Wright, G.; Flyer, N.; Yuen, D. A.; Monnereau, M.; Zhang, S.; Wang, S. M.

    2009-05-01

    Many numerical methods, such as finite-differences, finite-volume, their yin-yang variants, finite-elements and spectral methods have been employed to study 3-D mantle convection. All have their own strengths, but also serious weaknesses. Spectrally accurate methods do not practically allow for node refinement and often involve cumbersome algebra while finite difference, volume, or element methods are generally low-order, adding excessive numerical diffusion to the model. For the 3-D mantle convection problem, we have introduced a new mesh-free approach, using radial basis functions (RBF). This method has the advantage of being algorithmic simple, spectrally accurate for arbitrary node layouts in multi-dimensions and naturally allows for node-refinement. One virtue of the RBF scheme allows the user to use a simple Cartesian geometry, while implementing the required boundary conditions for the temperature, velocities and stress components on a spherical surface at both the planetary surface and the core-mantle boundary. We have studied time- dependent mantle convection, using both a RBF-pseudospectral code and a code which uses spherical- harmonics in the angular direction and second-order finite volume in the radial direction. We have employed a third code , which uses spherical harmonics and higher-order finite-difference method a la Fornberg in the radial coordinate.We first focus on the onset of time-dependence at Rayleigh number Ra of 70,000. We follow the development of stronger time-dependence to a Ra of one million, using high enough resolution with 120 to 200 points in the radial direction and 128 to 256 spherical harmonics.

  6. TACO (2D AND 3D). Taco

    SciTech Connect

    Mason, W.E.

    1983-03-01

    A set of finite element codes for the solution of nonlinear, two-dimensional (TACO2D) and three-dimensional (TACO3D) heat transfer problems. Performs linear and nonlinear analyses of both transient and steady state heat transfer problems. Has the capability to handle time or temperature dependent material properties. Materials may be either isotropic or orthotropic. A variety of time and temperature dependent boundary conditions and loadings are available including temperature, flux, convection, radiation, and internal heat generation.

  7. STEALTH: a Lagrange explicit finite difference code for solids, structural, and thermohydraulic analysis. Volume 7: implicit hydrodynamics. Computer code manual. [PWR; BWR

    SciTech Connect

    McKay, M.W.

    1982-06-01

    STEALTH is a family of computer codes that solve the equations of motion for a general continuum. These codes can be used to calculate a variety of physical processes in which the dynamic behavior of a continuum is involved. The versions of STEALTH described in this volume were designed for the calculation of problems involving low-speed fluid flow. They employ an implicit finite difference technique to solve the one- and two-dimensional equations of motion, written for an arbitrary coordinate system, for both incompressible and compressible fluids. The solution technique involves an iterative solution of the implicit, Lagrangian finite difference equations. Convection terms that result from the use of an arbitrarily-moving coordinate system are calculated separately. This volume provides the theoretical background, the finite difference equations, and the input instructions for the one- and two-dimensional codes; a discussion of several sample problems; and a listing of the input decks required to run those problems.

  8. Radiative transfer equation for predicting light propagation in biological media: comparison of a modified finite volume method, the Monte Carlo technique, and an exact analytical solution.

    PubMed

    Asllanaj, Fatmir; Contassot-Vivier, Sylvain; Liemert, André; Kienle, Alwin

    2014-01-01

    We examine the accuracy of a modified finite volume method compared to analytical and Monte Carlo solutions for solving the radiative transfer equation. The model is used for predicting light propagation within a two-dimensional absorbing and highly forward-scattering medium such as biological tissue subjected to a collimated light beam. Numerical simulations for the spatially resolved reflectance and transmittance are presented considering refractive index mismatch with Fresnel reflection at the interface, homogeneous and two-layered media. Time-dependent as well as steady-state cases are considered. In the steady state, it is found that the modified finite volume method is in good agreement with the other two methods. The relative differences between the solutions are found to decrease with spatial mesh refinement applied for the modified finite volume method obtaining <2.4%. In the time domain, the fourth-order Runge-Kutta method is used for the time semi-discretization of the radiative transfer equation. An agreement among the modified finite volume method, Runge-Kutta method, and Monte Carlo solutions are shown, but with relative differences higher than in the steady state. PMID:24390371

  9. Two coupled particle-finite volume methods using Delaunay-Voronoie meshes for the approximation of Vlasov-Poisson and Vlasov-Maxwell equations

    SciTech Connect

    Hermeline, F. )

    1993-05-01

    This paper deals with the approximation of Vlasov-Poisson and Vlasov-Maxwell equations. We present two coupled particle-finite volume methods which use the properties of Delaunay-Voronoi meshes. These methods are applied to benchmark calculations and engineering problems such as simulation of electron injector devices. 42 refs., 13 figs.

  10. Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers

    NASA Astrophysics Data System (ADS)

    Balsara, Dinshaw S.; Dumbser, Michael

    2015-10-01

    Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on

  11. A high-order finite-volume method for hyperbolic conservation laws on locally-refined grids

    SciTech Connect

    McCorquodale, Peter; Colella, Phillip

    2011-01-28

    We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on Cartesian grids with multiple levels of refinement. The underlying method is a generalization of that in [5] to nonlinear systems, and is based on using fourth-order accurate quadratures for computing fluxes on faces, combined with fourth-order accurate Runge?Kutta discretization in time. To interpolate boundary conditions at refinement boundaries, we interpolate in time in a manner consistent with the individual stages of the Runge-Kutta method, and interpolate in space by solving a least-squares problem over a neighborhood of each target cell for the coefficients of a cubic polynomial. The method also uses a variation on the extremum-preserving limiter in [8], as well as slope flattening and a fourth-order accurate artificial viscosity for strong shocks. We show that the resulting method is fourth-order accurate for smooth solutions, and is robust in the presence of complex combinations of shocks and smooth flows.

  12. An adaptive finite volume solver for steady Euler equations with non-oscillatory k-exact reconstruction

    NASA Astrophysics Data System (ADS)

    Hu, Guanghui; Yi, Nianyu

    2016-05-01

    In this paper, we present an adaptive finite volume method for steady Euler equations with a non-oscillatory k-exact reconstruction on unstructured mesh. The numerical framework includes a Newton method as an outer iteration to linearize the Euler equations, and a geometrical multigrid method as an inner iteration to solve the derived linear system. A non-oscillatory k-exact reconstruction of the conservative solution in each element is proposed for the high order and non-oscillatory behavior of the numerical solutions. The importance on handling the curved boundary in an appropriate way is also studied with the numerical experiments. The h-adaptive method is introduced to enhance the efficiency of the algorithm. The numerical tests show successfully that the quality solutions can be obtained smoothly with the proposed algorithm, i.e., the expected convergence order of the numerical solution with the mesh refinement can be reached, while the non-oscillation shock structure can be obtained. Furthermore, the mesh adaptive method with the appropriate error indicators can effectively enhance the implementation efficiency of numerical method, while the steady state convergence and numerical accuracy are kept in the meantime.

  13. Global energy and water balance: Characteristics from finite-volume atmospheric model of the IAP/LASG (FAMIL1)

    SciTech Connect

    Zhou, Linjiong; Bao, Qing; Liu, Yimin; Wu, Guoxiong; Wang, Wei-Chyung; Wang, Xiaocong; He, Bian; Yu, Haiyang; Li, Jiandong

    2015-03-01

    This paper documents version 1 of the Finite-volume Atmospheric Model of the IAP/LASG (FAMIL1), which has a flexible horizontal resolution up to a quarter of 1°. The model, currently running on the ‘‘Tianhe 1A’’ supercomputer, is the atmospheric component of the third-generation Flexible Global Ocean-Atmosphere-Land climate System model (FGOALS3) which will participate in the Coupled Model Intercomparison Project Phase 6 (CMIP6). In addition to describing the dynamical core and physical parameterizations of FAMIL1, this paper describes the simulated characteristics of energy and water balances and compares them with observational/reanalysis data. The comparisons indicate that the model simulates well the seasonal and geographical distributions of radiative fluxes at the top of the atmosphere and at the surface, as well as the surface latent and sensible heat fluxes. A major weakness in the energy balance is identified in the regions where extensive and persistent marine stratocumulus is present. Analysis of the global water balance also indicates realistic seasonal and geographical distributions with the global annual mean of evaporation minus precipitation being approximately 10⁻⁵ mm d⁻¹. We also examine the connections between the global energy and water balance and discuss the possible link between the two within the context of the findings from the reanalysis data. Finally, the model biases as well as possible solutions are discussed.

  14. Global energy and water balance: Characteristics from finite-volume atmospheric model of the IAP/LASG (FAMIL1)

    DOE PAGESBeta

    Zhou, Linjiong; Bao, Qing; Liu, Yimin; Wu, Guoxiong; Wang, Wei-Chyung; Wang, Xiaocong; He, Bian; Yu, Haiyang; Li, Jiandong

    2015-03-01

    This paper documents version 1 of the Finite-volume Atmospheric Model of the IAP/LASG (FAMIL1), which has a flexible horizontal resolution up to a quarter of 1°. The model, currently running on the ‘‘Tianhe 1A’’ supercomputer, is the atmospheric component of the third-generation Flexible Global Ocean-Atmosphere-Land climate System model (FGOALS3) which will participate in the Coupled Model Intercomparison Project Phase 6 (CMIP6). In addition to describing the dynamical core and physical parameterizations of FAMIL1, this paper describes the simulated characteristics of energy and water balances and compares them with observational/reanalysis data. The comparisons indicate that the model simulates well the seasonalmore » and geographical distributions of radiative fluxes at the top of the atmosphere and at the surface, as well as the surface latent and sensible heat fluxes. A major weakness in the energy balance is identified in the regions where extensive and persistent marine stratocumulus is present. Analysis of the global water balance also indicates realistic seasonal and geographical distributions with the global annual mean of evaporation minus precipitation being approximately 10⁻⁵ mm d⁻¹. We also examine the connections between the global energy and water balance and discuss the possible link between the two within the context of the findings from the reanalysis data. Finally, the model biases as well as possible solutions are discussed.« less

  15. XTROEM-FV: a new code for computational astrophysics based on very high order finite-volume methods - I. Magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Núñez-de la Rosa, Jonatan; Munz, Claus-Dieter

    2016-02-01

    The present work describes the building blocks of a new code for computational magnetohydrodynamics based on very high order finite volume methods on Cartesian meshes. Spatial high-order accuracy is obtained with a weighted essentially non-oscillatory (WENO) reconstruction operator up to seventh order, while the time discretization is performed with a fourth-order strong-stability preserving Runge-Kutta method. Based on a shock-detection approach, the reconstruction operator employs a very high order WENO scheme in smooth flow regions and a third-order WENO scheme in those parts of the flow with discontinuities or shocks. The generalized Lagrange multiplier method is employed to enforce the solenoidal constraint on the magnetic field. Extensive numerical computations in one and two space dimensions are reported. Convergence rates for smooth flows verify the high-order accuracy of the scheme, and tests with strong shocks, including the Orszag-Tang vortex, the cylindrical blast wave problem, the rotor problem, and the Kelvin-Helmholtz instability, confirm the robustness and stability of the approach.

  16. Finite-volume application of high order ENO schemes to multi-dimensional boundary-value problems

    NASA Technical Reports Server (NTRS)

    Casper, Jay; Dorrepaal, J. Mark

    1990-01-01

    The finite volume approach in developing multi-dimensional, high-order accurate essentially non-oscillatory (ENO) schemes is considered. In particular, a two dimensional extension is proposed for the Euler equation of gas dynamics. This requires a spatial reconstruction operator that attains formal high order of accuracy in two dimensions by taking account of cross gradients. Given a set of cell averages in two spatial variables, polynomial interpolation of a two dimensional primitive function is employed in order to extract high-order pointwise values on cell interfaces. These points are appropriately chosen so that correspondingly high-order flux integrals are obtained through each interface by quadrature, at each point having calculated a flux contribution in an upwind fashion. The solution-in-the-small of Riemann's initial value problem (IVP) that is required for this pointwise flux computation is achieved using Roe's approximate Riemann solver. Issues to be considered in this two dimensional extension include the implementation of boundary conditions and application to general curvilinear coordinates. Results of numerical experiments are presented for qualitative and quantitative examination. These results contain the first successful application of ENO schemes to boundary value problems with solid walls.

  17. A two-dimensional coupled flow-mass transport model based on an improved unstructured finite volume algorithm.

    PubMed

    Zhou, Jianzhong; Song, Lixiang; Kursan, Suncana; Liu, Yi

    2015-05-01

    A two-dimensional coupled water quality model is developed for modeling the flow-mass transport in shallow water. To simulate shallow flows on complex topography with wetting and drying, an unstructured grid, well-balanced, finite volume algorithm is proposed for numerical resolution of a modified formulation of two-dimensional shallow water equations. The slope-limited linear reconstruction method is used to achieve second-order accuracy in space. The algorithm adopts a HLLC-based integrated solver to compute the flow and mass transport fluxes simultaneously, and uses Hancock's predictor-corrector scheme for efficient time stepping as well as second-order temporal accuracy. The continuity and momentum equations are updated in both wet and dry cells. A new hybrid method, which can preserve the well-balanced property of the algorithm for simulations involving flooding and recession, is proposed for bed slope terms approximation. The effectiveness and robustness of the proposed algorithm are validated by the reasonable good agreement between numerical and reference results of several benchmark test cases. Results show that the proposed coupled flow-mass transport model can simulate complex flows and mass transport in shallow water. PMID:25686488

  18. A fully-implicit finite-volume method for multi-fluid reactive and collisional magnetized plasmas on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Alvarez Laguna, A.; Lani, A.; Deconinck, H.; Mansour, N. N.; Poedts, S.

    2016-08-01

    We present a Finite Volume scheme for solving Maxwell's equations coupled to magnetized multi-fluid plasma equations for reactive and collisional partially ionized flows on unstructured meshes. The inclusion of the displacement current allows for studying electromagnetic wave propagation in a plasma as well as charge separation effects beyond the standard magnetohydrodynamics (MHD) description, however, it leads to a very stiff system with characteristic velocities ranging from the speed of sound of the fluids up to the speed of light. In order to control the fulfillment of the elliptical constraints of the Maxwell's equations, we use the hyperbolic divergence cleaning method. In this paper, we extend the latter method applying the CIR scheme with scaled numerical diffusion in order to balance those terms with the Maxwell flux vectors. For the fluids, we generalize the AUSM+-up to multiple fluids of different species within the plasma. The fully implicit second-order method is first verified on the Hartmann flow (including comparison with its analytical solution), two ideal MHD cases with strong shocks, namely, Orszag-Tang and the MHD rotor, then validated on a much more challenging case, representing a two-fluid magnetic reconnection under solar chromospheric conditions. For the latter case, a comparison with pioneering results available in literature is provided.

  19. A Full Multi-Grid Method for the Solution of the Cell Vertex Finite Volume Cauchy-Riemann Equations

    NASA Technical Reports Server (NTRS)

    Borzi, A.; Morton, K. W.; Sueli, E.; Vanmaele, M.

    1996-01-01

    The system of inhomogeneous Cauchy-Riemann equations defined on a square domain and subject to Dirichlet boundary conditions is considered. This problem is discretised by using the cell vertex finite volume method on quadrilateral meshes. The resulting algebraic problem is overdetermined and the solution is defined in a least squares sense. By this approach a consistent algebraic problem is obtained which differs from the original one by O(h(exp 2)) perturbations of the right-hand side. A suitable cell-based convergent smoothing iteration is presented which is naturally linked to the least squares formulation. Hence, a standard multi-grid algorithm is reported which combines the given smoother and cell-based transfer operators. Some remarkable reduction properties of these operators are shown. A full multi-grid method is discussed which solves the discrete problem to the level of truncation error by employing one multi-grid cycle at each current level of discretisation. Experiments and applications of the full multi-grid scheme are presented.

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

    NASA Technical Reports Server (NTRS)

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

    2007-01-01

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

  1. A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries

    NASA Astrophysics Data System (ADS)

    Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.

    2013-03-01

    A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach.

  2. TRHD: Three-temperature radiation-hydrodynamics code with an implicit non-equilibrium radiation transport using a cell-centered monotonic finite volume scheme on unstructured-grids

    NASA Astrophysics Data System (ADS)

    Sijoy, C. D.; Chaturvedi, S.

    2015-05-01

    Three-temperature (3T), unstructured-mesh, non-equilibrium radiation hydrodynamics (RHD) code have been developed for the simulation of intense thermal radiation or high-power laser driven radiative shock hydrodynamics in two-dimensional (2D) axis-symmetric geometries. The governing hydrodynamics equations are solved using a compatible unstructured Lagrangian method based on a control volume differencing (CVD) scheme. A second-order predictor-corrector (PC) integration scheme is used for the temporal discretization of the hydrodynamics equations. For the radiation energy transport, frequency averaged gray model is used in which the flux-limited diffusion (FLD) approximation is used to recover the free-streaming limit of the radiation propagation in optically thin regions. The proposed RHD model allows to have different temperatures for the electrons and ions. In addition to this, the electron and thermal radiation temperatures are assumed to be in non-equilibrium. Therefore, the thermal relaxation between the electrons and ions and the coupling between the radiation and matter energies are required to be computed self-consistently. For this, the coupled flux limited electron heat conduction and the non-equilibrium radiation diffusion equations are solved simultaneously by using an implicit, axis-symmetric, cell-centered, monotonic, nonlinear finite volume (NLFV) scheme. In this paper, we have described the details of the 2D, 3T, non-equilibrium RHD code developed along with a suite of validation test problems to demonstrate the accuracy and performance of the algorithms. We have also conducted a performance analysis with different linearity preserving interpolation schemes that are used for the evaluation of the nodal values in the NLFV scheme. Finally, in order to demonstrate full capability of the code implementation, we have presented the simulation of laser driven thin Aluminum (Al) foil acceleration. The simulation results are found to be in good agreement

  3. Fast 2D flood modelling using GPU technology - recent applications and new developments

    NASA Astrophysics Data System (ADS)

    Crossley, Amanda; Lamb, Rob; Waller, Simon; Dunning, Paul

    2010-05-01

    In recent years there has been considerable interest amongst scientists and engineers in exploiting the potential of commodity graphics hardware for desktop parallel computing. The Graphics Processing Units (GPUs) that are used in PC graphics cards have now evolved into powerful parallel co-processors that can be used to accelerate the numerical codes used for floodplain inundation modelling. We report in this paper on experience over the past two years in developing and applying two dimensional (2D) flood inundation models using GPUs to achieve significant practical performance benefits. Starting with a solution scheme for the 2D diffusion wave approximation to the 2D Shallow Water Equations (SWEs), we have demonstrated the capability to reduce model run times in ‘real-world' applications using GPU hardware and programming techniques. We then present results from a GPU-based 2D finite volume SWE solver. A series of numerical test cases demonstrate that the model produces outputs that are accurate and consistent with reference results published elsewhere. In comparisons conducted for a real world test case, the GPU-based SWE model was over 100 times faster than the CPU version. We conclude with some discussion of practical experience in using the GPU technology for flood mapping applications, and for research projects investigating use of Monte Carlo simulation methods for the analysis of uncertainty in 2D flood modelling.

  4. MAGNUM-2D computer code: user's guide

    SciTech Connect

    England, R.L.; Kline, N.W.; Ekblad, K.J.; Baca, R.G.

    1985-01-01

    Information relevant to the general use of the MAGNUM-2D computer code is presented. This computer code was developed for the purpose of modeling (i.e., simulating) the thermal and hydraulic conditions in the vicinity of a waste package emplaced in a deep geologic repository. The MAGNUM-2D computer computes (1) the temperature field surrounding the waste package as a function of the heat generation rate of the nuclear waste and thermal properties of the basalt and (2) the hydraulic head distribution and associated groundwater flow fields as a function of the temperature gradients and hydraulic properties of the basalt. MAGNUM-2D is a two-dimensional numerical model for transient or steady-state analysis of coupled heat transfer and groundwater flow in a fractured porous medium. The governing equations consist of a set of coupled, quasi-linear partial differential equations that are solved using a Galerkin finite-element technique. A Newton-Raphson algorithm is embedded in the Galerkin functional to formulate the problem in terms of the incremental changes in the dependent variables. Both triangular and quadrilateral finite elements are used to represent the continuum portions of the spatial domain. Line elements may be used to represent discrete conduits. 18 refs., 4 figs., 1 tab.

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

    SciTech Connect

    Charest, Marc R.J.; Canfield, Thomas R.; Morgan, Nathaniel R.; Waltz, Jacob; Wohlbier, John G.

    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 linear 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.

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

    DOE PAGESBeta

    Charest, Marc R.J.; Canfield, Thomas R.; Morgan, Nathaniel R.; Waltz, Jacob; Wohlbier, John G.

    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

  7. GeoClawSed: A Model with Finite Volume and Adaptive Refinement Method for Tsunami Sediment Transport

    NASA Astrophysics Data System (ADS)

    Tang, H.; Weiss, R.

    2015-12-01

    The shallow-water and advection-diffusion equations are commonly used for tsunami sediment-transport modeling. GeoClawSed is based on GeoClaw and adds a bed updating and avalanching scheme to the two-dimensional coupled system combining the shallow- water and advection-diffusion equations, which is a set of hyperbolic integral conservation laws. The modeling system consists of three coupled model components: (1) the shallow-water equations for hydrodynamics; (2) advection-diffusion equation for sediment transport; and (3) an equation for morphodynamics. For the hydrodynamic part, the finite-volume wave propagation methods (high resolution Godunov-type methods) are applied to the shallow-water equations. The well-known Riemann solver in GeoClaw is capable of dealing with diverse flow regimes present during tsunami flows. For the sediment-transport part, the advection-diffusion equation is employed to calculate the distribution of sediment in the water column. In the fully-coupled version, the advection-diffusion equation is also included in the Riemann solver. The Van Leer method is applied for calculating sediment flux in each direction. The bed updating and avalanching scheme (morphodynamics) is used for updating topography during tsunami wave propagation. Adaptive refinement method is extended to hydrodynamic part, sediment transport model and topography. GeoClawSed can evolve different resolution and accurately capture discontinuities in both flow dynamic and sediment transport. Together, GeoClawSed is designed for modeling tsunami propagation, inundation, sediment transport as well as topography change. Finally, GeoClawSed is applied for studying marine and terrestrial deposit distribution after tsunami wave. Keywords: Tsunami; Sediment Transport; Shallow Water Equations; Advection-Diffusion Equation; Adaptive Refinement Method

  8. Stochastic Inversion of 2D Magnetotelluric Data

    2010-07-01

    The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function ismore » explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, it provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows« less

  9. Stochastic Inversion of 2D Magnetotelluric Data

    SciTech Connect

    Chen, Jinsong

    2010-07-01

    The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function is explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, it provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows

  10. Explicit 2-D Hydrodynamic FEM Program

    1996-08-07

    DYNA2D* is a vectorized, explicit, two-dimensional, axisymmetric and plane strain finite element program for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. DYNA2D* contains 13 material models and 9 equations of state (EOS) to cover a wide range of material behavior. The material models implemented in all machine versions are: elastic, orthotropic elastic, kinematic/isotropic elastic plasticity, thermoelastoplastic, soil and crushable foam, linear viscoelastic, rubber, high explosive burn, isotropic elastic-plastic, temperature-dependent elastic-plastic. Themore » isotropic and temperature-dependent elastic-plastic models determine only the deviatoric stresses. Pressure is determined by one of 9 equations of state including linear polynomial, JWL high explosive, Sack Tuesday high explosive, Gruneisen, ratio of polynomials, linear polynomial with energy deposition, ignition and growth of reaction in HE, tabulated compaction, and tabulated.« less

  11. Expansion and improvement of the FORMA system for response and load analysis. Volume 2C: Listings, finite element FORMA subroutines

    NASA Technical Reports Server (NTRS)

    Wohlen, R. L.

    1976-01-01

    A listing of the source deck of each finite element FORMA subroutine is given to remove the 'black-box' aura of the subroutines so that the analyst may better understand the detailed operations of each subroutine. The FORTRAN 4 programming language is used in all finite element FORMA subroutines.

  12. High divergent 2D grating

    NASA Astrophysics Data System (ADS)

    Wang, Jin; Ma, Jianyong; Zhou, Changhe

    2014-11-01

    A 3×3 high divergent 2D-grating with period of 3.842μm at wavelength of 850nm under normal incidence is designed and fabricated in this paper. This high divergent 2D-grating is designed by the vector theory. The Rigorous Coupled Wave Analysis (RCWA) in association with the simulated annealing (SA) is adopted to calculate and optimize this 2D-grating.The properties of this grating are also investigated by the RCWA. The diffraction angles are more than 10 degrees in the whole wavelength band, which are bigger than the traditional 2D-grating. In addition, the small period of grating increases the difficulties of fabrication. So we fabricate the 2D-gratings by direct laser writing (DLW) instead of traditional manufacturing method. Then the method of ICP etching is used to obtain the high divergent 2D-grating.

  13. The analytical solution of two interesting hyperbolic problems as a test case for a finite volume method with a new grid refinement technique

    NASA Astrophysics Data System (ADS)

    Heineken, Wolfram; Kunik, Matthias

    2008-05-01

    A finite volume method with grid adaption is applied to two hyperbolic problems: the ultra-relativistic Euler equations, and a scalar conservation law. Both problems are considered in two space dimensions and share the common feature of moving shock waves. In contrast to the classical Euler equations, the derivation of appropriate initial conditions for the ultra-relativistic Euler equations is a non-trivial problem that is solved using one-dimensional shock conditions and the Lorentz invariance of the system. The discretization of both problems is based on a finite volume method of second order in both space and time on a triangular grid. We introduce a variant of the min-mod limiter that avoids unphysical states for the Euler system. The grid is adapted during the integration process. The frequency of grid adaption is controlled automatically in order to guarantee a fine resolution of the moving shock fronts. We introduce the concept of "width refinement" which enlarges the width of strongly refined regions around the shock fronts; the optimal width is found by a numerical study. As a result we are able to improve efficiency by decreasing the number of adaption steps. The performance of the finite volume scheme is compared with several lower order methods.

  14. A simple robust and accurate a posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Dumbser, Michael; Loubère, Raphaël

    2016-08-01

    In this paper we propose a simple, robust and accurate nonlinear a posteriori stabilization of the Discontinuous Galerkin (DG) finite element method for the solution of nonlinear hyperbolic PDE systems on unstructured triangular and tetrahedral meshes in two and three space dimensions. This novel a posteriori limiter, which has been recently proposed for the simple Cartesian grid case in [62], is able to resolve discontinuities at a sub-grid scale and is substantially extended here to general unstructured simplex meshes in 2D and 3D. It can be summarized as follows: At the beginning of each time step, an approximation of the local minimum and maximum of the discrete solution is computed for each cell, taking into account also the vertex neighbors of an element. Then, an unlimited discontinuous Galerkin scheme of approximation degree N is run for one time step to produce a so-called candidate solution. Subsequently, an a posteriori detection step checks the unlimited candidate solution at time t n + 1 for positivity, absence of floating point errors and whether the discrete solution has remained within or at least very close to the bounds given by the local minimum and maximum computed in the first step. Elements that do not satisfy all the previously mentioned detection criteria are flagged as troubled cells. For these troubled cells, the candidate solution is discarded as inappropriate and consequently needs to be recomputed. Within these troubled cells the old discrete solution at the previous time tn is scattered onto small sub-cells (Ns = 2 N + 1 sub-cells per element edge), in order to obtain a set of sub-cell averages at time tn. Then, a more robust second order TVD finite volume scheme is applied to update the sub-cell averages within the troubled DG cells from time tn to time t n + 1. The new sub-grid data at time t n + 1 are finally gathered back into a valid cell-centered DG polynomial of degree N by using a classical conservative and higher order

  15. The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 2: User's manual

    NASA Technical Reports Server (NTRS)

    Nakazawa, Shohei

    1989-01-01

    The user options available for running the MHOST finite element analysis package is described. MHOST is a solid and structural analysis program based on the mixed finite element technology, and is specifically designed for 3-D inelastic analysis. A family of 2- and 3-D continuum elements along with beam and shell structural elements can be utilized, many options are available in the constitutive equation library, the solution algorithms and the analysis capabilities. The outline of solution algorithms is discussed along with the data input and output, analysis options including the user subroutines and the definition of the finite elements implemented in the program package.

  16. A conservative finite volume scheme with time-accurate local time stepping for scalar transport on unstructured grids

    NASA Astrophysics Data System (ADS)

    Cavalcanti, José Rafael; Dumbser, Michael; Motta-Marques, David da; Fragoso Junior, Carlos Ruberto

    2015-12-01

    In this article we propose a new conservative high resolution TVD (total variation diminishing) finite volume scheme with time-accurate local time stepping (LTS) on unstructured grids for the solution of scalar transport problems, which are typical in the context of water quality simulations. To keep the presentation of the new method as simple as possible, the algorithm is only derived in two space dimensions and for purely convective transport problems, hence neglecting diffusion and reaction terms. The new numerical method for the solution of the scalar transport is directly coupled to the hydrodynamic model of Casulli and Walters (2000) that provides the dynamics of the free surface and the velocity vector field based on a semi-implicit discretization of the shallow water equations. Wetting and drying is handled rigorously by the nonlinear algorithm proposed by Casulli (2009). The new time-accurate LTS algorithm allows a different time step size for each element of the unstructured grid, based on an element-local Courant-Friedrichs-Lewy (CFL) stability condition. The proposed method does not need any synchronization between different time steps of different elements and is by construction locally and globally conservative. The LTS scheme is based on a piecewise linear polynomial reconstruction in space-time using the MUSCL-Hancock method, to obtain second order of accuracy in both space and time. The new algorithm is first validated on some classical test cases for pure advection problems, for which exact solutions are known. In all cases we obtain a very good level of accuracy, showing also numerical convergence results; we furthermore confirm mass conservation up to machine precision and observe an improved computational efficiency compared to a standard second order TVD scheme for scalar transport with global time stepping (GTS). Then, the new LTS method is applied to some more complex problems, where the new scalar transport scheme has also been coupled to

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

    NASA Technical Reports Server (NTRS)

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

    2009-01-01

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

  18. The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 3: Systems' manual

    NASA Technical Reports Server (NTRS)

    Nakazawa, Shohei

    1989-01-01

    The internal structure is discussed of the MHOST finite element program designed for 3-D inelastic analysis of gas turbine hot section components. The computer code is the first implementation of the mixed iterative solution strategy for improved efficiency and accuracy over the conventional finite element method. The control structure of the program is covered along with the data storage scheme and the memory allocation procedure and the file handling facilities including the read and/or write sequences.

  19. New Advances In Multiphase Flow Numerical Modelling Using A General Domain Decomposition and Non-orthogonal Collocated Finite Volume Algorithm: Application To Industrial Fluid Catalytical Cracking Process and Large Scale Geophysical Fluids.

    NASA Astrophysics Data System (ADS)

    Martin, R.; Gonzalez Ortiz, A.

    In the industry as well as in the geophysical community, multiphase flows are mod- elled using a finite volume approach and a multicorrector algorithm in time in order to determine implicitly the pressures, velocities and volume fractions for each phase. Pressures, and velocities are generally determined at mid-half mesh step from each other following the staggered grid approach. This ensures stability and prevents os- cillations in pressure. It allows to treat almost all the Reynolds number ranges for all speeds and viscosities. The disadvantages appear when we want to treat more complex geometries or if a generalized curvilinear formulation of the conservation equations is considered. Too many interpolations have to be done and accuracy is then lost. In order to overcome these problems, we use here a similar algorithm in time and a Rhie and Chow interpolation (1983) of the collocated variables and essentially the velocities at the interface. The Rhie and Chow interpolation of the velocities at the finite volume interfaces allows to have no oscillatons of the pressure without checkerboard effects and to stabilize all the algorithm. In a first predictor step, fluxes at the interfaces of the finite volumes are then computed using 2nd and 3rd order shock capturing schemes of MUSCL/TVD or Van Leer type, and the orthogonal stress components are treated implicitly while cross viscous/diffusion terms are treated explicitly. A pentadiagonal system in 2D or a septadiagonal in 3D must be solve but here we have chosen to solve 3 tridiagonal linear systems (the so called Alternate Direction Implicit algorithm), one in each spatial direction, to reduce the cost of computation. Then a multi-correction of interpolated velocities, pressures and volumic fractions of each phase are done in the cartesian frame or the deformed local curvilinear coordinate system till convergence and mass conservation. At the end the energy conservation equations are solved. In all this process the

  20. STEALTH: a Lagrange explicit finite-difference code for solid, structural, and thermohydraulic analysis. Volume 8B. STEALTH/WHAMSE: a 3-D fluid-structure interaction code

    SciTech Connect

    Not Available

    1984-10-01

    STEALTH is a family of computer codes that can be used to calculate a variety of physical processes in which the dynamic behavior of a continuum is involved. The version of STEALTH described in this volume is designed for calculations of fluid-structure interaction. This version of the program consists of a hydrodynamic version of STEALTH which has been coupled to a finite-element code, WHAMSE. STEALTH computes the transient response of the fluid continuum, while WHAMSE computes the transient response of shell and beam structures under external fluid loadings. The coupling between STEALTH and WHAMSE is performed during each cycle or step of a calculation. Separate calculations of fluid response and structure response are avoided, thereby giving a more accurate model of the dynamic coupling between fluid and structure. This volume provides the theoretical background, the finite-difference equations, the finite-element equations, a discussion of several sample problems, a listing of the input decks for the sample problems, a programmer's manual and a description of the input records for the STEALTH/WHAMSE computer program.

  1. Extension and application of the Preissmann slot model to 2D transient mixed flows

    NASA Astrophysics Data System (ADS)

    Maranzoni, Andrea; Dazzi, Susanna; Aureli, Francesca; Mignosa, Paolo

    2015-08-01

    This paper presents an extension of the Preissmann slot concept for the modeling of highly transient two-dimensional (2D) mixed flows. The classic conservative formulation of the 2D shallow water equations for free surface flows is adapted by assuming that two fictitious vertical slots, aligned along the two Cartesian plane directions and normally intersecting, are added on the ceiling of each integration element. Accordingly, transitions between free surface and pressurized flow can be handled in a natural and straightforward way by using the same set of governing equations. The opportunity of coupling free surface and pressurized flows is actually useful not only in one-dimensional (1D) problems concerning sewer systems but also for modeling 2D flooding phenomena in which the pressurization of bridges, culverts, or other crossing hydraulic structures can be expected. Numerical simulations are performed by using a shock-capturing MUSCL-Hancock finite volume scheme combined with the FORCE (First-Order Centred) solver for the evaluation of the numerical fluxes. The validation of the mathematical model is accomplished on the basis of both exact solutions of 1D discontinuous initial value problems and reference radial solutions of idealized test cases with cylindrical symmetry. Furthermore, the capability of the model to deal with practical field-scale applications is assessed by simulating the transit of a bore under an arch bridge. Numerical results show that the proposed model is suitable for the prediction of highly transient 2D mixed flows.

  2. 2-d Collapsed Polymers on a Cylinder

    NASA Astrophysics Data System (ADS)

    Hsu, Hsiao-Ping; Grassberger, Peter

    2002-08-01

    Partially confined collapsed polymers with attractive interactions are studied in two dimensions. They are described by self-avoiding random walks with nearest-neighbour attractions on the surface of an infinitely long cylinder. We employ the pruned-enriched-Rosenbluth method (PERM) to study this model with different cylinder circumference h, to understand the properties of collapsed polymers affected by confining geometries. The cases of free polymers and of polymers confined to finite volumes were discussed already in [Phys. Rev. E 65, 031807 (2002)] by Grassberger and Hsu. There, we had verified the existence of a surface term in the infinite volume free energy, and a T-dependent bulk chemical potential. Here we present further results on the surface tension and it's T-dependence. We also show that the chemical potential has, in the limit of very long chains, a minimum at a finite value of h.

  3. 2D constant-loss taper for mode conversion

    NASA Astrophysics Data System (ADS)

    Horth, Alexandre; Kashyap, Raman; Quitoriano, Nathaniel J.

    2015-03-01

    Proposed in this manuscript is a novel taper geometry, the constant-loss taper (CLT). This geometry is derived with 1D slabs of silicon embedded in silicon dioxide using coupled-mode theory (CMT). The efficiency of the CLT is compared to both linear and parabolic tapers using CMT and 2D finite-difference time-domain simulations. It is shown that over a short 2D, 4.45 μm long taper the CLT's mode conversion efficiency is ~90% which is 10% and 18% more efficient than a 2D parabolic or linear taper, respectively.

  4. Determining the Hydrologic Impacts of Climate Variability on Florida's Everglades Through the Use of a Finite Volume Hydrologic Model

    NASA Astrophysics Data System (ADS)

    Senarath, S. U.; Novoa, R. J.; Niedzialek, J. M.; Zheng, F.

    2006-12-01

    A good understanding of climate variability and its impacts on the regional water budget are crucial for the restoration of Florida's Everglades. This is investigated by varying the two most sensitive climatic data sets, namely rainfall and evapotranspiration of a regional-scale hydrologic model. A 36-year long record, spanning from 1965 to 2000 is used in these assessments. Although not comprehensive, these data sets include several seasons with extremely high and low rainfall and evapotranspiration. The Everglades National Park, the Big Cypress National Preserve, and the Water Conservation Areas 3A and 3B are included in the study area. These watersheds jointly encompass an area of 10,158 square kilometers, and are home to many endangered and threatened species of fauna and flora. The Regional Simulation Model (RSM) developed by the South Florida Water Management District (SFWMD) is used in this study to evaluate and quantify the hydrologic responses caused due to climate variability. RSM is a finite-volume, regional-scale, distributed, continuous hydrologic model with fully coupled groundwater, canal and overland flow components. This model uses a variable triangular mesh that conforms to levees, canals and sub-basin boundaries. RSM can adequately simulate the low-relief topography, and high water tables, saturated hydraulic conductivities and surface roughnesses that exist in Florida's Everglades. The model uses the diffusive wave approximation of Saint-Venant's equation to simulate canal and overland flows. The Southern Everglades implementation of the RSM (hereafter, Southern Everglades Model or SEM) is calibrated and verified using stage data from 1988 to 1995, and 1996 to 2000, respectively. An irregular triangular mesh with 52,817 cells and a one-day time step are used in this implementation. For all simulations and assessments the model boundary conditions are obtained from the South Florida Water Management Model developed by the SFWMD. Two types of

  5. Use of a Distributed, Finite-Volume, Hydrologic Model to Assess the Sensitivity of the Everglades to De-compartmentalization

    NASA Astrophysics Data System (ADS)

    Senarath, S. U.

    2002-12-01

    The Everglades, the only remaining subtropical wilderness in the continental USA, is the home to a number of threatened and endangered species. Although the pre-drainage Everglades covered an area of approximately 11,048 km2, urbanization and farming have reduced its area by approximately 50%. The remaining Everglades has also changed as a result of drainage and compartmentalization by over 2,200 km of levees and canals. This area is also adversely affected by exotic species, nutrient enrichment, contaminants and altered freshwater flows. The \\8 billion Comprehensive Everglades Restoration Plan provides a ``framework and guide to restore, protect, and preserve the water resources of central and southern Florida, including the Everglades.'' The success of this project, one of the largest eco-system restoration projects in the world, depends heavily on our understanding of the quantity, quality, timing and distribution of South Florida's pre-drainage freshwater flow. Consequently, accurate hydrologic modeling is crucial for the restoration of the greater Everglades ecosystem. The Regional Simulation Model (RSM) developed by the South Florida Water Management District is currently being used to investigate the effect of de-compartmentalization on freshwater flow dynamics in parts of the remaining Everglades which includes the Everglades National Park and the Big Cypress National Preserve. The RSM is an implicit, finite-volume, continuous, distributed, integrated surface/ground-water model, capable of simulating one-dimensional canal flow and two-dimensional overland flow in arbitrarily shaped areas using a variable triangular mesh. It has physically-based formulations for the simulation of overland and groundwater flow, evapo-transpiration, infiltration, levee seepage, and canal and structure flows. It is capable of simulating features that are unique to South Florida such as low-relief topography, high water tables, saturation-excess runoff, depth

  6. Legislative history of Superfund Amendments and Reauthorization Act of 1986 (SARA), Public Law 99-499, 99th Congress, 2d Session, 100 Stat. 1613. Volume 2. H. R. 2817 (reports)

    SciTech Connect

    Not Available

    1988-05-01

    The report is complete in four volumes, which is the Legislative History of SARA is a comprehensive collection of materials of the 99th Congress that follows the progress of each of the predecessor bills of SARA from their introduction, committee actions, and mark-ups, proposed amendments, debates, and votes. Contents: Volume II: H.R. 2817.

  7. Robust autonomous model learning from 2D and 3D data sets.

    PubMed

    Langs, Georg; Donner, René; Peloschek, Philipp; Bischof, Horst

    2007-01-01

    In this paper we propose a weakly supervised learning algorithm for appearance models based on the minimum description length (MDL) principle. From a set of training images or volumes depicting examples of an anatomical structure, correspondences for a set of landmarks are established by group-wise registration. The approach does not require any annotation. In contrast to existing methods no assumptions about the topology of the data are made, and the topology can change throughout the data set. Instead of a continuous representation of the volumes or images, only sparse finite sets of interest points are used to represent the examples during optimization. This enables the algorithm to efficiently use distinctive points, and to handle texture variations robustly. In contrast to standard elasticity based deformation constraints the MDL criterion accounts for systematic deformations typical for training sets stemming from medical image data. Experimental results are reported for five different 2D and 3D data sets. PMID:18051152

  8. STEALTH: a Lagrange explicit finite difference code for solids, structural, and thermohydraulic analysis. Volume 3: programmer's manual. Computer code manual. [PWR; BWR

    SciTech Connect

    Hofmann, R.

    1981-11-01

    This volume contains a description of a programming and documentation structure for the STEALTH finite difference computer programs based on general principles applicable to most large scientific computer programs. Program modularization (as well as documentation format) is based entirely on the theoretical elements of analysis of a physical system that were presented in Volume 1. FORTRAN programming and naming conventions are also described. Among the programming formats presented is a FORTRAN manual (Appendix FTN) which can be used as the basis for developing portable codes. STEALTH was developed on a CDC 7600. However, it has been designed so that it can be installed on most large scientific computers. Installation documentation exists for some facilities and can be generated easily for others.

  9. 2-D stationary gas dynamics in a barred galaxy

    NASA Astrophysics Data System (ADS)

    Mulder, W. A.

    2015-06-01

    A code for solving the 2-D isothermal Euler equations of gas dynamics in a rotating disc is presented. The gravitational potential represents a weak bar and controls the flow. A damped Newton method solves the second-order upwind discretisation of the equations for a steady-state solution, using a consistent linearisation and a direct solver. Successive grid refinement, starting from a finite-volume grid with 8 by 8 cells, is applied to find solutions on subsequently finer meshes. On coarser meshes, a first-order spatial discretisation is used. The method obtains quadratic convergence once the solution approaches the steady state. The initial search is quick with the first-order scheme and slower with the second-order discretisation, up to 256 by 256 cells. Beyond, with 512 by 512 cells, the number of iterations becomes too large to be of practical use. Potential causes are discussed. The code can be applied as a tool for generating flow models if used on not too fine meshes.

  10. Stacking up 2D materials

    NASA Astrophysics Data System (ADS)

    Mayor, Louise

    2016-05-01

    Graphene might be the most famous example, but there are other 2D materials and compounds too. Louise Mayor explains how these atomically thin sheets can be layered together to create flexible “van der Waals heterostructures”, which could lead to a range of novel applications.

  11. Transport Equations Resolution By N-BEE Anti-Dissipative Scheme In 2D Model Of Low Pressure Glow Discharge

    SciTech Connect

    Kraloua, B.; Hennad, A.

    2008-09-23

    The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.

  12. Corner transfer matrices for 2D strongly coupled many-body Floquet systems

    NASA Astrophysics Data System (ADS)

    Kukuljan, Ivan; Prosen, Tomaž

    2016-04-01

    We develop, based on Baxter’s corner transfer matrices, a renormalizable numerically exact method for computation of the level density of the quasienergy spectra of two-dimensional (2D) locally interacting many-body Floquet systems. We demonstrate its functionality exemplified by the kicked 2D quantum Ising model. Using the method, we are able to treat systems of arbitrarily large finite size (for example lattices of the order of 108 spins). We clearly demonstrate that the density of the Floquet quasienergy spectrum tends to a flat function in the thermodynamic limit for generic values of model parameters. However, contrary to the prediction of random matrices of the circular orthogonal ensemble, the decay rates of the Fourier coefficients of the Floquet level density exhibit rich and non-trivial dependence on the system’s parameters. Remarkably, we find that the method is renormalizable and gives thermodynamically convergent results only in certain regions of the parameter space where the corner transfer matrices have effectively a finite rank for any system size. In the complementary regions, the corner transfer matrices effectively become of full rank and the method becomes non-renormalizable. This may indicate an interesting phase transition from an area- to volume-law of entanglement in the thermodynamic state of a Floquet system.

  13. Simplified 2D Bidomain Model of Whole Heart Electrical Activity and ECG Generation

    NASA Astrophysics Data System (ADS)

    Sovilj, Siniša; Magjarević, Ratko; Abed, Amr Al; Lovell, Nigel H.; Dokos, Socrates

    2014-06-01

    The aim of this study was the development of a geometrically simple and highly computationally-efficient two dimensional (2D) biophysical model of whole heart electrical activity, incorporating spontaneous activation of the sinoatrial node (SAN), the specialized conduction system, and realistic surface ECG morphology computed on the torso. The FitzHugh-Nagumo (FHN) equations were incorporated into a bidomain finite element model of cardiac electrical activity, which was comprised of a simplified geometry of the whole heart with the blood cavities, the lungs and the torso as an extracellular volume conductor. To model the ECG, we placed four electrodes on the surface of the torso to simulate three Einthoven leads VI, VII and VIII from the standard 12-lead system. The 2D model was able to reconstruct ECG morphology on the torso from action potentials generated at various regions of the heart, including the sinoatrial node, atria, atrioventricular node, His bundle, bundle branches, Purkinje fibers, and ventricles. Our 2D cardiac model offers a good compromise between computational load and model complexity, and can be used as a first step towards three dimensional (3D) ECG models with more complex, precise and accurate geometry of anatomical structures, to investigate the effect of various cardiac electrophysiological parameters on ECG morphology.

  14. A Piecewise Linear Finite Element Discretization of the Diffusion Equation for Arbitrary Polyhedral Grids

    SciTech Connect

    Bailey, T S; Adams, M L; Yang, B; Zika, M R

    2005-07-15

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.

  15. 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

  16. MOSS2D V1

    2001-01-31

    This software reduces the data from two-dimensional kSA MOS program, k-Space Associates, Ann Arbor, MI. Initial MOS data is recorded without headers in 38 columns, with one row of data per acquisition per lase beam tracked. The final MOSS 2d data file is reduced, graphed, and saved in a tab-delimited column format with headers that can be plotted in any graphing software.

  17. Finite-volume versus streaming-based lattice Boltzmann algorithm for fluid-dynamics simulations: A one-to-one accuracy and performance study.

    PubMed

    Shrestha, Kalyan; Mompean, Gilmar; Calzavarini, Enrico

    2016-02-01

    A finite-volume (FV) discretization method for the lattice Boltzmann (LB) equation, which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard streaming lattice Boltzmann equation algorithm. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken as the method of choice in fluid-dynamics LB simulations. For this reason the comparative analysis is further extended to the case of realistic flows, in particular thermally driven flows in turbulent conditions. We report the successful simulation of high-Rayleigh number convective flow performed by a lattice Boltzmann FV-based algorithm with wall grid refinement. PMID:26986438

  18. Finite-volume corrections to the CP-odd nucleon matrix elements of the electromagnetic current from the QCD vacuum angle

    NASA Astrophysics Data System (ADS)

    Akan, Tarik; Guo, Feng-Kun; Meißner, Ulf-G.

    2014-09-01

    Nucleon electric dipole moments originating from strong CP-violation are being calculated by several groups using lattice QCD. We revisit the finite volume corrections to the CP-odd nucleon matrix elements of the electromagnetic current, which can be related to the electric dipole moments in the continuum, in the framework of chiral perturbation theory up to next-to-leading order taking into account the breaking of Lorentz symmetry. A chiral extrapolation of the recent lattice results of both the neutron and proton electric dipole moments is performed, which results in dn=(-2.7±1.2)×10-16eθ0 cm and dp=(2.1±1.2)×10-16eθ0 cm.

  19. Investigation of a matrix-model for the artificial dissipation in a cell vertex finite volume scheme for solving the Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Brodersen, Olaf

    1992-06-01

    A matrix dissipation model is evaluated for the numerical solution of the Navier-Stokes equations. The numerical approach, a finite volume scheme with central differencing, was outlined and the necessity of artificially added dissipation was shown. The design of the dissipation term for modeling an upwind scheme is described for the one dimensional linear wave equation. Following this approach results in time consuming matrix multiplications for two dimensional and three dimensional cases. Because of a new splitting technique of the matrices found in the literature, it is now possible to use this dissipation model in a more efficient way. The basic effects were analyzed for viscous flow around the RAE 2822 airfoil. The results show a higher resolution of shocks and the boundary layer. Thus, it is possible to use coarser meshes so that CPU (Central Processing Unit) time is reduced by about a factor of three.

  20. Finite-volume versus streaming-based lattice Boltzmann algorithm for fluid-dynamics simulations: A one-to-one accuracy and performance study

    NASA Astrophysics Data System (ADS)

    Shrestha, Kalyan; Mompean, Gilmar; Calzavarini, Enrico

    2016-02-01

    A finite-volume (FV) discretization method for the lattice Boltzmann (LB) equation, which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard streaming lattice Boltzmann equation algorithm. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken as the method of choice in fluid-dynamics LB simulations. For this reason the comparative analysis is further extended to the case of realistic flows, in particular thermally driven flows in turbulent conditions. We report the successful simulation of high-Rayleigh number convective flow performed by a lattice Boltzmann FV-based algorithm with wall grid refinement.

  1. Large-eddy simulations of 3D Taylor-Green vortex: comparison of Smoothed Particle Hydrodynamics, Lattice Boltzmann and Finite Volume methods

    NASA Astrophysics Data System (ADS)

    Kajzer, A.; Pozorski, J.; Szewc, K.

    2014-08-01

    In the paper we present Large-eddy simulation (LES) results of 3D Taylor- Green vortex obtained by the three different computational approaches: Smoothed Particle Hydrodynamics (SPH), Lattice Boltzmann Method (LBM) and Finite Volume Method (FVM). The Smagorinsky model was chosen as a subgrid-scale closure in LES for all considered methods and a selection of spatial resolutions have been investigated. The SPH and LBM computations have been carried out with the use of the in-house codes executed on GPU and compared, for validation purposes, with the FVM results obtained using the open-source CFD software OpenFOAM. A comparative study in terms of one-point statistics and turbulent energy spectra shows a good agreement of LES results for all methods. An analysis of the GPU code efficiency and implementation difficulties has been made. It is shown that both SPH and LBM may offer a significant advantage over mesh-based CFD methods.

  2. Parallel computation of unsteady, three-dimensional, chemically reacting, nonequilibrium flow using a time-split finite-volume method on the Illiac IV

    NASA Technical Reports Server (NTRS)

    Reinhardt, W. A.

    1977-01-01

    A description is presented of the split finite-volume method which is a viable numerical procedure for performing with the aid of a modern special purpose vector computer numerical simulation studies of complicated flow fields, including chemical reactions, about geometrically complex bodies. Such numerical studies are needed for the development of atmospheric entry vehicles such as the space shuttle. The equations which are approximated are quite general and can be used in studies of combustion, pollution, and other chemically reacting flow phenomena, where convective transport effects dominate the influence of radiative, viscous, and other transport mechanisms. The shock perturbed flow about a shuttle orbiter flying at a large angle of attack during atmospheric entry is illustrated. The method uses a time splitting of the convection differencing operator to achieve efficient data management.

  3. Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

    NASA Technical Reports Server (NTRS)

    Bui, Trong T.; Mankbadi, Reda R.

    1995-01-01

    Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

  4. Simulating the interaction of the heliosphere with the local interstellar medium: MHD results from a finite volume approach, first bidimensional results

    NASA Technical Reports Server (NTRS)

    Chanteur, G.; Khanfir, R.

    1995-01-01

    We have designed a full compressible MHD code working on unstructured meshes in order to be able to compute accurately sharp structures embedded in large scale simulations. The code is based on a finite volume method making use of a kinetic flux splitting. A bidimensional version of the code has been used to simulate the interaction of a moving interstellar medium, magnetized or unmagnetized with a rotating and magnetized heliopspheric plasma source. Being aware that these computations are not realistic due to the restriction to two dimensions, we present it to demonstrate the ability of this new code to handle this problem. An axisymetric version, now under development, will be operational in a few months. Ultimately we plan to run a full 3d version.

  5. EM 2dV1.0.F

    2012-01-05

    Code is for a layered electric medium with 2d structure. Includes air-earth interface at node z=2.. The electric ex and ez fields are calculated on edges of elemental grid and magnetic field hy is calculated on the face of the elemental grid. The code allows for a layered earth with 2d structures. Solutions of coupled first order Maxwell's equations are solved in the two dimensional environment using a finite- difference scheme on a staggered spationamore » and temporal grid.« less

  6. Nanoimprint lithography: 2D or not 2D? A review

    NASA Astrophysics Data System (ADS)

    Schift, Helmut

    2015-11-01

    Nanoimprint lithography (NIL) is more than a planar high-end technology for the patterning of wafer-like substrates. It is essentially a 3D process, because it replicates various stamp topographies by 3D displacement of material and takes advantage of the bending of stamps while the mold cavities are filled. But at the same time, it keeps all assets of a 2D technique being able to pattern thin masking layers like in photon- and electron-based traditional lithography. This review reports about 20 years of development of replication techniques at Paul Scherrer Institut, with a focus on 3D aspects of molding, which enable NIL to stay 2D, but at the same time enable 3D applications which are "more than Moore." As an example, the manufacturing of a demonstrator for backlighting applications based on thermally activated selective topography equilibration will be presented. This technique allows generating almost arbitrary sloped, convex and concave profiles in the same polymer film with dimensions in micro- and nanometer scale.

  7. Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1998-01-01

    We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.

  8. First-principles study of intrinsic point defects in ZnO: Role of band structure, volume relaxation, and finite-size effects

    NASA Astrophysics Data System (ADS)

    Erhart, Paul; Albe, Karsten; Klein, Andreas

    2006-05-01

    Density-functional theory (DFT) calculations of intrinsic point defect properties in zinc oxide were performed in order to remedy the influence of finite-size effects and the improper description of the band structure. The generalized gradient approximation (GGA) with empirical self-interaction corrections (GGA+U) was applied to correct for the overestimation of covalency intrinsic to GGA-DFT calculations. Elastic as well as electrostatic image interactions were accounted for by application of extensive finite-size scaling and compensating charge corrections. Size-corrected formation enthalpies and volumes as well as their charge state dependence have been deduced. Our results partly confirm earlier calculations but reveal a larger number of transition levels: (1) For both the zinc interstitial as well as the oxygen vacancy, transition levels are close to the conduction band minimum. (2) The zinc vacancy shows a transition rather close to the valence band maximum and another one near the middle of the calculated band gap. (3) For the oxygen interstitials, transition levels occur both near the valence band maximum and the conduction band minimum.

  9. Assimilation of Cloud- and Land-Affected TOVS/ATOVS Level 1B Radiances in DAO's Next Generation Finite-Volume Data Assimilation System

    NASA Technical Reports Server (NTRS)

    Joiner, J.; daSilva, A.; Einaudi, Franco (Technical Monitor)

    2001-01-01

    The Physical-space/Finite-volume Data Assimilation System (fvDAS) is the next generation global atmospheric data assimilation system in development at the Data Assimilation Office (DAO) at NASA's Goddard Space Flight Center. It is based on a new finite-volume general circulation model jointly developed by NASA and NCAR, and on the Physical-Space Statistical Analysis System (PSAS) developed at the DAO. In this talk we will focus on the assimilation of data from the (Advanced) TIROS Operational Vertical Sounder (ATOVS), with emphasis on the impact of cloud- and land-affected level 1B radiances. Recently, it has been shown that the use of observations from satellite-borne microwave and infrared radiometers in data assimilation systems consistently increases forecast skill. Considerable effort has been expended over the past two decades, particularly with the (Advanced) TIROS Operational Vertical Sounder (ATOVS), to achieve this result. The positive impact on forecast skill has resulted from improvements in quality control algorithms, systematic error correction schemes, and more sophisticated data assimilation algorithms. Despite these advances, there are still many issues regarding the use of satellite data in data assimilation systems that remain unresolved. In particular, most operational centers still do not assimilate cloud- and land-affected TOVS data. In this study, we evaluate the impact of assimilating cloud-and land-affected TOVS/ATOVS level 1B data in DAO's next generation fvDAS, using a 1D variational scheme. We will discuss the impact of these data on both tropospheric and stratospheric forecasts, as well as on the general aspects of the earth climate system.

  10. Strain memory of 2D and 3D rigid inclusion populations in viscous flows - What is clast SPO telling us?

    NASA Astrophysics Data System (ADS)

    Stahr, Donald W.; Law, Richard D.

    2014-11-01

    We model the development of shape preferred orientation (SPO) of a large population of two- and three-dimensional (2D and 3D) rigid clasts suspended in a linear viscous matrix deformed by superposed steady and continuously non-steady plane strain flows to investigate the sensitivity of clasts to changing boundary conditions during a single or superposed deformation events. Resultant clast SPOs are compared to one developed by an identical initial population that experienced a steady flow history of constant kinematic vorticity and reached an identical finite strain state, allowing examination of SPO sensitivity to deformation path. Rotation paths of individual triaxial inclusions are complex, even for steady plane strain flow histories. It has been suggested that the 3D nature of the system renders predictions based on 2D models inadequate for applied clast-based kinematic vorticity gauges. We demonstrate that for a large population of clasts, simplification to a 2D model does provide a good approximation to the SPO predicted by full 3D analysis for steady and non-steady plane strain deformation paths. Predictions of shape fabric development from 2D models are not only qualitatively similar to the more complex 3D analysis, but they display the same limitations of techniques based on clast SPO commonly used as a quantitative kinematic vorticity gauge. Our model results from steady, superposed, and non-steady flow histories with a significant pure shearing component at a wide range of finite strain resemble predictions for an identical initial population that experienced a single steady simple shearing deformation. We conclude that individual 2D and 3D clasts respond instantaneously to changes in boundary conditions, however, in aggregate, the SPO of a population of rigid inclusions does not reflect the late-stage kinematics of deformation, nor is it an indicator of the unique 'mean' kinematic vorticity experienced by a deformed rock volume.

  11. The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 1: Theoretical manual

    NASA Technical Reports Server (NTRS)

    Nakazawa, Shohei

    1991-01-01

    Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.

  12. 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

  13. Numerical Modeling of Oxidized 2D C/SiC Composites in Air Environments Below 900 °C: Microstructure and Elastic Properties

    NASA Astrophysics Data System (ADS)

    Sun, Zhigang; Chen, Xihui; Shao, Hongyan; Song, Yingdong

    2016-08-01

    A numerical model is presented for simulation of the oxidation-affected behaviors of two dimensional carbon fiber-reinforced silcon carbide matrix composite (2D C/SiC) exposed to air oxidizing environments below 900 °C, which incorporates the modeling of oxidized microstructure and computing of degraded elastic properties. This model is based upon the analysis of the representative volume cell (RVC) of the composite. The multi-scale model of 2D C/SiC composites is concerned in the present study. Analysis results of such a composite can provide a guideline for the real 2D C/SiC composite. The micro-structure during oxidation process is firstly modeled in the RVC. The elastic moduli of oxidized composite under non-stress oxidation environment is computed by finite element analysis. The elastic properties of 2D-C/SiC composites in air oxidizing environment are evaluated and validated in comparison to experimental data. The oxidation time, temperature and fiber volume fractions of C/SiC composite are investigated to show their influences upon the elastic properties of 2D C/SiC composites.

  14. Numerical Modeling of Oxidized 2D C/SiC Composites in Air Environments Below 900 °C: Microstructure and Elastic Properties

    NASA Astrophysics Data System (ADS)

    Sun, Zhigang; Chen, Xihui; Shao, Hongyan; Song, Yingdong

    2016-04-01

    A numerical model is presented for simulation of the oxidation-affected behaviors of two dimensional carbon fiber-reinforced silcon carbide matrix composite (2D C/SiC) exposed to air oxidizing environments below 900 °C, which incorporates the modeling of oxidized microstructure and computing of degraded elastic properties. This model is based upon the analysis of the representative volume cell (RVC) of the composite. The multi-scale model of 2D C/SiC composites is concerned in the present study. Analysis results of such a composite can provide a guideline for the real 2D C/SiC composite. The micro-structure during oxidation process is firstly modeled in the RVC. The elastic moduli of oxidized composite under non-stress oxidation environment is computed by finite element analysis. The elastic properties of 2D-C/SiC composites in air oxidizing environment are evaluated and validated in comparison to experimental data. The oxidation time, temperature and fiber volume fractions of C/SiC composite are investigated to show their influences upon the elastic properties of 2D C/SiC composites.

  15. An inverse design method for 2D airfoil

    NASA Astrophysics Data System (ADS)

    Liang, Zhi-Yong; Cui, Peng; Zhang, Gen-Bao

    2010-03-01

    The computational method for aerodynamic design of aircraft is applied more universally than before, in which the design of an airfoil is a hot problem. The forward problem is discussed by most relative papers, but inverse method is more useful in practical designs. In this paper, the inverse design of 2D airfoil was investigated. A finite element method based on the variational principle was used for carrying out. Through the simulation, it was shown that the method was fit for the design.

  16. 2d PDE Linear Symmetric Matrix Solver

    1983-10-01

    ICCG2 (Incomplete Cholesky factorized Conjugate Gradient algorithm for 2d symmetric problems) was developed to solve a linear symmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as resistive MHD, spatial diffusive transport, and phase space transport (Fokker-Planck equation) problems. These problems share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized withmore » finite-difference or finite-element methods,the resulting matrix system is frequently of block-tridiagonal form. To use ICCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. The incomplete Cholesky conjugate gradient algorithm is used to solve the linear symmetric matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For matrices lacking symmetry, ILUCG2 should be used. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less

  17. 2d PDE Linear Asymmetric Matrix Solver

    1983-10-01

    ILUCG2 (Incomplete LU factorized Conjugate Gradient algorithm for 2d problems) was developed to solve a linear asymmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as plasma diffusion, equilibria, and phase space transport (Fokker-Planck equation) problems. These equations share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized with finite-difference or finite-elementmore » methods, the resulting matrix system is frequently of block-tridiagonal form. To use ILUCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. A generalization of the incomplete Cholesky conjugate gradient algorithm is used to solve the matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For problems having a symmetric matrix ICCG2 should be used since it runs up to four times faster and uses approximately 30% less storage. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source, containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less

  18. CALCULATION OF DELTA I = 3/2 KAON WEAK MATRIX ELEMENTS INCLUDING TWO-PION INTERACTION EFFECTS IN FINITE VOLUME.

    SciTech Connect

    YAMAZAKI, T.

    2006-07-23

    We calculate {Delta}I = 3/2 kaon decay matrix elements using domain wall fermions and the DBW2 gauge action at one coarse lattice spacing corresponding to a{sup -1} = 1.3 GeV. We employ the Lellouch and Luescher formula and its extension for non-zero total momentum to extract the infinite volume, center-of-mass frame decay amplitudes. The decay amplitudes obtained from the methods correspond to those from the indirect method with full order chiral perturbation theory. We confirm that the result is consistent with the previous result calculated with H-parity (anti-periodic) boundary condition by investigating the relative momentum dependence. We evaluate the decay amplitude ReA{sub 2} at the physical point by a chiral extrapolation with a polynomial function of m{sub {pi}}{sup 2} and the relative momentum as well as the {Delta}I = 3/2 electroweak penguin contributions to {var_epsilon}{prime}/{var_epsilon}. We found that the result of ReA{sub 2} reasonably agrees with the experiment.

  19. OFF, Open source Finite volume Fluid dynamics code: A free, high-order solver based on parallel, modular, object-oriented Fortran API

    NASA Astrophysics Data System (ADS)

    Zaghi, S.

    2014-07-01

    OFF, an open source (free software) code for performing fluid dynamics simulations, is presented. The aim of OFF is to solve, numerically, the unsteady (and steady) compressible Navier-Stokes equations of fluid dynamics by means of finite volume techniques: the research background is mainly focused on high-order (WENO) schemes for multi-fluids, multi-phase flows over complex geometries. To this purpose a highly modular, object-oriented application program interface (API) has been developed. In particular, the concepts of data encapsulation and inheritance available within Fortran language (from standard 2003) have been stressed in order to represent each fluid dynamics “entity” (e.g. the conservative variables of a finite volume, its geometry, etc…) by a single object so that a large variety of computational libraries can be easily (and efficiently) developed upon these objects. The main features of OFF can be summarized as follows: Programming LanguageOFF is written in standard (compliant) Fortran 2003; its design is highly modular in order to enhance simplicity of use and maintenance without compromising the efficiency; Parallel Frameworks Supported the development of OFF has been also targeted to maximize the computational efficiency: the code is designed to run on shared-memory multi-cores workstations and distributed-memory clusters of shared-memory nodes (supercomputers); the code’s parallelization is based on Open Multiprocessing (OpenMP) and Message Passing Interface (MPI) paradigms; Usability, Maintenance and Enhancement in order to improve the usability, maintenance and enhancement of the code also the documentation has been carefully taken into account; the documentation is built upon comprehensive comments placed directly into the source files (no external documentation files needed): these comments are parsed by means of doxygen free software producing high quality html and latex documentation pages; the distributed versioning system referred

  20. Probability distribution of the index in gauge theory on 2d non-commutative geometry

    NASA Astrophysics Data System (ADS)

    Aoki, Hajime; Nishimura, Jun; Susaki, Yoshiaki

    2007-10-01

    We investigate the effects of non-commutative geometry on the topological aspects of gauge theory using a non-perturbative formulation based on the twisted reduced model. The configuration space is decomposed into topological sectors labeled by the index ν of the overlap Dirac operator satisfying the Ginsparg-Wilson relation. We study the probability distribution of ν by Monte Carlo simulation of the U(1) gauge theory on 2d non-commutative space with periodic boundary conditions. In general the distribution is asymmetric under ν mapsto -ν, reflecting the parity violation due to non-commutative geometry. In the continuum and infinite-volume limits, however, the distribution turns out to be dominated by the topologically trivial sector. This conclusion is consistent with the instanton calculus in the continuum theory. However, it is in striking contrast to the known results in the commutative case obtained from lattice simulation, where the distribution is Gaussian in a finite volume, but the width diverges in the infinite-volume limit. We also calculate the average action in each topological sector, and provide deeper understanding of the observed phenomenon.