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Sample records for accurate finite volume

  1. 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.

  2. A time-accurate finite volume method valid at all flow velocities

    NASA Astrophysics Data System (ADS)

    Kim, S.-W.

    1993-07-01

    A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil

  3. Accurate Finite Difference Algorithms

    NASA Technical Reports Server (NTRS)

    Goodrich, John W.

    1996-01-01

    Two families of finite difference algorithms for computational aeroacoustics are presented and compared. All of the algorithms are single step explicit methods, they have the same order of accuracy in both space and time, with examples up to eleventh order, and they have multidimensional extensions. One of the algorithm families has spectral like high resolution. Propagation with high order and high resolution algorithms can produce accurate results after O(10(exp 6)) periods of propagation with eight grid points per wavelength.

  4. 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.

  5. 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

  6. On numerically accurate finite element

    NASA Technical Reports Server (NTRS)

    Nagtegaal, J. C.; Parks, D. M.; Rice, J. R.

    1974-01-01

    A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.

  7. 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

  8. A cell-centred finite volume method for the Poisson problem on non-graded quadtrees with second order accurate gradients

    NASA Astrophysics Data System (ADS)

    Batty, Christopher

    2017-02-01

    This paper introduces a two-dimensional cell-centred finite volume discretization of the Poisson problem on adaptive Cartesian quadtree grids which exhibits second order accuracy in both the solution and its gradients, and requires no grading condition between adjacent cells. At T-junction configurations, which occur wherever resolution differs between neighboring cells, use of the standard centred difference gradient stencil requires that ghost values be constructed by interpolation. To properly recover second order accuracy in the resulting numerical gradients, prior work addressing block-structured grids and graded trees has shown that quadratic, rather than linear, interpolation is required; the gradients otherwise exhibit only first order convergence, which limits potential applications such as fluid flow. However, previous schemes fail or lose accuracy in the presence of the more complex T-junction geometries arising in the case of general non-graded quadtrees, which place no restrictions on the resolution of neighboring cells. We therefore propose novel quadratic interpolant constructions for this case that enable second order convergence by relying on stencils oriented diagonally and applied recursively as needed. The method handles complex tree topologies and large resolution jumps between neighboring cells, even along the domain boundary, and both Dirichlet and Neumann boundary conditions are supported. Numerical experiments confirm the overall second order accuracy of the method in the L∞ norm.

  9. Second Order Accurate Finite Difference Methods

    DTIC Science & Technology

    1984-08-20

    a study of the idealized material has direct applications to some polymer structures (4, 5). Wave propagation studies in hyperelastic materials have...34Acceleration Wave Propagation in Hyperelastic Rods of Variable Cross- section. Wave Motion, V4, pp. 173-180, 1982. 9. M. Hirao and N. Sugimoto...Waves in Hyperelastic Road," Quart. Appl. Math., V37, pp. 377-399, 1979. 11. G. A. Sod. "A Survey of Several Finite Difference Methods for Systems of

  10. Accurate optical CD profiler based on specialized finite element method

    NASA Astrophysics Data System (ADS)

    Carrero, Jesus; Perçin, Gökhan

    2012-03-01

    As the semiconductor industry is moving to very low-k1 patterning solutions, the metrology problems facing process engineers are becoming much more complex. Choosing the right optical critical dimension (OCD) metrology technique is essential for bridging the metrology gap and achieving the required manufacturing volume throughput. The critical dimension scanning electron microscope (CD-SEM) measurement is usually distorted by the high aspect ratio of the photoresist and hard mask layers. CD-SEM measurements cease to correlate with complex three-dimensional profiles, such as the cases for double patterning and FinFETs, thus necessitating sophisticated, accurate and fast computational methods to bridge the gap. In this work, a suite of computational methods that complement advanced OCD equipment, and enabling them to operate at higher accuracies, are developed. In this article, a novel method for accurately modeling OCD profiles is presented. A finite element formulation in primal form is used to discretize the equations. The implementation uses specialized finite element spaces to solve Maxwell equations in two dimensions.

  11. 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.

  12. 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

  13. Finite volume hydromechanical simulation in porous media.

    PubMed

    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.

  14. 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.

  15. Finite-volume scheme for anisotropic diffusion

    SciTech Connect

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

    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.

  16. Accurate solutions for transonic viscous flow over finite wings

    NASA Technical Reports Server (NTRS)

    Vatsa, V. N.

    1986-01-01

    An explicit multistage Runge-Kutta type time-stepping scheme is used for solving the three-dimensional, compressible, thin-layer Navier-Stokes equations. A finite-volume formulation is employed to facilitate treatment of complex grid topologies encountered in three-dimensional calculations. Convergence to steady state is expedited through usage of acceleration techniques. Further numerical efficiency is achieved through vectorization of the computer code. The accuracy of the overall scheme is evaluated by comparing the computed solutions with the experimental data for a finite wing under different test conditions in the transonic regime. A grid refinement study ir conducted to estimate the grid requirements for adequate resolution of salient features of such flows.

  17. ACCURATE CHEMICAL MASTER EQUATION SOLUTION USING MULTI-FINITE BUFFERS

    PubMed Central

    Cao, Youfang; Terebus, Anna; Liang, Jie

    2016-01-01

    The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving dCMEs is intractable due to the exploding size of the state space. It is important to truncate the state space effectively with quantified errors, so accurate solutions can be computed. It is also important to know if all major probabilistic peaks have been computed. Here we introduce the Accurate CME (ACME) algorithm for obtaining direct solutions to dCMEs. With multi-finite buffers for reducing the state space by O(n!), exact steady-state and time-evolving network probability landscapes can be computed. We further describe a theoretical framework of aggregating microstates into a smaller number of macrostates by decomposing a network into independent aggregated birth and death processes, and give an a priori method for rapidly determining steady-state truncation errors. The maximal sizes of the finite buffers for a given error tolerance can also be pre-computed without costly trial solutions of dCMEs. We show exactly computed probability landscapes of three multi-scale networks, namely, a 6-node toggle switch, 11-node phage-lambda epigenetic circuit, and 16-node MAPK cascade network, the latter two with no known solutions. We also show how probabilities of rare events can be computed from first-passage times, another class of unsolved problems challenging for simulation-based techniques due to large separations in time scales. Overall, the ACME method enables accurate and efficient solutions of the dCME for a large class of networks. PMID:27761104

  18. ACCURATE CHEMICAL MASTER EQUATION SOLUTION USING MULTI-FINITE BUFFERS.

    PubMed

    Cao, Youfang; Terebus, Anna; Liang, Jie

    2016-01-01

    The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving dCMEs is intractable due to the exploding size of the state space. It is important to truncate the state space effectively with quantified errors, so accurate solutions can be computed. It is also important to know if all major probabilistic peaks have been computed. Here we introduce the Accurate CME (ACME) algorithm for obtaining direct solutions to dCMEs. With multi-finite buffers for reducing the state space by O(n!), exact steady-state and time-evolving network probability landscapes can be computed. We further describe a theoretical framework of aggregating microstates into a smaller number of macrostates by decomposing a network into independent aggregated birth and death processes, and give an a priori method for rapidly determining steady-state truncation errors. The maximal sizes of the finite buffers for a given error tolerance can also be pre-computed without costly trial solutions of dCMEs. We show exactly computed probability landscapes of three multi-scale networks, namely, a 6-node toggle switch, 11-node phage-lambda epigenetic circuit, and 16-node MAPK cascade network, the latter two with no known solutions. We also show how probabilities of rare events can be computed from first-passage times, another class of unsolved problems challenging for simulation-based techniques due to large separations in time scales. Overall, the ACME method enables accurate and efficient solutions of the dCME for a large class of networks.

  19. The Kπ Interaction in Finite Volume

    NASA Astrophysics Data System (ADS)

    Zhou, Dan; Cui, Er-Liang; Chen, Hua-Xing; Geng, Li-Sheng; Zhu, Li-Hua

    We calculate energy levels of the Kπ scattering in the K∗ channel in finite volume using chiral unitary theory. We use these energy levels to obtain the Kπ phase shifts and the K∗ meson properties. We also investigate their dependence on the pion mass and compare this with Lattice QCD calculations.

  20. 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.

  1. Accurate finite difference methods for time-harmonic wave propagation

    NASA Technical Reports Server (NTRS)

    Harari, Isaac; Turkel, Eli

    1994-01-01

    Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.

  2. High order accurate finite difference schemes based on symmetry preservation

    NASA Astrophysics Data System (ADS)

    Ozbenli, Ersin; Vedula, Prakash

    2016-11-01

    A new algorithm for development of high order accurate finite difference schemes for numerical solution of partial differential equations using Lie symmetries is presented. Considering applicable symmetry groups (such as those relevant to space/time translations, Galilean transformation, scaling, rotation and projection) of a partial differential equation, invariant numerical schemes are constructed based on the notions of moving frames and modified equations. Several strategies for construction of invariant numerical schemes with a desired order of accuracy are analyzed. Performance of the proposed algorithm is demonstrated using analysis of one-dimensional partial differential equations, such as linear advection diffusion equations inviscid Burgers equation and viscous Burgers equation, as our test cases. Through numerical simulations based on these examples, the expected improvement in accuracy of invariant numerical schemes (up to fourth order) is demonstrated. Advantages due to implementation and enhanced computational efficiency inherent in our proposed algorithm are presented. Extension of the basic framework to multidimensional partial differential equations is also discussed.

  3. Accurate interlaminar stress recovery from finite element analysis

    NASA Technical Reports Server (NTRS)

    Tessler, Alexander; Riggs, H. Ronald

    1994-01-01

    The accuracy and robustness of a two-dimensional smoothing methodology is examined for the problem of recovering accurate interlaminar shear stress distributions in laminated composite and sandwich plates. The smoothing methodology is based on a variational formulation which combines discrete least-squares and penalty-constraint functionals in a single variational form. The smoothing analysis utilizes optimal strains computed at discrete locations in a finite element analysis. These discrete strain data are smoothed with a smoothing element discretization, producing superior accuracy strains and their first gradients. The approach enables the resulting smooth strain field to be practically C1-continuous throughout the domain of smoothing, exhibiting superconvergent properties of the smoothed quantity. The continuous strain gradients are also obtained directly from the solution. The recovered strain gradients are subsequently employed in the integration o equilibrium equations to obtain accurate interlaminar shear stresses. The problem is a simply-supported rectangular plate under a doubly sinusoidal load. The problem has an exact analytic solution which serves as a measure of goodness of the recovered interlaminar shear stresses. The method has the versatility of being applicable to the analysis of rather general and complex structures built of distinct components and materials, such as found in aircraft design. For these types of structures, the smoothing is achieved with 'patches', each patch covering the domain in which the smoothed quantity is physically continuous.

  4. Nonlinear Conservation Laws and Finite Volume Methods

    NASA Astrophysics Data System (ADS)

    Leveque, Randall J.

    Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

  5. 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.

  6. Finite volume corrections to pi pi scattering

    SciTech Connect

    Sato, Ikuro; Bedaque, Paulo F.; Walker-Loud, Andre

    2006-01-13

    Lattice QCD studies of hadron-hadron interactions are performed by computing the energy levels of the system in a finite box. The shifts in energy levels proportional to inverse powers of the volume are related to scattering parameters in a model independent way. In addition, there are non-universal exponentially suppressed corrections that distort this relation. These terms are proportional to e-m{sub pi} L and become relevant as the chiral limit is approached. In this paper we report on a one-loop chiral perturbation theory calculation of the leading exponential corrections in the case of I=2 pi pi scattering near threshold.

  7. LARGE volume string compactifications at finite temperature

    SciTech Connect

    Anguelova, Lilia; Calò, Vincenzo; Cicoli, Michele E-mail: v.calo@qmul.ac.uk

    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 T{sub max}, above which the internal space decompactifies, as well as the temperature T{sub *}, that is reached after the decay of the heaviest moduli. The natural constraint T{sub *} < T{sub max} implies a lower bound on the allowed values of the internal volume V. We find that this restriction rules out a significant range of values corresponding to smaller volumes of the order V ∼ 10{sup 4}l{sub s}{sup 6}, which lead to standard GUT theories. Instead, the bound favours values of the order V ∼ 10{sup 15}l{sub s}{sup 6}, 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.

  8. 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.

  9. Resonance Extraction from the Finite Volume

    SciTech Connect

    Doring, Michael; Molina Peralta, Raquel

    2016-06-01

    The spectrum of excited hadrons becomes accessible in simulations of Quantum Chromodynamics on the lattice. Extensions of Lüscher's method allow to address multi-channel scattering problems using moving frames or modified boundary conditions to obtain more eigenvalues in finite volume. As these are at different energies, interpolations are needed to relate different eigenvalues and to help determine the amplitude. Expanding the T- or the K-matrix locally provides a controlled scheme by removing the known non-analyticities of thresholds. This can be stabilized by using Chiral Perturbation Theory. Different examples to determine resonance pole parameters and to disentangle resonances from thresholds are dis- cussed, like the scalar meson f0(980) and the excited baryons N(1535)1/2^- and Lambda(1405)1/2^-.

  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. Footbridge between finite volumes and finite elements with applications to CFD

    NASA Astrophysics Data System (ADS)

    Pascal, Frédéric; Ghidaglia, Jean-Michel

    2001-12-01

    The aim of this paper is to introduce a new algorithm for the discretization of second-order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier-Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright

  12. 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.

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

    NASA Astrophysics Data System (ADS)

    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 Navie-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.

  14. 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

  15. A Mixed Finite Volume Element Method for Flow Calculations in Porous Media

    NASA Technical Reports Server (NTRS)

    Jones, Jim E.

    1996-01-01

    A key ingredient in the simulation of flow in porous media is the accurate determination of the velocities that drive the flow. The large scale irregularities of the geology, such as faults, fractures, and layers suggest the use of irregular grids in the simulation. Work has been done in applying the finite volume element (FVE) methodology as developed by McCormick in conjunction with mixed methods which were developed by Raviart and Thomas. The resulting mixed finite volume element discretization scheme has the potential to generate more accurate solutions than standard approaches. The focus of this paper is on a multilevel algorithm for solving the discrete mixed FVE equations. The algorithm uses a standard cell centered finite difference scheme as the 'coarse' level and the more accurate mixed FVE scheme as the 'fine' level. The algorithm appears to have potential as a fast solver for large size simulations of flow in porous media.

  16. 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.

  17. Mixed finite element - discontinuous finite volume element discretization of a general class of multicontinuum models

    NASA Astrophysics Data System (ADS)

    Ruiz-Baier, Ricardo; Lunati, Ivan

    2016-10-01

    We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation

  18. Interactive Isogeometric Volume Visualization with Pixel-Accurate Geometry.

    PubMed

    Fuchs, Franz G; Hjelmervik, Jon M

    2016-02-01

    A recent development, called isogeometric analysis, provides a unified approach for design, analysis and optimization of functional products in industry. Traditional volume rendering methods for inspecting the results from the numerical simulations cannot be applied directly to isogeometric models. We present a novel approach for interactive visualization of isogeometric analysis results, ensuring correct, i.e., pixel-accurate geometry of the volume including its bounding surfaces. The entire OpenGL pipeline is used in a multi-stage algorithm leveraging techniques from surface rendering, order-independent transparency, as well as theory and numerical methods for ordinary differential equations. We showcase the efficiency of our approach on different models relevant to industry, ranging from quality inspection of the parametrization of the geometry, to stress analysis in linear elasticity, to visualization of computational fluid dynamics results.

  19. 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.

  20. Finite volume method for geodetic boundary value problem

    NASA Astrophysics Data System (ADS)

    Medľa, Matej; Mikula, Karol; Macák, Marek

    2016-04-01

    We present new finite volume numerical scheme for solving the Geodetic boundary value problem on non-uniform logically rentangular grids together with new second-order upwind treatment of the oblique derivative. First the logically rectangular grid is built above the Earth topography by evolving surface approach. Then the Laplace equation is solved on such grid by using the finite volume method in which the normal derivative on finite volume boundary face is split into derivative in tangential direction and a derivative in direction of the vector connecting representative points of neigbouring finite volumes. The oblique derivative boundary condition is understood as a stationary advection equation and second-order upwind method is developed for its discretization. The numerical experiments will be presented.

  1. Accurate colon residue detection algorithm with partial volume segmentation

    NASA Astrophysics Data System (ADS)

    Li, Xiang; Liang, Zhengrong; Zhang, PengPeng; Kutcher, Gerald J.

    2004-05-01

    Colon cancer is the second leading cause of cancer-related death in the United States. Earlier detection and removal of polyps can dramatically reduce the chance of developing malignant tumor. Due to some limitations of optical colonoscopy used in clinic, many researchers have developed virtual colonoscopy as an alternative technique, in which accurate colon segmentation is crucial. However, partial volume effect and existence of residue make it very challenging. The electronic colon cleaning technique proposed by Chen et al is a very attractive method, which is also kind of hard segmentation method. As mentioned in their paper, some artifacts were produced, which might affect the accurate colon reconstruction. In our paper, instead of labeling each voxel with a unique label or tissue type, the percentage of different tissues within each voxel, which we call a mixture, was considered in establishing a maximum a posterior probability (MAP) image-segmentation framework. A Markov random field (MRF) model was developed to reflect the spatial information for the tissue mixtures. The spatial information based on hard segmentation was used to determine which tissue types are in the specific voxel. Parameters of each tissue class were estimated by the expectation-maximization (EM) algorithm during the MAP tissue-mixture segmentation. Real CT experimental results demonstrated that the partial volume effects between four tissue types have been precisely detected. Meanwhile, the residue has been electronically removed and very smooth and clean interface along the colon wall has been obtained.

  2. 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.

  3. 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.

  4. 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

    2016-02-15

    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, 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. -- Highlights: •We performed a comprehensive study to verify and validate the turbulence models in Hydra-TH. •Hydra-TH delivers 2nd-order grid convergence for the incompressible Navier–Stokes equations. •Hydra-TH can accurately simulate the laminar boundary layers. •Hydra-TH can accurately simulate the turbulent boundary layers with RANS turbulence models. •Hydra-TH delivers high-fidelity LES capability for simulating turbulent flows in confined space.

  5. 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.

  6. 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.

  7. Treatment of internal sources in the finite-volume ELLAM

    USGS Publications Warehouse

    Healy, R.W.; ,; ,; ,; ,; ,

    2000-01-01

    The finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) is a mass-conservative approach for solving the advection-dispersion equation. The method has been shown to be accurate and efficient for solving advection-dominated problems of solute transport in ground water in 1, 2, and 3 dimensions. Previous implementations of FVELLAM have had difficulty in representing internal sources because the standard assumption of lowest order Raviart-Thomas velocity field does not hold for source cells. Therefore, tracking of particles within source cells is problematic. A new approach has been developed to account for internal sources in FVELLAM. It is assumed that the source is uniformly distributed across a grid cell and that instantaneous mixing takes place within the cell, such that concentration is uniform across the cell at any time. Sub-time steps are used in the time-integration scheme to track mass outflow from the edges of the source cell. This avoids the need for tracking within the source cell. We describe the new method and compare results for a test problem with a wide range of cell Peclet numbers.

  8. A finite volume model simulation for the Broughton Archipelago, Canada

    NASA Astrophysics Data System (ADS)

    Foreman, M. G. G.; Czajko, P.; Stucchi, D. J.; Guo, M.

    A finite volume circulation model is applied to the Broughton Archipelago region of British Columbia, Canada and used to simulate the three-dimensional velocity, temperature, and salinity fields that are required by a companion model for sea lice behaviour, development, and transport. The absence of a high resolution atmospheric model necessitated the installation of nine weather stations throughout the region and the development of a simple data assimilation technique that accounts for topographic steering in interpolating/extrapolating the measured winds to the entire model domain. The circulation model is run for the period of March 13-April 3, 2008 and correlation coefficients between observed and model currents, comparisons between model and observed tidal harmonics, and root mean square differences between observed and model temperatures and salinities all showed generally good agreement. The importance of wind forcing in the near-surface circulation, differences between this simulation and one computed with another model, the effects of bathymetric smoothing on channel velocities, further improvements necessary for this model to accurately simulate conditions in May and June, and the implication of near-surface current patterns at a critical location in the 'migration corridor' of wild juvenile salmon, are also discussed.

  9. 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.

  10. Polyakov-Nambu-Jona-Lasinio model in finite volumes

    NASA Astrophysics Data System (ADS)

    Bhattacharyya, Abhijit; Ghosh, Sanjay K.; Ray, Rajarshi; Saha, Kinkar; Upadhaya, Sudipa

    2016-12-01

    We discuss the 2+1 flavor Polyakov loop enhanced Nambu-Jona-Lasinio model in a finite volume. The main objective is to check the volume scaling of thermodynamic observables for various temperatures and chemical potentials. We observe the possible violation of the scaling with system size in a considerable window along the whole transition region in the T\\text-μq plane.

  11. The Meshfree Finite Volume Method with application to multi-phase porous media models

    NASA Astrophysics Data System (ADS)

    Foy, Brody H.; Perré, Patrick; Turner, Ian

    2017-03-01

    Numerical methods form a cornerstone of the analysis and investigation of mathematical models for physical processes. Many classical numerical schemes rely on the application of strict meshing structures to generate accurate solutions, which in some applications are an infeasible constraint. Within this paper we outline a new meshfree numerical scheme, which we call the Meshfree Finite Volume Method (MFVM). The MFVM uses interpolants to approximate fluxes in a disjoint finite volume scheme, allowing for the accurate solution of strong-form PDEs. We present a derivation of the MFVM, and give error bounds on the spatial and temporal approximations used within the scheme. We present a wide variety of applications of the method, showing key features, and advantages over traditional meshed techniques. We close with an application of the method to a non-linear multi-phase wood drying model, showing the potential for solving numerically challenging problems.

  12. Coupled-channel systems in a finite volume

    NASA Astrophysics Data System (ADS)

    Davoudi, Zohreh

    2012-10-01

    In this talk I will motivate studies of two-body coupled-channel systems in a finite volume in connection with the ultimate goal of studying nuclear reactions, as well as hadronic resonances, directly from lattice QCD. I will discuss how one can determine phase shifts and mixing parameters of coupled-channels such as that of pipi-KK isosinglet system from the energy spectrum in a finite volume with periodic boundary conditions. From the energy quantization condition, the volume dependence of electroweak matrix elements of two-hadron processes can also be extracted. This is necessary for studying weak processes that mix isosinglet-isotriplet two-nucleon states, e.g. proton-proton fusion. I will show how one can obtain such transition amplitudes from lattice QCD using the formalism developed.

  13. 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.

  14. Time domain solutions of Maxwell's equations using a finite-volume formulation

    SciTech Connect

    Noack, R.W.

    1991-01-01

    A new method for solving Maxwell's equations in the time domain was developed. The method approximates the integral form of the time-dependent Maxwell's equations using a finite-volume formulation. The method utilizes a staggered mesh and requires boundary conditions on the electric field or the magnetic field but not both. Predictions from the present method were compared to exact solutions for a full three-dimensional calculation of a sphere and experimental measurements for a generic missile body. These comparisons show that the method is capable of accurately solving the time-dependent Maxwell's equations and yields accurate predictions of the radar cross section for arbitrary geometries.

  15. A defect corrected finite element approach for the accurate evaluation of magnetic fields on unstructured grids

    NASA Astrophysics Data System (ADS)

    Römer, Ulrich; Schöps, Sebastian; De Gersem, Herbert

    2017-04-01

    In electromagnetic simulations of magnets and machines, one is often interested in a highly accurate and local evaluation of the magnetic field uniformity. Based on local post-processing of the solution, a defect correction scheme is proposed as an easy to realize alternative to higher order finite element or hybrid approaches. Radial basis functions (RBFs) are key for the generality of the method, which in particular can handle unstructured grids. Also, contrary to conventional finite element basis functions, higher derivatives of the solution can be evaluated, as required, e.g., for deflection magnets. Defect correction is applied to obtain a solution with improved accuracy and adjoint techniques are used to estimate the remaining error for a specific quantity of interest. Significantly improved (local) convergence orders are obtained. The scheme is also applied to the simulation of a Stern-Gerlach magnet currently in operation.

  16. Three-boson bound states in finite volume with EFT

    NASA Astrophysics Data System (ADS)

    Kreuzer, S.; Hammer, H.-W.

    2010-04-01

    The universal properties of a three-boson system with large scattering length are well understood within the framework of Effective Field Theory. They include a geometric spectrum of shallow three-body bound states called “Efimov states” and log-periodic dependence of scattering observables on the scattering length. We investigate the modification of this spectrum in a finite cubic box using a partial wave expansion. The dependence of the binding energies on the box size is calculated for systems with positive and negative two-body scattering length. We compare the full results to results obtained using an expansion around the infinite volume binding energy. The renormalization of the Effective Field Theory in the finite volume is verified explicitly.

  17. An hybrid finite volume finite element method for variable density incompressible flows

    NASA Astrophysics Data System (ADS)

    Calgaro, Caterina; Creusé, Emmanuel; Goudon, Thierry

    2008-04-01

    This paper is devoted to the numerical simulation of variable density incompressible flows, modeled by the Navier-Stokes system. We introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint. The breakthrough relies on the definition of a suitable footbridge between the two methods, through the design of compatibility condition. In turn, the method is very flexible and allows to deal with unstructured meshes. Several numerical tests are performed to show the scheme capabilities. In particular, the viscous Rayleigh-Taylor instability evolution is carefully investigated.

  18. Infinite volume of noncommutative black hole wrapped by finite surface

    NASA Astrophysics Data System (ADS)

    Zhang, Baocheng; You, Li

    2017-02-01

    The volume of a black hole under noncommutative spacetime background is found to be infinite, in contradiction with the surface area of a black hole, or its Bekenstein-Hawking (BH) entropy, which is well-known to be finite. Our result rules out the possibility of interpreting the entropy of a black hole by counting the number of modes wrapped inside its surface if the final evaporation stage can be properly treated. It implies the statistical interpretation for the BH entropy can be independent of the volume, provided spacetime is noncommutative. The effect of radiation back reaction is found to be small and doesn't influence the above conclusion.

  19. Packing Infinite Number of Cubes in a Finite Volume Box

    ERIC Educational Resources Information Center

    Yao, Haishen; Wajngurt, Clara

    2006-01-01

    Packing an infinite number of cubes into a box of finite volume is the focus of this article. The results and diagrams suggest two ways of packing these cubes. Specifically suppose an infinite number of cubes; the side length of the first one is 1; the side length of the second one is 1/2 , and the side length of the nth one is 1/n. Let n approach…

  20. A fourth order accurate finite difference scheme for the computation of elastic waves

    NASA Technical Reports Server (NTRS)

    Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.

    1986-01-01

    A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.

  1. Accurate Determination of the Volume of an Irregular Helium Balloon

    NASA Astrophysics Data System (ADS)

    Blumenthal, Jack; Bradvica, Rafaela; Karl, Katherine

    2013-02-01

    In a recent paper, Zable described an experiment with a near-spherical balloon filled with impure helium. Measuring the temperature and the pressure inside and outside the balloon, the lift of the balloon, and the mass of the balloon materials, he described how to use the ideal gas laws and Archimedes' principal to compute the average molecular mass and density of the impure helium. This experiment required that the volume of the near-spherical balloon be determined by some approach, such as measuring the girth. The accuracy of the experiment was largely determined by the balloon volume, which had a reported uncertainty of about 4%.

  2. Accurate measurement of gas volumes by liquid displacement

    NASA Technical Reports Server (NTRS)

    Christian, J. D.

    1972-01-01

    Mariotte bottle as liquid displacement device was used to measure gas volumes at flow rates that are far below threshold of wet test gas meters. Study of factors affecting amount of liquid displaced by gas flow was completed, and equations were derived which relate different variables.

  3. 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

  4. 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

  5. Quantum Monte Carlo calculations of two neutrons in finite volume

    DOE PAGES

    Klos, P.; Lynn, J. E.; Tews, I.; ...

    2016-11-18

    Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial formore » determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.« less

  6. Quantum Monte Carlo calculations of two neutrons in finite volume

    SciTech Connect

    Klos, P.; Lynn, J. E.; Tews, I.; Gandolfi, Stefano; Gezerlis, A.; Hammer, H. -W.; Hoferichter, M.; Schwenk, A.

    2016-11-18

    Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial for determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.

  7. 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.

  8. 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

  9. Accurate force fields and methods for modelling organic molecular crystals at finite temperatures.

    PubMed

    Nyman, Jonas; Pundyke, Orla Sheehan; Day, Graeme M

    2016-06-21

    We present an assessment of the performance of several force fields for modelling intermolecular interactions in organic molecular crystals using the X23 benchmark set. The performance of the force fields is compared to several popular dispersion corrected density functional methods. In addition, we present our implementation of lattice vibrational free energy calculations in the quasi-harmonic approximation, using several methods to account for phonon dispersion. This allows us to also benchmark the force fields' reproduction of finite temperature crystal structures. The results demonstrate that anisotropic atom-atom multipole-based force fields can be as accurate as several popular DFT-D methods, but have errors 2-3 times larger than the current best DFT-D methods. The largest error in the examined force fields is a systematic underestimation of the (absolute) lattice energy.

  10. 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.

  11. A high order accurate finite element algorithm for high Reynolds number flow prediction

    NASA Technical Reports Server (NTRS)

    Baker, A. J.

    1978-01-01

    A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

  12. Finite-difference and finite-volume methods for nonlinear standing ultrasonic waves in fluid media.

    PubMed

    Vanhille, C; Conde, C; Campos-Pozuelo, C

    2004-04-01

    In the framework of the application of high-power ultrasonics in industrial processing in fluid media, the mathematical prediction of the acoustical parameters inside resonators should improve the development of practical systems. This can be achieved by the use of numerical tools able to treat the nonlinear acoustics involved in these phenomena. In particular, effects like nonlinear distortion and nonlinear attenuation are fundamental in applications. In this paper, three one-dimensional numerical models in the time domain for calculating the nonlinear acoustic field inside a one-dimensional resonant cavity are presented and compared. They are based on the finite-difference and the finite-volume methods. These different algorithms solve the differential equations, from the linear up to the strongly nonlinear case (including weak shock). Some physical results obtained from the modelling of ultrasonic waves and a comparison of the efficiency of the different algorithms are presented.

  13. A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems

    NASA Technical Reports Server (NTRS)

    Casper, Jay; Atkins, H. L.

    1993-01-01

    The finite-volume approach is presently used to obtain a 2D, high-order accurate and basically nonoscillatory shock-capture method whose high-order spatial accuracy is obtained by means of a piecewise polynomial approximation of the solution from cell averages. Attention is given to a high-order spatial operator that is able to both retain high-order accuracy in smooth regions and avoid the oscillations that are associated with interpolations across steep gradients. The operator is extended to hyperbolic systems of equations and curvilinear meshes.

  14. 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.

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

    DOE PAGES

    McCorquodale, P. W.; Colella, P.; Dorr, M. R.; ...

    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.

  16. 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.

  17. 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.

  18. 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.

  19. GPU-based volume visualization from high-order finite element fields.

    PubMed

    Nelson, Blake; Kirby, Robert M; Haimes, Robert

    2014-01-01

    This paper describes a new volume rendering system for spectral/hp finite-element methods that has as its goal to be both accurate and interactive. Even though high-order finite element methods are commonly used by scientists and engineers, there are few visualization methods designed to display this data directly. Consequently, visualizations of high-order data are generally created by first sampling the high-order field onto a regular grid and then generating the visualization via traditional methods based on linear interpolation. This approach, however, introduces error into the visualization pipeline and requires the user to balance image quality, interactivity, and resource consumption. We first show that evaluation of the volume rendering integral, when applied to the composition of piecewise-smooth transfer functions with the high-order scalar field, typically exhibits second-order convergence for a wide range of high-order quadrature schemes, and has worst case first-order convergence. This result provides bounds on the ability to achieve high-order convergence to the volume rendering integral. We then develop an algorithm for optimized evaluation of the volume rendering integral, based on the categorization of each ray according to the local behavior of the field and transfer function. We demonstrate the effectiveness of our system by running performance benchmarks on several high-order fluid-flow simulations.

  20. Pion mass dependence of the K l3 semileptonic scalar form factor within finite volume

    NASA Astrophysics Data System (ADS)

    Ghorbani, K.; Yazdanpanah, M. M.; Mirjalili, A.

    2011-06-01

    We calculate the scalar semileptonic kaon decay in finite volume at the momentum transfer t m =( m K - m π )2, using chiral perturbation theory. At first we obtain the hadronic matrix element to be calculated in finite volume. We then evaluate the finite size effects for two volumes with L=1.83 fm and L=2.73 fm and find that the difference between the finite volume corrections of the two volumes are larger than the difference as quoted in Boyle et al. (Phys. Rev. Lett. 100:141601, 2008). It appears then that the pion masses used for the scalar form factor in ChPT are large which result in large finite volume corrections. If appropriate values for pion mass are used, we believe that the finite size effects estimated in this paper can be useful for lattice data to extrapolate at large lattice size.

  1. 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.

  2. 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.

  3. 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.

  4. Frost Formation: Optimizing solutions under a finite volume approach

    NASA Astrophysics Data System (ADS)

    Bartrons, E.; Perez-Segarra, C. D.; Oliet, C.

    2016-09-01

    A three-dimensional transient formulation of the frost formation process is developed by means of a finite volume approach. Emphasis is put on the frost surface boundary condition as well as the wide range of empirical correlations related to the thermophysical and transport properties of frost. A study of the numerical solution is made, establishing the parameters that ensure grid independence. Attention is given to the algorithm, the discretised equations and the code optimization through dynamic relaxation techniques. A critical analysis of four cases is carried out by comparing solutions of several empirical models against tested experiments. As a result, a discussion on the performance of such parameters is started and a proposal of the most suitable models is presented.

  5. 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.

  6. Time domain solutions of Maxwell's equations using a finite-volume formulation

    SciTech Connect

    Noack, R.W.; Anderson, D.A. )

    1992-01-01

    A new method for solving Maxwell's equations in the time domain has been developed. The method approximates the integral form of the time-dependent Maxwell's equations using a finite-volume formulation. The method utilizes a staggered mesh and requires boundary conditions on the electric field or the magnetic field but not both. Predictions from the present method have been compared to exact solutions for a full three-dimensional calculation of a sphere and experimental measurements for a generic missile body. These comparisons show that the method is capable of accurately solving the time-dependent Maxwell's equations and yields accurate predictions of the radar cross section for arbitrary geometries. 38 refs.

  7. 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.

  8. Conservative high-order-accurate finite-difference methods for curvilinear grids

    NASA Technical Reports Server (NTRS)

    Rai, Man M.; Chakrvarthy, Sukumar

    1993-01-01

    Two fourth-order-accurate finite-difference methods for numerically solving hyperbolic systems of conservation equations on smooth curvilinear grids are presented. The first method uses the differential form of the conservation equations; the second method uses the integral form of the conservation equations. Modifications to these schemes, which are required near boundaries to maintain overall high-order accuracy, are discussed. An analysis that demonstrates the stability of the modified schemes is also provided. Modifications to one of the schemes to make it total variation diminishing (TVD) are also discussed. Results that demonstrate the high-order accuracy of both schemes are included in the paper. In particular, a Ringleb-flow computation demonstrates the high-order accuracy and the stability of the boundary and near-boundary procedures. A second computation of supersonic flow over a cylinder demonstrates the shock-capturing capability of the TVD methodology. An important contribution of this paper is the dear demonstration that higher order accuracy leads to increased computational efficiency.

  9. 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.

  10. Flow simulation of a Pelton bucket using finite volume particle method

    NASA Astrophysics Data System (ADS)

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

    2014-03-01

    The objective of the present paper is to perform an accurate numerical simulation of the high-speed water jet impinging on a Pelton bucket. To reach this goal, the Finite Volume Particle Method (FVPM) is used to discretize the governing equations. FVPM is an arbitrary Lagrangian-Eulerian method, which combines attractive features of Smoothed Particle Hydrodynamics and conventional mesh-based Finite Volume Method. This method is able to satisfy free surface and no-slip wall boundary conditions precisely. The fluid flow is assumed weakly compressible and the wall boundary is represented by one layer of particles located on the bucket surface. In the present study, the simulations of the flow in a stationary bucket are investigated for three different impinging angles: 72°, 90° and 108°. The particles resolution is first validated by a convergence study. Then, the FVPM results are validated with available experimental data and conventional grid-based Volume Of Fluid simulations. It is shown that the wall pressure field is in good agreement with the experimental and numerical data. Finally, the torque evolution and water sheet location are presented for a simulation of five rotating Pelton buckets.

  11. 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.

  12. 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.

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

    DOE PAGES

    Xia, Yidong; Wang, Chuanjin; Luo, Hong; ...

    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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. High resolution finite volume parallel simulations of mould filling and binary alloy solidification on unstructured 3-D meshes

    SciTech Connect

    Reddy, A.V.; Kothe, D.B.; Lam, K.L.

    1997-06-01

    The Los Alamos National Laboratory (LANL) is currently developing a new casting simulation tool (known as Telluride) that employs robust, high-resolution finite volume algorithms for incompressible fluid flow, volume tracking of interfaces, and solidification physics on three-dimensional (3-D) unstructured meshes. Their finite volume algorithms are based on colocated cell-centered schemes that are formally second order in time and space. The flow algorithm is a 3-D extension of recent work on projection method solutions of the Navier-Stokes (NS) equations. Their volume tracking algorithm can accurately track topologically complex interfaces by approximating the interface geometry as piecewise planar. Coupled to their fluid flow algorithm is a comprehensive binary alloy solidification model that incorporates macroscopic descriptions of heat transfer, solute redistribution, and melt convection as well as a microscopic description of segregation. The finite volume algorithms, which are efficient, parallel, and robust, can yield high-fidelity solutions on a variety of meshes, ranging from those that are structured orthogonal to fully unstructured (finite element). The authors discuss key computer science issues that have enabled them to efficiently parallelize their unstructured mesh algorithms on both distributed and shared memory computing platforms. These include their functionally object-oriented use of Fortran 90 and new parallel libraries for gather/scatter functions (PGSLib) and solutions of linear systems of equations (JTpack90). Examples of their current capabilities are illustrated with simulations of mold filling and solidification of complex 3-D components currently being poured in LANL foundries.

  19. 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.

  20. Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation

    NASA Astrophysics Data System (ADS)

    Bispen, Georgij; Lukáčová-Medvid'ová, Mária; Yelash, Leonid

    2017-04-01

    In this paper we will present and analyze a new class of the IMEX finite volume schemes for the Euler equations with a gravity source term. We will in particular concentrate on a singular limit of weakly compressible flows when the Mach number M ≪ 1. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non-stiff nonlinear part that models nonlinear advection effects. For time discretization we use a special class of the so-called globally stiffly accurate IMEX schemes and approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. For spatial discretization the finite volume approximation is used with the central and Rusanov/Lax-Friedrichs numerical fluxes for the linear and nonlinear subsystem, respectively. In the case of a constant background potential temperature we prove theoretically that the method is asymptotically consistent and asymptotically stable uniformly with respect to small Mach number. We also analyze experimentally convergence rates in the singular limit when the Mach number tends to zero.

  1. A Hybrid Boundary Element-Finite Volume Method for Unsteady Transonic Airfoil Flows

    NASA Technical Reports Server (NTRS)

    Hu, Hong; Kandil, Osama A.

    1996-01-01

    A hybrid boundary element finite volume method for unsteady transonic flow computation has been developed. In this method, the unsteady Euler equations in a moving frame of reference are solved in a small embedded domain (inner domain) around the airfoil using an implicit finite volume scheme. The unsteady full-potential equation, written in the same frame of reference and in the form of the Poisson equation. is solved in the outer domain using the integral equation boundary element method to provide the boundary conditions for the inner Euler domain. The solution procedure is a time-accurate stepping procedure, where the outer boundary conditions for the inner domain are updated using the integral equation -- boundary element solution over the outer domain. The method is applied to unsteady transonic flows around the NACA0012 airfoil undergoing pitching oscillation and ramp motion. The results are compared with those of an implicit Euler equation solver, which is used throughout a large computational domain, and experimental data.

  2. 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.

  3. 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.

  4. Generalized source Finite Volume Method for radiative transfer equation in participating media

    NASA Astrophysics Data System (ADS)

    Zhang, Biao; Xu, Chuan-Long; Wang, Shi-Min

    2017-03-01

    Temperature monitoring is very important in a combustion system. In recent years, non-intrusive temperature reconstruction has been explored intensively on the basis of calculating arbitrary directional radiative intensities. In this paper, a new method named Generalized Source Finite Volume Method (GSFVM) was proposed. It was based on radiative transfer equation and Finite Volume Method (FVM). This method can be used to calculate arbitrary directional radiative intensities and is proven to be accurate and efficient. To verify the performance of this method, six test cases of 1D, 2D, and 3D radiative transfer problems were investigated. The numerical results show that the efficiency of this method is close to the radial basis function interpolation method, but the accuracy and stability is higher than that of the interpolation method. The accuracy of the GSFVM is similar to that of the Backward Monte Carlo (BMC) algorithm, while the time required by the GSFVM is much shorter than that of the BMC algorithm. Therefore, the GSFVM can be used in temperature reconstruction and improvement on the accuracy of the FVM.

  5. [Definition of accurate planning target volume margins for esophageal cancer radiotherapy].

    PubMed

    Lesueur, P; Servagi-Vernat, S

    2016-10-01

    More than 4000 cases of esophagus neoplasms are diagnosed every year in France. Radiotherapy, which can be delivered in preoperative or exclusive with a concomitant chemotherapy, plays a central role in treatment of esophagus cancer. Even if efficacy of radiotherapy no longer has to be proved, the prognosis of esophagus cancer remains unfortunately poor with a high recurrence rate. Toxicity of esophageal radiotherapy is correlated with the irradiation volume, and limits dose escalation and local control. Esophagus is a deep thoracic organ, which undergoes cardiac and respiratory motion, making the radiotherapy delivery more difficult and increasing the planning target volume margins. Definition of accurate planning target volume margins, taking into account the esophagus' intrafraction motion and set up margins is very important to be sure to cover the clinical target volume and restrains acute and late radiotoxicity. In this article, based on a review of the literature, we propose planning target volume margins adapted to esophageal radiotherapy.

  6. 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.

  7. A GPU-enabled Finite Volume solver for global magnetospheric simulations on unstructured grids

    NASA Astrophysics Data System (ADS)

    Lani, Andrea; Yalim, Mehmet Sarp; Poedts, Stefaan

    2014-10-01

    This paper describes an ideal Magnetohydrodynamics (MHD) solver for global magnetospheric simulations based on a B1 +B0 splitting approach, which has been implemented within the COOLFluiD platform and adapted to run on modern heterogeneous architectures featuring General Purpose Graphical Processing Units (GPGPUs). The code is based on a state-of-the-art Finite Volume discretization for unstructured grids and either explicit or implicit time integration, suitable for both steady and time accurate problems. Innovative object-oriented design and coding techniques mixing C++ and CUDA are discussed. Performance results of the modified code on single and multiple processors are presented and compared with those provided by the original solver.

  8. 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.

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. Highly Accurate Beam Torsion Solutions Using the p-Version Finite Element Method

    NASA Technical Reports Server (NTRS)

    Smith, James P.

    1996-01-01

    A new treatment of the classical beam torsion boundary value problem is applied. Using the p-version finite element method with shape functions based on Legendre polynomials, torsion solutions for generic cross-sections comprised of isotropic materials are developed. Element shape functions for quadrilateral and triangular elements are discussed, and numerical examples are provided.

  14. A conservative finite volume method for incompressible Navier-Stokes equations on locally refined nested Cartesian grids

    NASA Astrophysics Data System (ADS)

    Sifounakis, Adamandios; Lee, Sangseung; You, Donghyun

    2016-12-01

    A second-order-accurate finite-volume method is developed for the solution of incompressible Navier-Stokes equations on locally refined nested Cartesian grids. Numerical accuracy and stability on locally refined nested Cartesian grids are achieved using a finite-volume discretization of the incompressible Navier-Stokes equations based on higher-order conservation principles - i.e., in addition to mass and momentum conservation, kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithms. Hanging nodes at the interface are virtually slanted to improve the pressure-velocity projection, while the other parts of the grid maintain an orthogonal Cartesian grid topology. The present method is straight-forward to implement and shows superior conservation of mass, momentum, and kinetic energy compared to the conventional methods employing interpolation at the interface between coarse and fine grids.

  15. A finite volume method for solving the Navier-Stokes equations on composite overlapping grids

    SciTech Connect

    Brown, D.L.

    1990-01-01

    The simulation of compressible fluid flows describing engineering applications using finite difference or finite volume methods is complicated by both the difficulty in representing complex geometries using rectangular grids and by the memory size and speed of modern supercomputers. The composite overlapping grid approach can be used to represent complicated geometries using a set of logically rectangular grids, thus allowing the use of finite difference or finite volume methods to approximate the partial differential equations. This approach can also be used to accomplish local mesh refinement for the purpose of resolving locally detailed behavior in the flow fields. This paper discusses the composite overlapping grid method, in particular presenting the modifications necessary to the standard finite volume approach in order to use these grids. Computed examples from compressible hypersonic flow are present as well. 15 refs., 4 figs.

  16. Accurate finite-difference time-domain simulation of anisotropic media by subpixel smoothing.

    PubMed

    Oskooi, Ardavan F; Kottke, Chris; Johnson, Steven G

    2009-09-15

    Finite-difference time-domain methods suffer from reduced accuracy when discretizing discontinuous materials. We previously showed that accuracy can be significantly improved by using subpixel smoothing of the isotropic dielectric function, but only if the smoothing scheme is properly designed. Using recent developments in perturbation theory that were applied to spectral methods, we extend this idea to anisotropic media and demonstrate that the generalized smoothing consistently reduces the errors and even attains second-order convergence with resolution.

  17. 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.

  18. A combined discontinuous Galerkin and finite volume scheme for multi-dimensional VPFP system

    SciTech Connect

    Asadzadeh, M.; Bartoszek, K.

    2011-05-20

    We construct a numerical scheme for the multi-dimensional Vlasov-Poisson-Fokker-Planck system based on a combined finite volume (FV) method for the Poisson equation in spatial domain and the streamline diffusion (SD) and discontinuous Galerkin (DG) finite element in time, phase-space variables for the Vlasov-Fokker-Planck equation.

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

    DOE PAGES

    Christ, N.  H.; Feng, X.; Martinelli, G.; ...

    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

  20. A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method.

    PubMed

    Renteria Marquez, I A; Bolborici, V

    2017-05-01

    This manuscript presents a method to model in detail the piezoelectric traveling wave rotary ultrasonic motor (PTRUSM) stator response under the action of DC and AC voltages. The stator is modeled with a discrete two dimensional system of equations using the finite volume method (FVM). In order to obtain accurate results, a model of the stator bridge is included into the stator model. The model of the stator under the action of DC voltage is presented first, and the results of the model are compared versus a similar model using the commercial finite element software COMSOL Multiphysics. One can observe that there is a difference of less than 5% between the displacements of the stator using the proposed model and the one with COMSOL Multiphysics. After that, the model of the stator under the action of AC voltages is presented. The time domain analysis shows the generation of the traveling wave in the stator surface. One can use this model to accurately calculate the stator surface velocities, elliptical motion of the stator surface and the amplitude and shape of the stator traveling wave. A system of equations discretized with the finite volume method can easily be transformed into electrical circuits, because of that, FVM may be a better choice to develop a model-based control strategy for the PTRUSM.

  1. 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.

  2. 2D and 3D Non-planar Dynamic Rupture by a Finite Volume Method

    NASA Astrophysics Data System (ADS)

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

    2006-12-01

    Understanding the physics of the rupture process requires very sophisticated and accurate tools in which both the geometry of the fault surface and realistic frictional behaviours could interact during rupture propagation. New formulations have been recently proposed for modelling the dynamic shear rupture of non-planar faults (Ando et al., 2004; Cruz-Atienza &Virieux, 2004; Huang &Costanzo, 2004) providing highly accurate field estimates nearby the crack edges at the expanse of a simple medium description or high computational cost. We propose a new method based on the finite volume formulation to model the dynamic rupture propagation of non-planar faults. After proper transformations of the velocity-stress elastodynamic system of partial differential equations following an explicit conservative law, we construct an unstructured time-domain numerical formulation of the crack problem. As a result, arbitrary non-planar faults can be explicitly represented without extra computational cost. The analysis of the total discrete energy through the fault surface leads us to the specification of dynamic rupture boundary conditions which insure the correct discrete energy time variation and, therefore, the system stability. These boundary conditions are set on stress fluxes and not on stress values, which makes the fracture to have no thickness. Different shapes of cracks are analysed. We present an example of a bidimensional non-planar spontaneous fault growth in heterogeneous media as well as preliminary results of a highly efficient extension to the three dimensional rupture model based on the standard MPI.

  3. 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.

  4. 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.

  5. An implicit control-volume finite element method for well-reservoir modelling

    NASA Astrophysics Data System (ADS)

    Pavlidis, Dimitrios; Salinas, Pablo; Xie, Zhihua; Pain, Christopher; Matar, Omar

    2016-11-01

    Here a novel implicit approach (embodied within the IC-Ferst) is presented for modelling wells with potentially a large number of laterals within reservoirs. IC-Ferst is a conservative and consistent, control-volume finite element method (CV-FEM) model and fully unstructured/geology conforming meshes with anisotropic mesh adaptivity. As far as the wells are concerned, a multi-phase/multi-well approach, where well systems are represented as phases, is taken here. Phase volume fraction conservation equations are solved for in both the reservoir and the wells, in addition, the field within wells is also solved for. A second novel aspect of the work is the combination of modelling and resolving of the motherbore and laterals. In this case wells do not have to be explicitly discretised in space. This combination proves to be accurate (in many situations) as well as computationally efficient. The method is applied to a number of multi-phase reservoir problems in order to gain an insight into the effectiveness, in terms of production rate, of perforated laterals. Model results are compared with semi-analytical solutions for simple cases and industry-standard codes for more complicated cases. EPSRC UK Programme Grant MEMPHIS (EP/K003976/1).

  6. An efficient implicit unstructured finite volume solver for generalised Newtonian fluids

    NASA Astrophysics Data System (ADS)

    Jalali, Alireza; Sharbatdar, Mahkame; Ollivier-Gooch, Carl

    2016-03-01

    An implicit finite volume solver is developed for the steady-state solution of generalised Newtonian fluids on unstructured meshes in 2D. The pseudo-compressibility technique is employed to couple the continuity and momentum equations by transforming the governing equations into a hyperbolic system. A second-order accurate spatial discretisation is provided by performing a least-squares gradient reconstruction within each control volume of unstructured meshes. A central flux function is used for the convective terms and a solution jump term is added to the averaged component for the viscous terms. Global implicit time-stepping using successive evolution-relaxation is utilised to accelerate the convergence to steady-state solutions. The performance of our flow solver is examined for power-law and Carreau-Yasuda non-Newtonian fluids in different geometries. The effects of model parameters and Reynolds number are studied on the convergence rate and flow features. Our results verify second-order accuracy of the discretisation and also fast and efficient convergence to the steady-state solution for a wide range of flow variables.

  7. 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.

  8. 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.

  9. An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

    DOE PAGES

    McCorquodale, Peter; Ullrich, Paul; Johansen, Hans; ...

    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.

  10. 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.

  11. SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters

    NASA Astrophysics Data System (ADS)

    Ghosh, Swarnava; Suryanarayana, Phanish

    2017-03-01

    As the first component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory (DFT) for isolated clusters. Specifically, utilizing a local reformulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local component of the force, we develop a framework using the finite-difference representation that enables the efficient evaluation of energies and atomic forces to within the desired accuracies in DFT. Through selected examples consisting of a variety of elements, we demonstrate that SPARC obtains exponential convergence in energy and forces with domain size; systematic convergence in the energy and forces with mesh-size to reference plane-wave result at comparably high rates; forces that are consistent with the energy, both free from any noticeable 'egg-box' effect; and accurate ground-state properties including equilibrium geometries and vibrational spectra. In addition, for systems consisting up to thousands of electrons, SPARC displays weak and strong parallel scaling behavior that is similar to well-established and optimized plane-wave implementations, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for practical DFT simulations of isolated clusters.

  12. Are portable bladder scanning and real-time ultrasound accurate measures of bladder volume in postnatal women?

    PubMed

    Mathew, S; Horne, A W; Murray, L S; Tydeman, G; McKinley, C A

    2007-08-01

    Real-time ultrasound and portable bladder scanners are commonly used instead of catheterisation to determine bladder volumes in postnatal women but it is not known whether these are accurate. Change in bladder volumes measured by ultrasound and portable scanners were compared with actual voided volume (VV) in 100 postnatal women. The VV was on average 41 ml (CI 29 - 54 ml) higher than that measured by ultrasound, and 33 ml (CI 17 - 48 ml) higher than that measured by portable scanners. Portable scanner volumes were 9 ml (CI -8 - 26 ml) higher than those measured by ultrasound. Neither method is an accurate tool for detecting bladder volume in postnatal women.

  13. Accurate mass replacement method for the sediment concentration measurement with a constant volume container

    NASA Astrophysics Data System (ADS)

    Ban, Yunyun; Chen, Tianqin; Yan, Jun; Lei, Tingwu

    2017-04-01

    The measurement of sediment concentration in water is of great importance in soil erosion research and soil and water loss monitoring systems. The traditional weighing method has long been the foundation of all the other measuring methods and instrument calibration. The development of a new method to replace the traditional oven-drying method is of interest in research and practice for the quick and efficient measurement of sediment concentration, especially field measurements. A new method is advanced in this study for accurately measuring the sediment concentration based on the accurate measurement of the mass of the sediment-water mixture in the confined constant volume container (CVC). A sediment-laden water sample is put into the CVC to determine its mass before the CVC is filled with water and weighed again for the total mass of the water and sediments in the container. The known volume of the CVC, the mass of sediment-laden water, and sediment particle density are used to calculate the mass of water, which is replaced by sediments, therefore sediment concentration of the sample is calculated. The influence of water temperature was corrected by measuring water density to determine the temperature of water before measurements were conducted. The CVC was used to eliminate the surface tension effect so as to obtain the accurate volume of water and sediment mixture. Experimental results showed that the method was capable of measuring the sediment concentration from 0.5 up to 1200 kg m‑3. A good liner relationship existed between the designed and measured sediment concentrations with all the coefficients of determination greater than 0.999 and the averaged relative error less than 0.2%. All of these seem to indicate that the new method is capable of measuring a full range of sediment concentration above 0.5 kg m‑3 to replace the traditional oven-drying method as a standard method for evaluating and calibrating other methods.

  14. Simplified versus geometrically accurate models of forefoot anatomy to predict plantar pressures: A finite element study.

    PubMed

    Telfer, Scott; Erdemir, Ahmet; Woodburn, James; Cavanagh, Peter R

    2016-01-25

    Integration of patient-specific biomechanical measurements into the design of therapeutic footwear has been shown to improve clinical outcomes in patients with diabetic foot disease. The addition of numerical simulations intended to optimise intervention design may help to build on these advances, however at present the time and labour required to generate and run personalised models of foot anatomy restrict their routine clinical utility. In this study we developed second-generation personalised simple finite element (FE) models of the forefoot with varying geometric fidelities. Plantar pressure predictions from barefoot, shod, and shod with insole simulations using simplified models were compared to those obtained from CT-based FE models incorporating more detailed representations of bone and tissue geometry. A simplified model including representations of metatarsals based on simple geometric shapes, embedded within a contoured soft tissue block with outer geometry acquired from a 3D surface scan was found to provide pressure predictions closest to the more complex model, with mean differences of 13.3kPa (SD 13.4), 12.52kPa (SD 11.9) and 9.6kPa (SD 9.3) for barefoot, shod, and insole conditions respectively. The simplified model design could be produced in <1h compared to >3h in the case of the more detailed model, and solved on average 24% faster. FE models of the forefoot based on simplified geometric representations of the metatarsal bones and soft tissue surface geometry from 3D surface scans may potentially provide a simulation approach with improved clinical utility, however further validity testing around a range of therapeutic footwear types is required.

  15. 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

  16. ElVis: A System for the Accurate and Interactive Visualization of High-Order Finite Element Solutions.

    PubMed

    Nelson, B; Liu, E; Kirby, R M; Haimes, R

    2012-12-01

    This paper presents the Element Visualizer (ElVis), a new, open-source scientific visualization system for use with high-order finite element solutions to PDEs in three dimensions. This system is designed to minimize visualization errors of these types of fields by querying the underlying finite element basis functions (e.g., high-order polynomials) directly, leading to pixel-exact representations of solutions and geometry. The system interacts with simulation data through runtime plugins, which only require users to implement a handful of operations fundamental to finite element solvers. The data in turn can be visualized through the use of cut surfaces, contours, isosurfaces, and volume rendering. These visualization algorithms are implemented using NVIDIA's OptiX GPU-based ray-tracing engine, which provides accelerated ray traversal of the high-order geometry, and CUDA, which allows for effective parallel evaluation of the visualization algorithms. The direct interface between ElVis and the underlying data differentiates it from existing visualization tools. Current tools assume the underlying data is composed of linear primitives; high-order data must be interpolated with linear functions as a result. In this work, examples drawn from aerodynamic simulations-high-order discontinuous Galerkin finite element solutions of aerodynamic flows in particular-will demonstrate the superiority of ElVis' pixel-exact approach when compared with traditional linear-interpolation methods. Such methods can introduce a number of inaccuracies in the resulting visualization, making it unclear if visual artifacts are genuine to the solution data or if these artifacts are the result of interpolation errors. Linear methods additionally cannot properly visualize curved geometries (elements or boundaries) which can greatly inhibit developers' debugging efforts. As we will show, pixel-exact visualization exhibits none of these issues, removing the visualization scheme as a source of

  17. 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.

  18. 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.

  19. 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.

  20. Accurate tracking of tumor volume change during radiotherapy by CT-CBCT registration with intensity correction

    NASA Astrophysics Data System (ADS)

    Park, Seyoun; Robinson, Adam; Quon, Harry; Kiess, Ana P.; Shen, Colette; Wong, John; Plishker, William; Shekhar, Raj; Lee, Junghoon

    2016-03-01

    In this paper, we propose a CT-CBCT registration method to accurately predict the tumor volume change based on daily cone-beam CTs (CBCTs) during radiotherapy. CBCT is commonly used to reduce patient setup error during radiotherapy, but its poor image quality impedes accurate monitoring of anatomical changes. Although physician's contours drawn on the planning CT can be automatically propagated to daily CBCTs by deformable image registration (DIR), artifacts in CBCT often cause undesirable errors. To improve the accuracy of the registration-based segmentation, we developed a DIR method that iteratively corrects CBCT intensities by local histogram matching. Three popular DIR algorithms (B-spline, demons, and optical flow) with the intensity correction were implemented on a graphics processing unit for efficient computation. We evaluated their performances on six head and neck (HN) cancer cases. For each case, four trained scientists manually contoured the nodal gross tumor volume (GTV) on the planning CT and every other fraction CBCTs to which the propagated GTV contours by DIR were compared. The performance was also compared with commercial image registration software based on conventional mutual information (MI), VelocityAI (Varian Medical Systems Inc.). The volume differences (mean±std in cc) between the average of the manual segmentations and automatic segmentations are 3.70+/-2.30 (B-spline), 1.25+/-1.78 (demons), 0.93+/-1.14 (optical flow), and 4.39+/-3.86 (VelocityAI). The proposed method significantly reduced the estimation error by 9% (B-spline), 38% (demons), and 51% (optical flow) over the results using VelocityAI. Although demonstrated only on HN nodal GTVs, the results imply that the proposed method can produce improved segmentation of other critical structures over conventional methods.

  1. Evaluation of Smagorinsky-based subgrid-scale models in a finite-volume computation

    NASA Astrophysics Data System (ADS)

    Majander, Petri; Siikonen, Timo

    2002-10-01

    Smagorinsky-based models are assessed in a turbulent channel flow simulation at Reb=2800 and Reb=12500. The Navier-Stokes equations are solved with three different grid resolutions by using a co-located finite-volume method. Computations are repeated with Smagorinsky-based subgrid-scale models. A traditional Smagorinsky model is implemented with a van Driest damping function. A dynamic model assumes a similarity of the subgrid and the subtest Reynolds stresses and an explicit filtering operation is required. A top-hat test filter is implemented with a trapezoidal and a Simpson rule. At the low Reynolds number computation none of the tested models improves the results at any grid level compared to the calculations with no model. The effect of the subgrid-scale model is reduced as the grid is refined. The numerical implementation of the test filter influences on the result. At the higher Reynolds number the subgrid-scale models stabilize the computation. An analysis of an accurately resolved flow field reveals that the discretization error overwhelms the subgrid term at Reb=2800 in the most part of the computational domain.

  2. Direct numerical simulation of scalar transport using unstructured finite-volume schemes

    NASA Astrophysics Data System (ADS)

    Rossi, Riccardo

    2009-03-01

    An unstructured finite-volume method for direct and large-eddy simulations of scalar transport in complex geometries is presented and investigated. The numerical technique is based on a three-level fully implicit time advancement scheme and central spatial interpolation operators. The scalar variable at cell faces is obtained by a symmetric central interpolation scheme, which is formally first-order accurate, or by further employing a high-order correction term which leads to formal second-order accuracy irrespective of the underlying grid. In this framework, deferred-correction and slope-limiter techniques are introduced in order to avoid numerical instabilities in the resulting algebraic transport equation. The accuracy and robustness of the code are initially evaluated by means of basic numerical experiments where the flow field is assigned a priori. A direct numerical simulation of turbulent scalar transport in a channel flow is finally performed to validate the numerical technique against a numerical dataset established by a spectral method. In spite of the linear character of the scalar transport equation, the computed statistics and spectra of the scalar field are found to be significantly affected by the spectral-properties of interpolation schemes. Although the results show an improved spectral-resolution and greater spatial-accuracy for the high-order operator in the analysis of basic scalar transport problems, the low-order central scheme is found superior for high-fidelity simulations of turbulent scalar transport.

  3. 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.

  4. 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.

  5. ADER-WENO finite volume schemes with space-time adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Dumbser, Michael; Zanotti, Olindo; Hidalgo, Arturo; Balsara, Dinshaw S.

    2013-09-01

    We present the first high order one-step ADER-WENO finite volume scheme with adaptive mesh refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resulting algorithm is particularly well suited for an AMR strategy on space-time adaptive meshes, i.e. with time-accurate local time stepping. The AMR property has been implemented 'cell-by-cell', with a standard tree-type algorithm, while the scheme has been parallelized via the message passing interface (MPI) paradigm. The new scheme has been tested over a wide range of examples for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations of compressible gas dynamics and the equations of magnetohydrodynamics (MHD). High order in space and time have been confirmed via a numerical convergence study and a detailed analysis of the computational speed-up with respect to highly refined uniform meshes is also presented. We also show test problems where the presented high order AMR scheme behaves clearly better than traditional second order AMR methods. The proposed scheme that combines for the first time high order ADER methods with space-time adaptive grids in two and three space dimensions is likely to become a useful tool in several fields of computational physics, applied mathematics and mechanics.

  6. 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.

  7. Accurately measuring volume of soil samples using low cost Kinect 3D scanner

    NASA Astrophysics Data System (ADS)

    van der Sterre, B.; Hut, R.; Van De Giesen, N.

    2012-12-01

    The 3D scanner of the Kinect game controller can be used to increase the accuracy and efficiency of determining in situ soil moisture content. Soil moisture is one of the principal hydrological variables in both the water and energy interactions between soil and atmosphere. Current in situ measurements of soil moisture either rely on indirect measurements (of electromagnetic constants or heat capacity) or on physically taking a sample and weighing it in a lab. The bottleneck in accurately retrieving soil moisture using samples is the determining of the volume of the sample. Currently this is mostly done by the very time consuming "sand cone method" in which the volume were the sample used to sit is filled with sand. We show that 3D scanner that is part of the $150 game controller extension "Kinect" can be used to make 3D scans before and after taking the sample. The accuracy of this method is tested by scanning forms of known volume. This method is less time consuming and less error-prone than using a sand cone.

  8. Accurately measuring volume of soil samples using low cost Kinect 3D scanner

    NASA Astrophysics Data System (ADS)

    van der Sterre, Boy-Santhos; Hut, Rolf; van de Giesen, Nick

    2013-04-01

    The 3D scanner of the Kinect game controller can be used to increase the accuracy and efficiency of determining in situ soil moisture content. Soil moisture is one of the principal hydrological variables in both the water and energy interactions between soil and atmosphere. Current in situ measurements of soil moisture either rely on indirect measurements (of electromagnetic constants or heat capacity) or on physically taking a sample and weighing it in a lab. The bottleneck in accurately retrieving soil moisture using samples is the determining of the volume of the sample. Currently this is mostly done by the very time consuming "sand cone method" in which the volume were the sample used to sit is filled with sand. We show that 3D scanner that is part of the 150 game controller extension "Kinect" can be used to make 3D scans before and after taking the sample. The accuracy of this method is tested by scanning forms of known volume. This method is less time consuming and less error-prone than using a sand cone.

  9. Full vectorial simulation for characterizing loss or gain in optical devices with an accurate and automated finite-element program.

    PubMed

    Tzolov, V P; Fontaine, M; Sewell, G; Delâge, A

    1997-01-20

    An efficient, accurate, and automated vectorial finite-element method is described to characterize arbitrarily shaped optical devices having loss or gain properties. The method can be easily implemented inside the pde 2 d software environment, where an interactive session allows the user to specify the problem in a easy-to-use format. For the method to be validated, modal dispersion characteristics of high loss metal-coated optical fibers that have recently been used in applications in scanning near-field optical microscopy are presented and compared with results obtained with two vectorial approaches, i.e., the field expansion and the multiple-multipole methods. These results clearly illustrate the flexibility, accuracy, and ease of implementation of the method.

  10. Finite volume numerical solution to a blood flow problem in human artery

    NASA Astrophysics Data System (ADS)

    Wijayanti Budiawan, Inge; Mungkasi, Sudi

    2017-01-01

    In this paper, we solve a one dimensional blood flow model in human artery. This model is of a non-linear hyperbolic partial differential equation system which can generate either continuous or discontinuous solution. We use the Lax–Friedrichs finite volume method to solve this model. Particularly, we investigate how a pulse propagates in human artery. For this simulation, we give a single sine wave with a small time period as an impluse input on the left boundary. The finite volume method is successful in simulating how the pulse propagates in the artery. It detects the positions of the pulse for the whole time period.

  11. A finite volume method for two-sided fractional diffusion equations on non-uniform meshes

    NASA Astrophysics Data System (ADS)

    Simmons, Alex; Yang, Qianqian; Moroney, Timothy

    2017-04-01

    We derive a finite volume method for two-sided fractional diffusion equations with Riemann-Liouville derivatives in one spatial dimension. The method applies to non-uniform meshes, with arbitrary nodal spacing. The discretisation utilises the integral definition of the fractional derivatives, and we show that it leads to a diagonally dominant matrix representation, and a provably stable numerical scheme. Being a finite volume method, the numerical scheme is fully conservative, and the ability to locally refine the mesh can produce solutions with more accuracy for the same number of nodes compared to a uniform mesh, as we demonstrate numerically.

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

    DOE PAGES

    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

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

    DOE PAGES

    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

  15. 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.

  16. 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.

  17. Electric field calculations in brain stimulation based on finite elements: an optimized processing pipeline for the generation and usage of accurate individual head models.

    PubMed

    Windhoff, Mirko; Opitz, Alexander; Thielscher, Axel

    2013-04-01

    The need for realistic electric field calculations in human noninvasive brain stimulation is undisputed to more accurately determine the affected brain areas. However, using numerical techniques such as the finite element method (FEM) is methodologically complex, starting with the creation of accurate head models to the integration of the models in the numerical calculations. These problems substantially limit a more widespread application of numerical methods in brain stimulation up to now. We introduce an optimized processing pipeline allowing for the automatic generation of individualized high-quality head models from magnetic resonance images and their usage in subsequent field calculations based on the FEM. The pipeline starts by extracting the borders between skin, skull, cerebrospinal fluid, gray and white matter. The quality of the resulting surfaces is subsequently improved, allowing for the creation of tetrahedral volume head meshes that can finally be used in the numerical calculations. The pipeline integrates and extends established (and mainly free) software for neuroimaging, computer graphics, and FEM calculations into one easy-to-use solution. We demonstrate the successful usage of the pipeline in six subjects, including field calculations for transcranial magnetic stimulation and transcranial direct current stimulation. The quality of the head volume meshes is validated both in terms of capturing the underlying anatomy and of the well-shapedness of the mesh elements. The latter is crucial to guarantee the numerical robustness of the FEM calculations. The pipeline will be released as open-source, allowing for the first time to perform realistic field calculations at an acceptable methodological complexity and moderate costs.

  18. Accurate measurement of volume and shape of resting and activated blood platelets from light scattering

    NASA Astrophysics Data System (ADS)

    Moskalensky, Alexander E.; Yurkin, Maxim A.; Konokhova, Anastasiya I.; Strokotov, Dmitry I.; Nekrasov, Vyacheslav M.; Chernyshev, Andrei V.; Tsvetovskaya, Galina A.; Chikova, Elena D.; Maltsev, Valeri P.

    2013-01-01

    We introduce a novel approach for determination of volume and shape of individual blood platelets modeled as an oblate spheroid from angle-resolved light scattering with flow-cytometric technique. The light-scattering profiles (LSPs) of individual platelets were measured with the scanning flow cytometer and the platelet characteristics were determined from the solution of the inverse light-scattering problem using the precomputed database of theoretical LSPs. We revealed a phenomenon of parameter compensation, which is partly explained in the framework of anomalous diffraction approximation. To overcome this problem, additional a priori information on the platelet refractive index was used. It allowed us to determine the size of each platelet with subdiffraction precision and independent of the particular value of the platelet aspect ratio. The shape (spheroidal aspect ratio) distributions of platelets showed substantial differences between native and activated by 10 μM adenosine diphosphate samples. We expect that the new approach may find use in hematological analyzers for accurate measurement of platelet volume distribution and for determination of the platelet activation efficiency.

  19. 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.

  20. 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.

  1. 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.

  2. A positivity-preserving high order finite volume compact-WENO scheme for compressible Euler equations

    NASA Astrophysics Data System (ADS)

    Guo, Yan; Xiong, Tao; Shi, Yufeng

    2014-10-01

    In this paper, a positivity-preserving fifth-order finite volume compact-WENO scheme is proposed for solving compressible Euler equations. As it is known, conservative compact finite volume schemes have high resolution properties while WENO (Weighted Essentially Non-Oscillatory) schemes are essentially non-oscillatory near flow discontinuities. We extend the idea of WENO schemes to some classical finite volume compact schemes [30], where lower order compact stencils are combined with WENO nonlinear weights to get a higher order finite volume compact-WENO scheme. The newly developed positivity-preserving limiter [43,42] is used to preserve positive density and internal energy for compressible Euler equations of fluid dynamics. The HLLC (Harten, Lax, and van Leer with Contact) approximate Riemann solver [37,4] is used to get the numerical flux at the cell interfaces. Numerical tests are presented to demonstrate the high-order accuracy, positivity-preserving, high-resolution and robustness of the proposed scheme.

  3. 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.

  4. 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...

  5. Comparison between staggered grid finite-volume and edge-based finite-element modelling of geophysical electromagnetic data on unstructured grids

    NASA Astrophysics Data System (ADS)

    Jahandari, Hormoz; Ansari, SeyedMasoud; Farquharson, Colin G.

    2017-03-01

    This study compares two finite-element (FE) and three finite-volume (FV) schemes which use unstructured tetrahedral grids for the modelling of electromagnetic (EM) data. All these schemes belong to a group of differential methods where the electric field is defined along the edges of the elements. The FE and FV schemes are based on both the EM-field and the potential formulations of Maxwell's equations. The EM-field FE scheme uses edge-based (vector) basis functions while the potential FE scheme uses vector and scalar basis functions. All the FV schemes use staggered tetrahedral-Voronoï grids. Three examples are used for comparisons in terms of accuracy and in terms of the computation resources required by generic iterative and direct solvers for solving the problems. Two of these examples represent survey scenarios with electric and magnetic sources and the results are compared with those from the literature while the third example is a comparison against analytical solutions for an electric dipole source. Exactly the same mesh is used for all examples to allow for direct comparison of the various schemes. The results show that while the FE and FV schemes are comparable in terms of accuracy and computation resources, the FE schemes are slightly more accurate but also more expensive than the FV schemes.

  6. Accurate Analysis of the Change in Volume, Location, and Shape of Metastatic Cervical Lymph Nodes During Radiotherapy

    SciTech Connect

    Takao, Seishin; Tadano, Shigeru; Taguchi, Hiroshi; Yasuda, Koichi; Onimaru, Rikiya; Ishikawa, Masayori; Bengua, Gerard; Suzuki, Ryusuke; Shirato, Hiroki

    2011-11-01

    Purpose: To establish a method for the accurate acquisition and analysis of the variations in tumor volume, location, and three-dimensional (3D) shape of tumors during radiotherapy in the era of image-guided radiotherapy. Methods and Materials: Finite element models of lymph nodes were developed based on computed tomography (CT) images taken before the start of treatment and every week during the treatment period. A surface geometry map with a volumetric scale was adopted and used for the analysis. Six metastatic cervical lymph nodes, 3.5 to 55.1 cm{sup 3} before treatment, in 6 patients with head and neck carcinomas were analyzed in this study. Three fiducial markers implanted in mouthpieces were used for the fusion of CT images. Changes in the location of the lymph nodes were measured on the basis of these fiducial markers. Results: The surface geometry maps showed convex regions in red and concave regions in blue to ensure that the characteristics of the 3D tumor geometries are simply understood visually. After the irradiation of 66 to 70 Gy in 2 Gy daily doses, the patterns of the colors had not changed significantly, and the maps before and during treatment were strongly correlated (average correlation coefficient was 0.808), suggesting that the tumors shrank uniformly, maintaining the original characteristics of the shapes in all 6 patients. The movement of the gravitational center of the lymph nodes during the treatment period was everywhere less than {+-}5 mm except in 1 patient, in whom the change reached nearly 10 mm. Conclusions: The surface geometry map was useful for an accurate evaluation of the changes in volume and 3D shapes of metastatic lymph nodes. The fusion of the initial and follow-up CT images based on fiducial markers enabled an analysis of changes in the location of the targets. Metastatic cervical lymph nodes in patients were suggested to decrease in size without significant changes in the 3D shape during radiotherapy. The movements of the

  7. 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.

  8. 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

  9. An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

    NASA Astrophysics Data System (ADS)

    Kühnlein, Christian; Smolarkiewicz, Piotr K.

    2017-04-01

    An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity-the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.

  10. An adaptive control volume finite element method for simulation of multi-scale flow in heterogeneous porous media

    NASA Astrophysics Data System (ADS)

    Mostaghimi, P.; Percival, J. R.; Pavlidis, D.; Gorman, G.; Jackson, M.; Neethling, S.; Pain, C. C.

    2013-12-01

    Numerical simulation of multiphase flow in porous media is of importance in a wide range of applications in science and engineering. We present a novel control volume finite element method (CVFEM) to solve for multi-scale flow in heterogeneous geological formations. It employs a node centred control volume approach to discretize the saturation equation, while a control volume finite element method is applied for the pressure equation. We embed the discrete continuity equation into the pressure equation and assure that the continuity is exactly enforced. Anisotropic mesh adaptivity is used to accurately model the fine grained features of multiphase flow. The adaptive algorithm uses a metric tensor field based on solution error estimates to locally control the size and shape of elements in the metric. Moreover, it uses metric advection between adaptive meshes in order to predict the future required density of mesh thereby reducing numerical dispersion at the saturation front. The scheme is capable of capturing multi-scale heterogeneity such as those in fractured porous media through the use of several constraints on the element size in different regions of porous media. We show the application of our method for simulation of flow in some challenging benchmark problems. For flow in fractured reservoirs, the scheme adapts the mesh as the flow penetrates through the fracture and the matrix. The constraints for the element size within the fracture are smaller by several orders of magnitude than the generated mesh within the matrix. We show that the scheme captures the key multi-scale features of flow while preserving the geometry. We demonstrate that mesh adaptation can be used to accurately simulate flow in heterogeneous porous media at low computational cost.

  11. 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...

  12. A projection hybrid finite volume/element method for low-Mach number flows

    NASA Astrophysics Data System (ADS)

    Bermúdez, A.; Ferrín, J. L.; Saavedra, L.; Vázquez-Cendón, M. E.

    2014-08-01

    The purpose of this article is to introduce a projection hybrid finite volume/element method for low-Mach number flows of viscous or inviscid fluids. Starting with a 3D tetrahedral finite element mesh of the computational domain, the equation of the transport-diffusion stage is discretized by a finite volume method associated with a dual mesh where the nodes of the volumes are the barycenters of the faces of the initial tetrahedra. The transport-diffusion stage is explicit. Upwinding of convective terms is done by classical Riemann solvers as the Q-scheme of van Leer or the Rusanov scheme. Concerning the projection stage, the pressure correction is computed by a piecewise linear finite element method associated with the initial tetrahedral mesh. Passing the information from one stage to the other is carefully made in order to get a stable global scheme. Numerical results for several test examples aiming at evaluating the convergence properties of the method are shown.

  13. 1D finite volume model of unsteady flow over mobile bed

    NASA Astrophysics Data System (ADS)

    Zhang, Shiyan; Duan, Jennifer G.

    2011-07-01

    SummaryA one dimensional (1D) finite volume method (FVM) model was developed for simulating unsteady flow, such as dam break flow, and flood routing over mobile alluvium. The governing equation is the modified 1D shallow water equation and the Exner equation that take both bed load and suspended load transport into account. The non-equilibrium sediment transport algorithm was adopted in the model, and the van Rijn method was employed to calculate the bed-load transport rate and the concentration of suspended sediment at the reference level. Flux terms in the governing equations were discretised using the upwind flux scheme, Harten et al. (1983) (HLL) and HLLC schemes, Roe's scheme and the Weighted Average Flux (WAF) schemes with the Double Minmod and Minmod flux limiters. The model was tested under a fixed bed condition to evaluate the performance of several different numerical schemes and then applied to an experimental case of dam break flow over a mobile bed and a flood event in the Rillito River, Tucson, Arizona. For dam break flow over movable bed, all tested schemes were proved to be capable of reasonably simulating water surface profiles, but failed to accurately capture the hydraulic jump. The WAF schemes produced slight spurious oscillations at the water surface and bed profiles and over-estimated the scour depth. When applying the model to the Rillito River, the simulated results generally agreed well with the field measurements of flow discharges and bed elevation changes. Modeling results of bed elevation changes were sensitive to the suspended load recovery coefficient and the bed load adaptation length, which require further theoretical and experimental investigations.

  14. 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.

  15. Accurate Automatic Delineation of Heterogeneous Functional Volumes in Positron Emission Tomography for Oncology Applications

    SciTech Connect

    Hatt, Mathieu; Cheze le Rest, Catherine; Descourt, Patrice; Dekker, Andre; De Ruysscher, Dirk; Oellers, Michel; Lambin, Philippe; Pradier, Olivier; Visvikis, Dimitris

    2010-05-01

    Purpose: Accurate contouring of positron emission tomography (PET) functional volumes is now considered crucial in image-guided radiotherapy and other oncology applications because the use of functional imaging allows for biological target definition. In addition, the definition of variable uptake regions within the tumor itself may facilitate dose painting for dosimetry optimization. Methods and Materials: Current state-of-the-art algorithms for functional volume segmentation use adaptive thresholding. We developed an approach called fuzzy locally adaptive Bayesian (FLAB), validated on homogeneous objects, and then improved it by allowing the use of up to three tumor classes for the delineation of inhomogeneous tumors (3-FLAB). Simulated and real tumors with histology data containing homogeneous and heterogeneous activity distributions were used to assess the algorithm's accuracy. Results: The new 3-FLAB algorithm is able to extract the overall tumor from the background tissues and delineate variable uptake regions within the tumors, with higher accuracy and robustness compared with adaptive threshold (T{sub bckg}) and fuzzy C-means (FCM). 3-FLAB performed with a mean classification error of less than 9% +- 8% on the simulated tumors, whereas binary-only implementation led to errors of 15% +- 11%. T{sub bckg} and FCM led to mean errors of 20% +- 12% and 17% +- 14%, respectively. 3-FLAB also led to more robust estimation of the maximum diameters of tumors with histology measurements, with <6% standard deviation, whereas binary FLAB, T{sub bckg} and FCM lead to 10%, 12%, and 13%, respectively. Conclusion: These encouraging results warrant further investigation in future studies that will investigate the impact of 3-FLAB in radiotherapy treatment planning, diagnosis, and therapy response evaluation.

  16. Actuator line simulations of a Joukowsky and Tjæreborg rotor using spectral element and finite volume methods

    NASA Astrophysics Data System (ADS)

    Kleusberg, E.; Sarmast, S.; Schlatter, P.; Ivanell, S.; Henningson, D. S.

    2016-09-01

    The wake structure behind a wind turbine, generated by the spectral element code Nek5000, is compared with that from the finite volume code EllipSys3D. The wind turbine blades are modeled using the actuator line method. We conduct the comparison on two different setups. One is based on an idealized rotor approximation with constant circulation imposed along the blades corresponding to Glauert's optimal operating condition, and the other is the Tjffireborg wind turbine. The focus lies on analyzing the differences in the wake structures entailed by the different codes and corresponding setups. The comparisons show good agreement for the defining parameters of the wake such as the wake expansion, helix pitch and circulation of the helical vortices. Differences can be related to the lower numerical dissipation in Nek5000 and to the domain differences at the rotor center. At comparable resolution Nek5000 yields more accurate results. It is observed that in the spectral element method the helical vortices, both at the tip and root of the actuator lines, retain their initial swirl velocity distribution for a longer distance in the near wake. This results in a lower vortex core growth and larger maximum vorticity along the wake. Additionally, it is observed that the break down process of the spiral tip vortices is significantly different between the two methods, with vortex merging occurring immediately after the onset of instability in the finite volume code, while Nek5000 simulations exhibit a 2-3 radii period of vortex pairing before merging.

  17. Full Discretisations for Nonlinear Evolutionary Inequalities Based on Stiffly Accurate Runge-Kutta and hp-Finite Element Methods.

    PubMed

    Gwinner, J; Thalhammer, M

    The convergence of full discretisations by implicit Runge-Kutta and nonconforming Galerkin methods applied to nonlinear evolutionary inequalities is studied. The scope of applications includes differential inclusions governed by a nonlinear operator that is monotone and fulfills a certain growth condition. A basic assumption on the considered class of stiffly accurate Runge-Kutta time discretisations is a stability criterion which is in particular satisfied by the Radau IIA and Lobatto IIIC methods. In order to allow nonconforming hp-finite element approximations of unilateral constraints, set convergence of convex subsets in the sense of Glowinski-Mosco-Stummel is utilised. An appropriate formulation of the fully discrete variational inequality is deduced on the basis of a characteristic example of use, a Signorini-type initial-boundary value problem. Under hypotheses close to the existence theory of nonlinear first-order evolutionary equations and inequalities involving a monotone main part, a convergence result for the piecewise constant in time interpolant is established.

  18. Development and experimental verification of a finite element method for accurate analysis of a surface acoustic wave device

    NASA Astrophysics Data System (ADS)

    Mohibul Kabir, K. M.; Matthews, Glenn I.; Sabri, Ylias M.; Russo, Salvy P.; Ippolito, Samuel J.; Bhargava, Suresh K.

    2016-03-01

    Accurate analysis of surface acoustic wave (SAW) devices is highly important due to their use in ever-growing applications in electronics, telecommunication and chemical sensing. In this study, a novel approach for analyzing the SAW devices was developed based on a series of two-dimensional finite element method (FEM) simulations, which has been experimentally verified. It was found that the frequency response of the two SAW device structures, each having slightly different bandwidth and center lobe characteristics, can be successfully obtained utilizing the current density of the electrodes via FEM simulations. The two SAW structures were based on XY Lithium Niobate (LiNbO3) substrates and had two and four electrode finger pairs in both of their interdigital transducers, respectively. Later, SAW devices were fabricated in accordance with the simulated models and their measured frequency responses were found to correlate well with the obtained simulations results. The results indicated that better match between calculated and measured frequency response can be obtained when one of the input electrode finger pairs was set at zero volts and all the current density components were taken into account when calculating the frequency response of the simulated SAW device structures.

  19. Extrusion Process by Finite Volume Method Using OpenFoam Software

    SciTech Connect

    Matos Martins, Marcelo; Tonini Button, Sergio; Divo Bressan, Jose; Ivankovic, Alojz

    2011-01-17

    The computational codes are very important tools to solve engineering problems. In the analysis of metal forming process, such as extrusion, this is not different because the computational codes allow analyzing the process with reduced cost. Traditionally, the Finite Element Method is used to solve solid mechanic problems, however, the Finite Volume Method (FVM) have been gaining force in this field of applications. This paper presents the velocity field and friction coefficient variation results, obtained by numerical simulation using the OpenFoam Software and the FVM to solve an aluminum direct cold extrusion process.

  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. Accurate B-spline-based 3-D interpolation scheme for digital volume correlation.

    PubMed

    Ren, Maodong; Liang, Jin; Wei, Bin

    2016-12-01

    An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.

  2. 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.

  3. Numerical simulation of dam-break problem using staggered finite volume method

    NASA Astrophysics Data System (ADS)

    Budiasih, L. K.; Wiryanto, L. H.

    2016-02-01

    A problem in a dam-break is when a wall separating two sides of water is removed. A shock wave occurs and propagates. The behavior of the wave is interesting to be investigated with respect to the water depth and its wave speed. The aim of this research is to model dam-break problem using the non-linear shallow water equations and solve them numerically using staggered finite volume method. The solution is used to simulate the dam-break on a wet bed. Our numerical solution will be compared to the analytical solution of shallow water equations for dam-break problem. The momentum non-conservative finite volume scheme on a staggered grid will give a good agreement for dam-break problem on a wet bed, for depth ratios greater than 0.25.

  4. One spatial dimensional finite volume three-body interaction for a short-range potential

    NASA Astrophysics Data System (ADS)

    Guo, Peng

    2017-03-01

    In this work, we use McGuire's model to describe scattering of three spinless identical particles in one spatial dimension; we first present analytic solutions of Faddeev's equation for scattering of three spinless particles in free space. The three particles interaction in finite volume is derived subsequently, and the quantization conditions by matching wave functions in free space and finite volume are presented in terms of two-body scattering phase shifts. The quantization conditions obtained in this work for the short-range interaction are Lüscher's formula-like and consistent with Yang's results [Phys. Rev. Lett. 19, 1312 (1967), 10.1103/PhysRevLett.19.1312].

  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. Content-Adaptive Finite Element Mesh Generation of 3-D Complex MR Volumes for Bioelectromagnetic Problems.

    PubMed

    Lee, W; Kim, T-S; Cho, M; Lee, S

    2005-01-01

    In studying bioelectromagnetic problems, finite element method offers several advantages over other conventional methods such as boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropy. Mesh generation is the first requirement in the finite element analysis and there are many different approaches in mesh generation. However conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes, resulting in numerous elements in the smaller volume regions, thereby increasing computational load and demand. In this work, we present an improved content-adaptive mesh generation scheme that is efficient and fast along with options to change the contents of meshes. For demonstration, mesh models of the head from a volume MRI are presented in 2-D and 3-D.

  7. A numerical study of 2D detonation waves with adaptive finite volume methods on unstructured grids

    NASA Astrophysics Data System (ADS)

    Hu, Guanghui

    2017-02-01

    In this paper, a framework of adaptive finite volume solutions for the reactive Euler equations on unstructured grids is proposed. The main ingredients of the algorithm include a second order total variation diminishing Runge-Kutta method for temporal discretization, and the finite volume method with piecewise linear solution reconstruction of the conservative variables for the spatial discretization in which the least square method is employed for the reconstruction, and weighted essentially nonoscillatory strategy is used to restrain the potential numerical oscillation. To resolve the high demanding on the computational resources due to the stiffness of the system caused by the reaction term and the shock structure in the solutions, the h-adaptive method is introduced. OpenMP parallelization of the algorithm is also adopted to further improve the efficiency of the implementation. Several one and two dimensional benchmark tests on the ZND model are studied in detail, and numerical results successfully show the effectiveness of the proposed method.

  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. 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.

  10. A nonoscillatory, characteristically convected, finite volume scheme for multidimensional convection problems

    NASA Technical Reports Server (NTRS)

    Yokota, Jeffrey W.; Huynh, Hung T.

    1989-01-01

    A new, nonoscillatory upwind scheme is developed for the multidimensional convection equation. The scheme consists of an upwind, nonoscillatory interpolation of data to the surfaces of an intermediate finite volume; a characteristic convection of surface data to a midpoint time level; and a conservative time integration based on the midpoint rule. This procedure results in a convection scheme capable of resolving discontinuities neither aligned with, nor convected along, grid lines.

  11. 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.

  12. 1-D Heat Transfer in Multilayer Materials Using a Finite Volume Approach

    DTIC Science & Technology

    2014-01-01

    AEROSPACE REPORT NO. TR-2014-01128 1-D Heat Transfer in Multilayer Materials Using a Finite Volume Approach January 1, 2014 Marcus A...unlimited. The cost to prepare this document: $395 This report was submitted by The Aerospace Corporation, El Segundo...project officer for the Development Planning (XR) program. This report has been reviewed by the Public Affairs Office (PAS) and is releasable to the

  13. 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.

  14. A finite rate of innovation algorithm for fast and accurate spike detection from two-photon calcium imaging

    NASA Astrophysics Data System (ADS)

    Oñativia, Jon; Schultz, Simon R.; Dragotti, Pier Luigi

    2013-08-01

    Objective. Inferring the times of sequences of action potentials (APs) (spike trains) from neurophysiological data is a key problem in computational neuroscience. The detection of APs from two-photon imaging of calcium signals offers certain advantages over traditional electrophysiological approaches, as up to thousands of spatially and immunohistochemically defined neurons can be recorded simultaneously. However, due to noise, dye buffering and the limited sampling rates in common microscopy configurations, accurate detection of APs from calcium time series has proved to be a difficult problem. Approach. Here we introduce a novel approach to the problem making use of finite rate of innovation (FRI) theory (Vetterli et al 2002 IEEE Trans. Signal Process. 50 1417-28). For calcium transients well fit by a single exponential, the problem is reduced to reconstructing a stream of decaying exponentials. Signals made of a combination of exponentially decaying functions with different onset times are a subclass of FRI signals, for which much theory has recently been developed by the signal processing community. Main results. We demonstrate for the first time the use of FRI theory to retrieve the timing of APs from calcium transient time series. The final algorithm is fast, non-iterative and parallelizable. Spike inference can be performed in real-time for a population of neurons and does not require any training phase or learning to initialize parameters. Significance. The algorithm has been tested with both real data (obtained by simultaneous electrophysiology and multiphoton imaging of calcium signals in cerebellar Purkinje cell dendrites), and surrogate data, and outperforms several recently proposed methods for spike train inference from calcium imaging data.

  15. Finite-volume QED corrections to decay amplitudes in lattice QCD

    NASA Astrophysics Data System (ADS)

    Lubicz, V.; Martinelli, G.; Sachrajda, C. T.; Sanfilippo, F.; Simula, S.; Tantalo, N.

    2017-02-01

    We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at O (α ) are universal; i.e. they are independent of the structure of the meson. This is analogous to a similar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading nonuniversal, structure-dependent terms are of O (1 /L2) [compared to the O (1 /L3) leading nonuniversal corrections in the spectrum]. We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final-state lepton). The result can be included in the strategy proposed in Ref. [N. Carrasco et al.,Phys. Rev. D 91, 074506 (2015)., 10.1103/PhysRevD.91.074506] for using lattice simulations to compute the decay widths at O (α ), with the remaining finite-volume effects starting at order O (1 /L2). The methods developed in this paper can be generalized to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavor physics.

  16. Composite grid and finite-volume LU implicit scheme for turbine flow analysis

    NASA Technical Reports Server (NTRS)

    Choo, Yung K.; Yoon, Seokkwan; Civinskas, Kestutis C.

    1987-01-01

    A composite grid was generated in an attempt to improve grid quality for a typical turbine blade with large camber in terms of mesh control, smoothness, and orthogonality. This composite grid consists of the C grid (or O grid) in the immediate vicinity of the blade and the H grid in the upstream region and in the middle of the blade passage between the C grids. It provides a good boundary layer resolution around the leading edge region for viscous calculation, has orthogonality at the blade surface and slope continuity at the C-H (or O-H) interface, and has flexibility in controlling the mesh distribution in the upstream region without using excessive grid points. This composite grid eliminates the undesirable qualities of a single grid when generated for a typical turbine geometry. A finite-volume lower-upper (LU) implicit scheme can be used in solving for the turbine flows on the composite grid. This grid has a special grid node that is connected to more than four neighboring nodes in two dimensions and to more than six nodes in three dimensions. But the finite-volume approach poses no problem at the special point because each interior cell has only four neighboring cells in two dimensions and only six cells in three dimensions. The finite-volume LU implicit scheme was demonstrated to be robust and efficient for both external and internal flows in a broad flow regime.

  17. Specific volume coupling and convergence properties in hybrid particle/finite volume algorithms for turbulent reactive flows

    NASA Astrophysics Data System (ADS)

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

    2015-08-01

    We investigate the coupling between the two components of a Large Eddy Simulation/Probability Density Function (LES/PDF) algorithm for the simulation of turbulent reacting flows. In such an algorithm, the Large Eddy Simulation (LES) component provides a solution to the hydrodynamic equations, whereas the Lagrangian Monte Carlo Probability Density Function (PDF) component solves for the PDF of chemical compositions. Special attention is paid to the transfer of specific volume information from the PDF to the LES code: the specific volume field contains probabilistic noise due to the nature of the Monte Carlo PDF solution, and thus the use of the specific volume field in the LES pressure solver needs careful treatment. Using a test flow based on the Sandia/Sydney Bluff Body Flame, we determine the optimal strategy for specific volume feedback. Then, the overall second-order convergence of the entire LES/PDF procedure is verified using a simple vortex ring test case, with special attention being given to bias errors due to the number of particles per LES Finite Volume (FV) cell.

  18. Parallel Adaptive Mesh Refinement for High-Order Finite-Volume Schemes in Computational Fluid Dynamics

    NASA Astrophysics Data System (ADS)

    Schwing, Alan Michael

    For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable

  19. 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

  20. 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.

  1. A technique for fast and accurate measurement of hand volumes using Archimedes' principle.

    PubMed

    Hughes, S; Lau, J

    2008-03-01

    A new technique for measuring hand volumes using Archimedes principle is described. The technique involves the immersion of a hand in a water container placed on an electronic balance. The volume is given by the change in weight divided by the density of water. This technique was compared with the more conventional technique of immersing an object in a container with an overflow spout and collecting and weighing the volume of overflow water. The hand volume of two subjects was measured. Hand volumes were 494 +/- 6 ml and 312 +/- 7 ml for the immersion method and 476 +/- 14 ml and 302 +/- 8 ml for the overflow method for the two subjects respectively. Using plastic test objects, the mean difference between the actual and measured volume was -0.3% and 2.0% for the immersion and overflow techniques respectively. This study shows that hand volumes can be obtained more quickly than the overflow method. The technique could find an application in clinics where frequent hand volumes are required.

  2. Archimedes Revisited: A Faster, Better, Cheaper Method of Accurately Measuring the Volume of Small Objects

    ERIC Educational Resources Information Center

    Hughes, Stephen W.

    2005-01-01

    A little-known method of measuring the volume of small objects based on Archimedes' principle is described, which involves suspending an object in a water-filled container placed on electronic scales. The suspension technique is a variation on the hydrostatic weighing technique used for measuring volume. The suspension method was compared with two…

  3. 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.

  4. 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.

  5. A multi-moment constrained finite volume method on arbitrary unstructured grids for incompressible flows

    NASA Astrophysics Data System (ADS)

    Xie, Bin; Xiao, Feng

    2016-12-01

    We proposed a multi-moment constrained finite volume method which can simulate incompressible flows of high Reynolds number in complex geometries. Following the underlying idea of the volume-average/point-value multi-moment (VPM) method (Xie et al. (2014) [71]), this formulation is developed on arbitrary unstructured hybrid grids by employing the point values (PV) at both cell vertex and barycenter as the prognostic variables. The cell center value is updated via an evolution equation derived from a constraint condition of finite volume form, which ensures the rigorous numerical conservativeness. Novel numerical formulations based on the local PVs over compact stencil are proposed to enhance the accuracy, robustness and efficiency of computations on unstructured meshes of hybrid and arbitrary elements. Numerical experiments demonstrate that the present numerical model has nearly 3-order convergence rate with numerical errors much smaller than the VPM method. The numerical dissipation has been significantly suppressed, which facilitates numerical simulations of high Reynolds number flows in complex geometries.

  6. 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.

  7. Development of the meshless finite volume particle method with exact and efficient calculation of interparticle area

    NASA Astrophysics Data System (ADS)

    Quinlan, Nathan J.; Lobovský, Libor; Nestor, Ruairi M.

    2014-06-01

    The Finite Volume Particle Method (FVPM) is a meshless method based on a definition of interparticle area which is closely analogous to cell face area in the classical finite volume method. In previous work, the interparticle area has been computed by numerical integration, which is a source of error and is extremely expensive. We show that if the particle weight or kernel function is defined as a discontinuous top-hat function, the particle interaction vectors may be evaluated exactly and efficiently. The new formulation reduces overall computational time by a factor between 6.4 and 8.2. In numerical experiments on a viscous flow with an analytical solution, the method converges under all conditions. Significantly, in contrast with standard FVPM and SPH, error depends on particle size but not on particle overlap (as long as the computational domain is completely covered by particles). The new method is shown to be superior to standard FVPM for shock tube flow and inviscid steady transonic flow. In benchmarking on a viscous multiphase flow application, FVPM with exact interparticle area is shown to be competitive with a mesh-based volume-of-fluid solver in terms of computational time required to resolve the structure of an interface.

  8. A unified and preserved Dirichlet boundary treatment for the cell-centered finite volume discrete Boltzmann method

    NASA Astrophysics Data System (ADS)

    Chen, Leitao; Schaefer, Laura A.

    2015-02-01

    A new boundary treatment is proposed for the finite volume discrete Boltzmann method (FVDBM) that can be used for accurate simulations of curved boundaries and complicated flow conditions. First, a brief review of different boundary treatments for the general Boltzmann simulations is made in order to primarily explain what type of boundary treatment will be developed in this paper for the cell-centered FVDBM. After that, the new boundary treatment along with the cell-centered FVDBM model is developed in detail. Next, the proposed boundary treatment is applied to a series of numerical tests with a detailed discussion of its qualitative and quantitative properties. From the results, it can be concluded that the new boundary treatment is at least first-order accurate for a variety of Dirichlet boundary conditions (BCs). It can handle both the velocity and density Dirichlet BCs in a unified way and further realize some BCs that the conventional lattice Boltzmann model fails to simulate. In addition, such a boundary treatment can incorporate different lattice models without changing its framework, and it can preserve the Dirichlet BCs up to machine accuracy in different situations.

  9. 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.

  10. 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

  11. Finite-volume effects and the electromagnetic contributions to kaon and pion masses

    SciTech Connect

    Basak, Subhasish; Bazavov, Alexei; Bernard, Claude; Detar, Carleton; Freeland, Elizabeth; Foley, Justin; Gottlieb, Steven; Heller, Urs M.; Komijani, Javad; Laiho, Jack; Levkova, Ludmila; Osborn, James; Sugar, Robert; Torok, Aaron; Toussaint, Doug; Van de Water, Ruth S.; Zhou, Ran

    2014-09-25

    We report on the MILC Collaboration calculation of electromagnetic effects on light pseudoscalar mesons. The simulations employ asqtad staggered dynamical quarks in QCD plus quenched photons, with lattice spacings varying from 0.12 to 0.06 fm. Finite volume corrections for the MILC realization of lattice electrodynamics have been calculated in chiral perturbation theory and applied to the lattice data. These corrections differ from those calculated by Hayakawa and Uno because our treatment of zero modes differs from theirs. Updated results for the corrections to "Dashen's theorem" are presented.

  12. Effect of variables in inert gas condensation processing on nanoparticle trajectory simulated by finite volume method.

    PubMed

    Lee, Kwang-Min; Juhng, Woo-Nam; Choi, Bo-Young

    2006-11-01

    The finite volume method was applied to the determination of the three-dimensional convection current during inert gas condensation (IGC) processing by using the commercially available software, "Fluent". The lower velocity of the convection current at higher evaporation temperature resulted from the lower value of the coefficient of thermal expansion. The velocity of the convection current increased with increasing chamber pressure, because the driving force of the buoyancy was directly proportional to the gas density. 13% and 17.3% of the particles were trapped during the first period of circulation in the case of the single and double heaters, respectively.

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

    NASA Astrophysics Data System (ADS)

    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.

  14. Determining finite volume elements for the 2D Navier-Stokes equations

    SciTech Connect

    Jones, D.A. . Dept. of Mathematics); Titi, E.S. . Dept. of Mathematics Cornell Univ., Ithaca, NY . Mathematical Sciences Inst.)

    1991-01-01

    We consider the 2D Navier-Stokes equations on a square with periodic boundary conditions. Dividing the square into N equal subsquares, we show that if the asymptotic behavior of the average of solutions on these subsquares (finite volume elements) is known, then the large time behavior of the solution itself is completely determined, provided N is large enough. We also establish a rigorous upper bound for N needed to determine the solutions to the Navier-Stokes equation in terms of the physical parameters of the problem. 34 refs.

  15. 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.

  16. Influence of finite volume and magnetic field effects on the QCD phase diagram

    NASA Astrophysics Data System (ADS)

    Magdy, Niseem; Csanád, M.; Lacey, Roy A.

    2017-02-01

    The 2 + 1 SU(3) Polyakov linear sigma model is used to investigate the respective influence of a finite volume and a magnetic field on the quark-hadron phase boundary in the plane of baryon chemical potential ({μ }B) versus temperature (T) of the quantum chromodynamics (QCD) phase diagram. The calculated results indicate sizable shifts of the quark-hadron phase boundary to lower values of ({μ }B {and} T) for increasing magnetic field strength, and an opposite shift to higher values of ({μ }B {and} T) for decreasing system volume. Such shifts could have important implications for the extraction of the thermodynamic properties of the QCD phase diagram from heavy ion data.

  17. Small and cheap: accurate differential blood count with minimal sample volume by laser scanning cytometry (LSC)

    NASA Astrophysics Data System (ADS)

    Mittag, Anja; Lenz, Dominik; Smith, Paul J.; Pach, Susanne; Tarnok, Attila

    2005-04-01

    Aim: In patients, e.g. with congenital heart diseases, a differential blood count is needed for diagnosis. To this end by standard automatic analyzers 500 μl of blood is required from the patients. In case of newborns and infants this is a substantial volume, especially after operations associated with blood loss. Therefore, aim of this study was to develop a method to determine a differential blood picture with a substantially reduced specimen volume. Methods: To generate a differential blood picture 10 μl EDTA blood were mixed with 10 μl of a DRAQ5 solution (500μM, Biostatus) and 10 μl of an antibody mixture (CD45-FITC, CD14-PE, diluted with PBS). 20 μl of this cell suspension was filled into a Neubauer counting chamber. Due to the defined volume of the chamber it is possible to determine the cell count per volume. The trigger for leukocyte counting was set on DRAQ5 signal in order to be able to distinguish nucleated white blood cells from erythrocytes. Different leukocyte subsets could be distinguished due to the used fluorescence labeled antibodies. For erythrocyte counting cell suspension was diluted another 150 times. 20 μl of this dilution was analyzed in a microchamber by LSC with trigger set on forward scatter signal. Results: This method allows a substantial decrease of blood sample volume for generation of a differential blood picture (10 μl instead of 500μl). There was a high correlation between our method and the results of routine laboratory (r2=0.96, p<0.0001 n=40). For all parameters intra-assay variance was less than 7 %. Conclusions: In patients with low blood volume such as neonates and in critically ill infants every effort has to be taken to reduce the blood volume needed for diagnostics. With this method only 2% of standard sample volume is needed to generate a differential blood picture. Costs are below that of routine laboratory. We suggest this method to be established in paediatric cardiology for routine diagnostics and for

  18. The Finite-volumE Sea ice-Ocean Model (FESOM2)

    NASA Astrophysics Data System (ADS)

    Danilov, Sergey; Sidorenko, Dmitry; Wang, Qiang; Jung, Thomas

    2017-02-01

    Version 2 of the unstructured-mesh Finite-Element Sea ice-Ocean circulation Model (FESOM) is presented. It builds upon FESOM1.4 (Wang et al., 2014) but differs by its dynamical core (finite volumes instead of finite elements), and is formulated using the arbitrary Lagrangian Eulerian (ALE) vertical coordinate, which increases model flexibility. The model inherits the framework and sea ice model from the previous version, which minimizes the efforts needed from a user to switch from one version to the other. The ocean states simulated with FESOM1.4 and FESOM2.0 driven by CORE-II forcing are compared on a mesh used for the CORE-II intercomparison project. Additionally, the performance on an eddy-permitting mesh with uniform resolution is discussed. The new version improves the numerical efficiency of FESOM in terms of CPU time by at least 3 times while retaining its fidelity in simulating sea ice and the ocean. From this it is argued that FESOM2.0 provides a major step forward in establishing unstructured-mesh models as valuable tools in climate research.

  19. 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.

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

    NASA Technical Reports Server (NTRS)

    Nicholson, S.; Moore, J.

    1986-01-01

    The finite volume explicit time marching method was refined and improved. Previously, extension had been made to the finite volume method to improve the accuracy of the calculation of total pressure in inviscid flow, extend the method to allow the calculation of laminar and turbulent boundary layers in internal flows, and improve the shock capturing properties of the method by introducing a Mach number dependent interpolation scheme for the pressure used in the calculating the density. The current work extends these developments by using the new pressure interpolation scheme in two dimensional viscous calculations, including a more complete description of the viscous stresses, introducing a criteria for the transverse upwind differencing which is a function of the ratio of transverse and streamwise mass fluxes, and allowing the calculation of internal flow where boundary layers are present on both walls of the duct. The manner in which the viscous stresses are evaluated in the nonorthogonal, nonuniform grid is detailed. The convergence is investigated and results for calculations of laminar flow in a converging duct are presented. Results for calculations of transonic flow in a converging-diverging nozzle are presented and the results are compared with Sajben's measurements and calculations by others.

  1. 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.

  2. 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.

  3. Reliable and Accurate Calcium Volume Measurement in Coronary Artery Using Intravascular Ultrasound Videos.

    PubMed

    Araki, Tadashi; Banchhor, Sumit K; Londhe, Narendra D; Ikeda, Nobutaka; Radeva, Petia; Shukla, Devarshi; Saba, Luca; Balestrieri, Antonella; Nicolaides, Andrew; Shafique, Shoaib; Laird, John R; Suri, Jasjit S

    2016-03-01

    Quantitative assessment of calcified atherosclerotic volume within the coronary artery wall is vital for cardiac interventional procedures. The goal of this study is to automatically measure the calcium volume, given the borders of coronary vessel wall for all the frames of the intravascular ultrasound (IVUS) video. Three soft computing fuzzy classification techniques were adapted namely Fuzzy c-Means (FCM), K-means, and Hidden Markov Random Field (HMRF) for automated segmentation of calcium regions and volume computation. These methods were benchmarked against previously developed threshold-based method. IVUS image data sets (around 30,600 IVUS frames) from 15 patients were collected using 40 MHz IVUS catheter (Atlantis® SR Pro, Boston Scientific®, pullback speed of 0.5 mm/s). Calcium mean volume for FCM, K-means, HMRF and threshold-based method were 37.84 ± 17.38 mm(3), 27.79 ± 10.94 mm(3), 46.44 ± 19.13 mm(3) and 35.92 ± 16.44 mm(3) respectively. Cross-correlation, Jaccard Index and Dice Similarity were highest between FCM and threshold-based method: 0.99, 0.92 ± 0.02 and 0.95 + 0.02 respectively. Student's t-test, z-test and Wilcoxon-test are also performed to demonstrate consistency, reliability and accuracy of the results. Given the vessel wall region, the system reliably and automatically measures the calcium volume in IVUS videos. Further, we validated our system against a trained expert using scoring: K-means showed the best performance with an accuracy of 92.80%. Out procedure and protocol is along the line with method previously published clinically.

  4. Are tidal volume measurements in neonatal pressure-controlled ventilation accurate?

    PubMed

    Chow, Lily C; Vanderhal, Andre; Raber, Jorge; Sola, Augusto

    2002-09-01

    Bedside pulmonary mechanics monitors (PMM) have become useful in ventilatory management in neonates. These monitors are used more frequently due to recent improvements in data-processing capabilities. PMM devices are often part of the ventilator or are separate units. The accuracy and reliability of these systems have not been carefully evaluated. We compared a single ventilatory parameter, tidal volume (V(t)), as measured by several systems. We looked at two freestanding PMMs: the Ventrak Respiratory Monitoring System (Novametrix, Wallingford, CT) and the Bicore CP-100 Neonatal Pulmonary Monitor (Allied Health Care Products, Riverside, CA), and three ventilators with built-in PMM: the VIP Bird Ventilator (Bird Products Corp., Palm Springs, CA), Siemens Servo 300A (Siemens-Elema AB, Solna, Sweden), and Drager Babylog 8000 (Drager, Inc., Chantilly, VA). A calibrated syringe (Hans Rudolph, Inc., Kansas City, MO) was used to deliver tidal volumes of 4, 10, and 20 mL to each ventilator system coupled with a freestanding PMM. After achieving steady state, six consecutive V(t) readings were taken simultaneously from the freestanding PMM and each ventilator. In a second portion of the bench study, we used pressure-control ventilation and measured exhaled tidal volume (V(te)) while ventilating a Bear Test Lung with the same three ventilators. We adjusted peak inspiratory pressure (PIP) under controlled conditions to achieve the three different targeted tidal volumes on the paired freestanding PMM. Again, six V(te) measurements were recorded for each tidal volume. Means and standard deviations were calculated.The percentage difference in measurement of V(t) delivered by calibrated syringe varied greatly, with the greatest discrepancy seen in the smallest tidal volumes, by up to 28%. In pressure control mode, V(te) as measured by the Siemens was significantly overestimated by 20-95%, with the biggest discrepancy at the smallest V(te), particularly when paired with the Bicore

  5. Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

    NASA Technical Reports Server (NTRS)

    Mostrel, M. M.

    1988-01-01

    New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

  6. Accurate extraction of Lagrangian coherent structures over finite domains with application to flight data analysis over Hong Kong International Airport

    NASA Astrophysics Data System (ADS)

    Tang, Wenbo; Chan, Pak Wai; Haller, George

    2010-03-01

    Locating Lagrangian coherent structures (LCS) for dynamical systems defined on a spatially limited domain present a challenge because trajectory integration must be stopped at the boundary for lack of further velocity data. This effectively turns the domain boundary into an attractor, introduces edge effects resulting in spurious ridges in the associated finite-time Lyapunov exponent (FTLE) field, and causes some of the real ridges of the FTLE field to be suppressed by strong spurious ridges. To address these issues, we develop a finite-domain FTLE method that renders LCS with an accuracy and fidelity that is suitable for automated feature detection. We show the application of this technique to the analysis of velocity data from aircraft landing at the Hong Kong International Airport.

  7. Simple and accurate empirical absolute volume calibration of a multi-sensor fringe projection system

    NASA Astrophysics Data System (ADS)

    Gdeisat, Munther; Qudeisat, Mohammad; AlSa`d, Mohammed; Burton, David; Lilley, Francis; Ammous, Marwan M. M.

    2016-05-01

    This paper suggests a novel absolute empirical calibration method for a multi-sensor fringe projection system. The optical setup of the projector-camera sensor can be arbitrary. The term absolute calibration here means that the centre of the three dimensional coordinates in the resultant calibrated volume coincides with a preset centre to the three-dimensional real-world coordinate system. The use of a zero-phase fringe marking spot is proposed to increase depth calibration accuracy, where the spot centre is determined with sub-pixel accuracy. Also, a new method is proposed for transversal calibration. Depth and transversal calibration methods have been tested using both single sensor and three-sensor fringe projection systems. The standard deviation of the error produced by this system is 0.25 mm. The calibrated volume produced by this method is 400 mm×400 mm×140 mm.

  8. Can virtual simulation of breast tangential portals accurately predict lung and heart volumes?

    PubMed

    Cooke, Stacey; Rattray, Greg

    2003-03-01

    A treatment portal or simulator image has traditionally been used to demonstrate the lung and heart coverage of the breast tangential portal. In many cases, these images were acquired as a planning session on the linear accelerator. The patients were also CT scanned to assess the lung/heart volume and to determine the surgical site depth for the electron-boost energy. A study using 50 consecutive patients was performed comparing the digitally reconstructed radiograph (DRR) from the virtual simulation with treatment portal images. Modification to the patient's arm position is required when performing the planning CT scans due to the aperture size of the CT scanner. Virtual simulation was used to assess the potential variation of lung and heart measurements. The average difference in lung volume between the DRR and portal image was less than 2 mm, with a range of 0-5 mm. Arm position did not have a significant impact on field deviation; however, great care was taken to minimize any changes in arm position. The modification of the arm position for CT scanning did not lead to significant variations between the DRRs and portal images. The Advantage Sim software has proven capable of producing good quality DRR images, providing a realistic representation of the lung and heart volume included in the treatment portal.

  9. 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.

  10. A three-dimensional hybrid finite element-volume tracking model for mould filling in casting processes

    NASA Astrophysics Data System (ADS)

    Gao, D. M.

    1999-04-01

    Metal casting is a complicated process in which flow momentum plays a crucial role in the mould filling process due to the high velocity of the liquid metal. Inertia and gravity effects may cause splashing, jetting or undesirable filling of the metal flow into the mould cavity. When considering complex parts, the accurate prediction of mould filling behaviour using empirical knowledge and intuition is nearly impossible. Therefore, numerical modelling and simulation are essential to predict such a complex physical problem and assist in part with mould design. A mould filling analysis can help the mould designer to determine the size and location of the gate as well as a proper runner system design for ensuring a complete and balanced filling of the part. Such an analysis can also be used to predict potential product defects, such as air entrapment, porosities, and help in correct positioning of overflows and venting systems. A three-dimensional finite element model combined with a volume tracking method has been developed in this work to simulate the cavity filling for casting processes. A mixed formulation based on a four node tetrahedral element with a bubble function at the centroid (P1+/P1) is employed to solve the flow equations. Such a finite element provides a small dimension of the element matrices and satisfies the Brezzi-Babuska condition to ensure a stable solution of the Navier-Stokes equations. A slip boundary condition combined with a friction model is implemented to better simulate the metal flow near the mould walls. An algebraic model is used to account for the turbulence effects during the mould filling. The flow fronts are tracked by a volume tracking method developed for the tetrahedral elements. This method can handle complicated flow front shapes and complex situations like merging and separation of flow fronts. The combination of a volume tracking technique with a FEM flow solver in three-dimensional unstructured meshes constitutes the major

  11. Can endocranial volume be estimated accurately from external skull measurements in great-tailed grackles (Quiscalus mexicanus)?

    PubMed Central

    Palmstrom, Christin R.

    2015-01-01

    There is an increasing need to validate and collect data approximating brain size on individuals in the field to understand what evolutionary factors drive brain size variation within and across species. We investigated whether we could accurately estimate endocranial volume (a proxy for brain size), as measured by computerized tomography (CT) scans, using external skull measurements and/or by filling skulls with beads and pouring them out into a graduated cylinder for male and female great-tailed grackles. We found that while females had higher correlations than males, estimations of endocranial volume from external skull measurements or beads did not tightly correlate with CT volumes. We found no accuracy in the ability of external skull measures to predict CT volumes because the prediction intervals for most data points overlapped extensively. We conclude that we are unable to detect individual differences in endocranial volume using external skull measurements. These results emphasize the importance of validating and explicitly quantifying the predictive accuracy of brain size proxies for each species and each sex. PMID:26082858

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

    NASA Technical Reports Server (NTRS)

    Moore, J.; Nicholson, S.; Moore, J. G.

    1985-01-01

    Research at NASA Lewis Research Center gave the opportunity to incorporate new control volumes in the Denton 3-D finite-volume time marching code. For duct flows, the new control volumes require no transverse smoothing and this allows calculations with large transverse gradients in properties without significant numerical total pressure losses. Possibilities for improving the Denton code to obtain better distributions of properties through shocks were demonstrated. Much better total pressure distributions through shocks are obtained when the interpolated effective pressure, needed to stabilize the solution procedure, is used to calculate the total pressure. This simple change largely eliminates the undershoot in total pressure down-stream of a shock. Overshoots and undershoots in total pressure can then be further reduced by a factor of 10 by adopting the effective density method, rather than the effective pressure method. Use of a Mach number dependent interpolation scheme for pressure then removes the overshoot in static pressure downstream of a shock. The stability of interpolation schemes used for the calculation of effective density is analyzed and a Mach number dependent scheme is developed, combining the advantages of the correct perfect gas equation for subsonic flow with the stability of 2-point and 3-point interpolation schemes for supersonic flow.

  13. How accurately do we know interannual variations of surface mass balance and firn volume in Antarctica?

    NASA Astrophysics Data System (ADS)

    Horwath, Martin; van den Broeke, Michiel R.; Lenaerts, Jan T. M.; Ligtenberg, Stefan R. M.; Legrésy, Benoît; Blarel, Fabien

    2013-04-01

    Knowing the interannual variations in the Antarctic ice sheet net snow accumulation, or surface mass balance (SMB), is essential for analyzing and interpreting present-day observations. For example, accumulation events like the one in East Antarctica in 2009 (Shepherd et al. 2012, Science, doi: 10.1126/science.1228102) challenge our ability to interpret observed decadal-scale trends in terms of long-term changes versus natural fluctuations. SMB variations cause changes in the firn density structure, which need to be accounted for when converting volume trends from satellite altimetry into mass trends. Recent assessments of SMB and firn volume variations mainly rely on atmospheric modeling and firn densification modeling (FDM). The modeling results need observational validation, which has been limited by now. Geodetic observations by satellite altimetry and satellite gravimetry reflect interannual firn volume and mass changes, among other signals like changes in ice flow dynamics. Therefore, these observations provide a means of validating modeling results over the observational period. We present comprehensive comparisons between interannual volume variations from ENVISAT radar altimetry (RA) and firn densification modeling (FDM), and between interannual mass variations from SMB modeling by the regional atmospheric climate model RACMO2 and GRACE satellite gravimetry. The comparisons are performed based on time series with approximately monthly sampling and with the overlapping period from 2002 to 2010. The RA-FDM comparison spans the spatial scales from 27 km to the continental scale. The mass comparison refers to the regional (drainage basin) and continental scale. Overall, we find good agreement between the interannual variations described by the models and by the geodetic observations. This agreement proves our ability to track and understand SMB-related ice sheet variations from year to year. The assessment of differences between modeling and observations

  14. Finite Element Modelling of a Field-Sensed Magnetic Suspended System for Accurate Proximity Measurement Based on a Sensor Fusion Algorithm with Unscented Kalman Filter.

    PubMed

    Chowdhury, Amor; Sarjaš, Andrej

    2016-09-15

    The presented paper describes accurate distance measurement for a field-sensed magnetic suspension system. The proximity measurement is based on a Hall effect sensor. The proximity sensor is installed directly on the lower surface of the electro-magnet, which means that it is very sensitive to external magnetic influences and disturbances. External disturbances interfere with the information signal and reduce the usability and reliability of the proximity measurements and, consequently, the whole application operation. A sensor fusion algorithm is deployed for the aforementioned reasons. The sensor fusion algorithm is based on the Unscented Kalman Filter, where a nonlinear dynamic model was derived with the Finite Element Modelling approach. The advantage of such modelling is a more accurate dynamic model parameter estimation, especially in the case when the real structure, materials and dimensions of the real-time application are known. The novelty of the paper is the design of a compact electro-magnetic actuator with a built-in low cost proximity sensor for accurate proximity measurement of the magnetic object. The paper successively presents a modelling procedure with the finite element method, design and parameter settings of a sensor fusion algorithm with Unscented Kalman Filter and, finally, the implementation procedure and results of real-time operation.

  15. Finite Element Modelling of a Field-Sensed Magnetic Suspended System for Accurate Proximity Measurement Based on a Sensor Fusion Algorithm with Unscented Kalman Filter

    PubMed Central

    Chowdhury, Amor; Sarjaš, Andrej

    2016-01-01

    The presented paper describes accurate distance measurement for a field-sensed magnetic suspension system. The proximity measurement is based on a Hall effect sensor. The proximity sensor is installed directly on the lower surface of the electro-magnet, which means that it is very sensitive to external magnetic influences and disturbances. External disturbances interfere with the information signal and reduce the usability and reliability of the proximity measurements and, consequently, the whole application operation. A sensor fusion algorithm is deployed for the aforementioned reasons. The sensor fusion algorithm is based on the Unscented Kalman Filter, where a nonlinear dynamic model was derived with the Finite Element Modelling approach. The advantage of such modelling is a more accurate dynamic model parameter estimation, especially in the case when the real structure, materials and dimensions of the real-time application are known. The novelty of the paper is the design of a compact electro-magnetic actuator with a built-in low cost proximity sensor for accurate proximity measurement of the magnetic object. The paper successively presents a modelling procedure with the finite element method, design and parameter settings of a sensor fusion algorithm with Unscented Kalman Filter and, finally, the implementation procedure and results of real-time operation. PMID:27649197

  16. A Non-Dissipative Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwell's Equations

    NASA Technical Reports Server (NTRS)

    Yefet, Amir; Petropoulos, Peter G.

    1999-01-01

    We consider a divergence-free non-dissipative fourth-order explicit staggered finite difference scheme for the hyperbolic Maxwell's equations. Special one-sided difference operators are derived in order to implement the scheme near metal boundaries and dielectric interfaces. Numerical results show the scheme is long-time stable, and is fourth-order convergent over complex domains that include dielectric interfaces and perfectly conducting surfaces. We also examine the scheme's behavior near metal surfaces that are not aligned with the grid axes, and compare its accuracy to that obtained by the Yee scheme.

  17. A three-dimensional finite volume method for conservation laws in conjunction with modified solution for nonlinear coupled constitutive relations

    NASA Astrophysics Data System (ADS)

    Jiang, Zhongzheng; Zhao, Wenwen; Chen, Weifang

    2016-11-01

    Non-equilibrium effects play a vital role in high-speed and rarefied gas flows and the accurate simulation of these flow regimes are far beyond the capability of near-local-equilibrium Navier-Stokes-Fourier equations. Eu proposed generalized hydrodynamic equations which are consistent with the laws of irreversible thermodynamics to solve this problem. Based on Eu's generalized hydrodynamics equations, a computation model, namely the nonlinear coupled constitutive relations (NCCR), was developed by R.S. Myong and applied successfully to one-dimensional shock wave structure and two-dimensional rarefied flows. In this paper, finite volume schemes, including LU-SGS time advance scheme, MUSCL interpolation and AUSMPW+ scheme, are firstly adopted to investigate NCCR model's validity and potential in three-dimensional complex hypersonic rarefied gas flows. Moreover, in order to solve the computational stability problems in 3D complex flows, a modified solution is developed for the NCCR model. Finally, the modified solution is tested for a slip complex flow over a 3D hollow cylinder-flare configuration. The numerical results show that the NCCR model by the modified solution yields good solutions in better agreement with the DSMC results and experimental data than NSF equations, and imply NCCR model's great potential capability in further application.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. A finite-volume Euler solver for computing rotary-wing aerodynamics on unstructured meshes

    NASA Technical Reports Server (NTRS)

    Strawn, Roger C.; Barth, Timothy J.

    1992-01-01

    An unstructured-grid solver for the unsteady Euler equations has been developed for predicting the aerodynamics of helicopter rotor blades. This flow solver is a finite-volume scheme that computes flow quantities at the vertices of the mesh. Special treatments are used for the flux differencing and boundary conditions in order to compute rotary-wing flowfields, and these are detailed in the paper. The unstructured-grid solver permits adaptive grid refinement in order to improve the resolution of flow features such as shocks, rotor wakes and acoustic waves. These capabilities are demonstrated in the paper. Example calculations are presented for two hovering rotors. In both cases, adaptive-grid refinement is used to resolve high gradients near the rotor surface and also to capture the vortical regions in the rotor wake. The computed results show good agreement with experimental results for surface airloads and wake geometry.

  9. A 3D finite-volume scheme for the Euler equations on adaptive tetrahedral grids

    SciTech Connect

    Vijayan, P.; Kallinderis, Y. )

    1994-08-01

    The paper describes the development and application of a new Euler solver for adaptive tetrahedral grids. Spatial discretization uses a finite-volume, node-based scheme that is of central-differencing type. A second-order Taylor series expansion is employed to march the solution in time according to the Lax-Wendroff approach. Special upwind-like smoothing operators for unstructured grids are developed for shock-capturing, as well as for suppression of solution oscillations. The scheme is formulated so that all operations are edge-based, which reduces the computational effort significantly. An adaptive grid algorithm is employed in order to resolve local flow features. This is achieved by dividing the tetrahedral cells locally, guided by a flow feature detection algorithm. Application cases include transonic flow around the ONERA M6 wing and transonic flow past a transport aircraft configuration. Comparisons with experimental data evaluate accuracy of the developed adaptive solver. 31 refs., 33 figs.

  10. 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.

  11. 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.

  12. 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.

  13. 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

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

    NASA Technical Reports Server (NTRS)

    Harten, A.; Tal-Ezer, H.

    1981-01-01

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

  15. A parallel high-order accurate finite element nonlinear Stokes ice sheet model and benchmark experiments: A PARALLEL FEM STOKES ICE SHEET MODEL

    SciTech Connect

    Leng, Wei; Ju, Lili; Gunzburger, Max; Price, Stephen; Ringler, Todd

    2012-01-04

    The numerical modeling of glacier and ice sheet evolution is a subject of growing interest, in part because of the potential for models to inform estimates of global sea level change. This paper focuses on the development of a numerical model that determines the velocity and pressure fields within an ice sheet. Our numerical model features a high-fidelity mathematical model involving the nonlinear Stokes system and combinations of no-sliding and sliding basal boundary conditions, high-order accurate finite element discretizations based on variable resolution grids, and highly scalable parallel solution strategies, all of which contribute to a numerical model that can achieve accurate velocity and pressure approximations in a highly efficient manner. We demonstrate the accuracy and efficiency of our model by analytical solution tests, established ice sheet benchmark experiments, and comparisons with other well-established ice sheet models.

  16. 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.

  17. 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.

  18. Implications of Poincaré symmetry for thermal field theories in finite-volume

    NASA Astrophysics Data System (ADS)

    Giusti, Leonardo; Meyer, Harvey B.

    2013-01-01

    The analytic continuation to an imaginary velocity i ξ of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. Writing the Boltzmann factor as [InlineEquation not available: see fulltext.], the Poincaré invariance underlying a relativistic theory implies a dependence of the free-energy on L 0 and the shift ξ only through the combination [InlineEquation not available: see fulltext.]. This in turn implies a set of Ward identities, some of which were previously derived by us, among the correlators of the energy-momentum tensor. In the infinite-volume limit they lead to relations among the cumulants of the total energy distribution and those of the momentum, i.e. they connect the energy and the momentum distributions in the canonical ensemble. In finite volume the Poincaré symmetry translates into exact relations among partition functions and correlation functions defined with different sets of (generalized) periodic boundary conditions. They have interesting applications in lattice field theory. In particular, they offer Ward identities to renormalize non-perturbatively the energy-momentum tensor and novel ways to compute thermodynamic potentials. At fixed bare parameters they also provide a simple method to vary the temperature in much smaller steps than with the standard procedure.

  19. 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.

  20. 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.

  1. 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

  2. How accurately can subject-specific finite element models predict strains and strength of human femora? Investigation using full-field measurements.

    PubMed

    Grassi, Lorenzo; Väänänen, Sami P; Ristinmaa, Matti; Jurvelin, Jukka S; Isaksson, Hanna

    2016-03-21

    Subject-specific finite element models have been proposed as a tool to improve fracture risk assessment in individuals. A thorough laboratory validation against experimental data is required before introducing such models in clinical practice. Results from digital image correlation can provide full-field strain distribution over the specimen surface during in vitro test, instead of at a few pre-defined locations as with strain gauges. The aim of this study was to validate finite element models of human femora against experimental data from three cadaver femora, both in terms of femoral strength and of the full-field strain distribution collected with digital image correlation. The results showed a high accuracy between predicted and measured principal strains (R(2)=0.93, RMSE=10%, 1600 validated data points per specimen). Femoral strength was predicted using a rate dependent material model with specific strain limit values for yield and failure. This provided an accurate prediction (<2% error) for two out of three specimens. In the third specimen, an accidental change in the boundary conditions occurred during the experiment, which compromised the femoral strength validation. The achieved strain accuracy was comparable to that obtained in state-of-the-art studies which validated their prediction accuracy against 10-16 strain gauge measurements. Fracture force was accurately predicted, with the predicted failure location being very close to the experimental fracture rim. Despite the low sample size and the single loading condition tested, the present combined numerical-experimental method showed that finite element models can predict femoral strength by providing a thorough description of the local bone mechanical response.

  3. A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Kwak, Dochan (Technical Monitor)

    1995-01-01

    A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind

  4. 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.

  5. 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

  6. Applications of a finite-volume algorithm for incompressible MHD problems

    NASA Astrophysics Data System (ADS)

    Vantieghem, S.; Sheyko, A.; Jackson, A.

    2016-02-01

    We present the theory, algorithms and implementation of a parallel finite-volume algorithm for the solution of the incompressible magnetohydrodynamic (MHD) equations using unstructured grids that are applicable for a wide variety of geometries. Our method implements a mixed Adams-Bashforth/Crank-Nicolson scheme for the nonlinear terms in the MHD equations and we prove that it is stable independent of the time step. To ensure that the solenoidal condition is met for the magnetic field, we use a method whereby a pseudo-pressure is introduced into the induction equation; since we are concerned with incompressible flows, the resulting Poisson equation for the pseudo-pressure is solved alongside the equivalent Poisson problem for the velocity field. We validate our code in a variety of geometries including periodic boxes, spheres, spherical shells, spheroids and ellipsoids; for the finite geometries we implement the so-called ferromagnetic or pseudo-vacuum boundary conditions appropriate for a surrounding medium with infinite magnetic permeability. This implies that the magnetic field must be purely perpendicular to the boundary. We present a number of comparisons against previous results and against analytical solutions, which verify the code's accuracy. This documents the code's reliability as a prelude to its use in more difficult problems. We finally present a new simple drifting solution for thermal convection in a spherical shell that successfully sustains a magnetic field of simple geometry. By dint of its rapid stabilization from the given initial conditions, we deem it suitable as a benchmark against which other self-consistent dynamo codes can be tested.

  7. Adaptive moving finite volume scheme for flood inundation modeling under dry and complex topography

    NASA Astrophysics Data System (ADS)

    Zhou, F.; Chen, G.

    2012-04-01

    To assess and alleviate the risk of flood inundation on local scale, the use of numerical models with high accuracy, spatial resolution, and efficiency is crucial for the reliability of the solutions to provide the forecasts and early-warnings of flood inundation at large or meso-scales. Different with traditional numerical models on fixed meshes, an adaptive moving finite volume scheme on moving meshes is proposed for flood inundation modeling under dry and complex topography, this scheme aims to improve the predictive accuracy, spatial resolution, and computational efficiency as well as the satisfaction of well-balanced positivity preserving properties. The crucial feature of our scheme is to move fixed number of unstructured triangular meshes adaptively for approximating the time-variant patterns of flow variables and then to update flow variables through PDEs discretization on new meshes. At each time step of simulation, this scheme consists of three parts, giving in time n for instance: (1) adaptive mesh movement equation for adapting vertex from xij(n, v) to xij(n,v+1) where v is the iteration step, this equation can be transferred as Euler-Lagrange ones⛛· (ω⛛x) = 0, in which the monitor functionω is determined by the solution and the gradient of solution; (2) geometrical conservative interpolation for remapping flow variables from Ui(n, v) to Ui(n,v+1), when ||xij(n,v+1)-xij(n, v)||≤10-6 or v=5, then set xij(n, +∞):= xij(n,v+1) and Uj(n, +∞):= Uj(n,v+1), and (3) HLL-based PDEs discretization for updating flow variables from Ui(n,+∞) to Ui(n+1,0), the treatments of bed slope source terms and wet-dry interface are based on second-order reconstruction of Audusse et al., (2004) and Audusse and Bristeau (2005). Two analytical and two experimental test cases were performed to verify the advantages of the proposed scheme over non-adaptive methods. The results revealed two attractive features: (i) this scheme could achieve high-accuracy and high

  8. 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.

  9. Modified electrochemical parameter estimation of NCR18650BD battery using implicit finite volume method

    NASA Astrophysics Data System (ADS)

    Ashwin, T. R.; McGordon, A.; Widanage, W. D.; Jennings, P. A.

    2017-02-01

    The Pseudo Two Dimensional (P2D) porous electrode model is less preferred for real time calculations due to the high computational expense and complexity in obtaining the wide range of electro-chemical parameters despite of its superior accuracy. This paper presents a finite volume based method for re-parametrising the P2D model for any cell chemistry with uncertainty in determining precise electrochemical parameters. The re-parametrisation is achieved by solving a quadratic form of the Butler-Volmer equation and modifying the anode open circuit voltage based on experimental values. Thus the only experimental result, needed to re-parametrise the cell, reduces to the measurement of discharge voltage for any C-rate. The proposed method is validated against the 1C discharge data and an actual drive cycle of a NCR18650BD battery with NCA chemistry when driving in an urban environment with frequent accelerations and regenerative braking events. The error limit of the present model is compared with the electro-chemical prediction of LiyCoO2 battery and found to be superior to the accuracy of the model presented in the literature.

  10. B_sπ -Bbar{K} interactions in finite volume and X(5568)

    NASA Astrophysics Data System (ADS)

    Lu, Jun-Xu; Ren, Xiu-Lei; Geng, Li-Sheng

    2017-02-01

    The recent observation of X(5568) by the D0 Collaboration has aroused a lot of interest both theoretically and experimentally. In the present work, we first point out that X(5568) and D_{s0}^*(2317) cannot simultaneously be of molecular nature, from the perspective of heavy-quark symmetry and chiral symmetry, based on a previous study of the lattice QCD scattering lengths of DK and its coupled channels. Then we compute the discrete energy levels of the B_sπ and Bbar{K} system in finite volume using unitary chiral perturbation theory. The comparison with the latest lattice QCD simulation, which disfavors the existence of X(5568), supports our picture where the B_sπ and Bbar{K} interactions are weak and X(5568) cannot be a B_sπ and Bbar{K} molecular state. In addition, we show that the extended Weinberg compositeness condition also indicates that X(5568) cannot be a molecular state made from B_sπ and Bbar{K} interactions.

  11. Quantification of spurious dissipation and mixing - Discrete variance decay in a Finite-Volume framework

    NASA Astrophysics Data System (ADS)

    Klingbeil, Knut; Mohammadi-Aragh, Mahdi; Gräwe, Ulf; Burchard, Hans

    2014-09-01

    It is well known that in numerical models the advective transport relative to fixed or moving grids needs to be discretised with sufficient accuracy to minimise the spurious decay of tracer variance (spurious mixing). In this paper a general analysis of discrete variance decay (DVD) caused by advective and diffusive fluxes is established. Lacking a general closed derivation for the local DVD rate, two non-invasive methods to estimate local DVD during model runtime are discussed. Whereas the first was presented recently by Burchard and Rennau (2008), the second is a newly proposed alternative. This alternative analysis method is argued to have a more consistent foundation. In particular, it recovers a physically sound definition of discrete variance in a Finite-Volume cell. The diagnosed DVD can be separated into physical and numerical (spurious) contributions, with the latter originating from discretisation errors. Based on the DVD analysis, a 3D dissipation analysis is developed to quantify the physically and numerically induced loss of kinetic energy. This dissipation analysis provides a missing piece of information to assess the discrete energy conservation of an ocean model. Analyses are performed and evaluated for three test cases, with complexities ranging from idealised 1D advection to a realistic ocean modelling application to the Western Baltic Sea. In all test cases the proposed alternative DVD analysis method is demonstrated to provide a reliable diagnostic tool for the local quantification of physically and numerically induced dissipation and mixing.

  12. Correlators of left charges and weak operators in finite volume chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Hernández, Pilar; Laine, Mikko

    2003-01-01

    We compute the two-point correlator between left-handed flavour charges, and the three-point correlator between two left-handed charges and one strangeness violating DeltaI = 3/2 weak operator, at next-to-leading order in finite volume SU(3)L × SU(3)R chiral perturbation theory, in the so-called epsilon-regime. Matching these results with the corresponding lattice measurements would in principle allow to extract the pion decay constant F, and the effective chiral theory parameter g27, which determines the Delta I = 3/2 amplitude of the weak decays K to pipi as well as the kaon mixing parameter BK in the chiral limit. We repeat the calculations in the replica formulation of quenched chiral perturbation theory, finding only mild modifications. In particular, a properly chosen ratio of the three-point and two-point functions is shown to be identical in the full and quenched theories at this order.

  13. 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.

  14. 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.

  15. High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates

    NASA Astrophysics Data System (ADS)

    Mignone, A.

    2014-08-01

    High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the zone-average values to reconstruct left and right interface states from within a computational zone to arbitrary order of accuracy by inverting a Vandermonde-like linear system of equations with spatially varying coefficients. The approach is general and can be used on uniform and non-uniform meshes although explicit expressions are derived for polynomials from second to fifth degree in cylindrical and spherical geometries with uniform grid spacing. It is shown that, in regions of large curvature, the resulting expressions differ considerably from their Cartesian counterparts and that the lack of such corrections can severely degrade the accuracy of the solution close to the coordinate origin. Limiting techniques and monotonicity constraints are revised for conventional reconstruction schemes, namely, the piecewise linear method (PLM), third-order weighted essentially non-oscillatory (WENO) scheme and the piecewise parabolic method (PPM). The performance of the improved reconstruction schemes is investigated in a number of selected numerical benchmarks involving the solution of both scalar and systems of nonlinear equations (such as the equations of gas dynamics and magnetohydrodynamics) in cylindrical and spherical geometries in one and two dimensions. Results confirm that the proposed approach yields considerably smaller errors, higher convergence rates and it avoid spurious numerical effects at a symmetry axis.

  16. Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem

    NASA Astrophysics Data System (ADS)

    Terekhov, Kirill M.; Mallison, Bradley T.; Tchelepi, Hamdi A.

    2017-02-01

    We present two new cell-centered nonlinear finite-volume methods for the heterogeneous, anisotropic diffusion problem. The schemes split the interfacial flux into harmonic and transversal components. Specifically, linear combinations of the transversal vector and the co-normal are used that lead to significant improvements in terms of the mesh-locking effects. The harmonic component of the flux is represented using a conventional monotone two-point flux approximation; the component along the parameterized direction is treated nonlinearly to satisfy either positivity of the solution as in [29], or the discrete maximum principle as in [9]. In order to make the method purely cell-centered, we derive a homogenization function that allows for seamless interpolation in the presence of heterogeneity following a strategy similar to [46]. The performance of the new schemes is compared with existing multi-point flux approximation methods [3,5]. The robustness of the scheme with respect to the mesh-locking problem is demonstrated using several challenging test cases.

  17. Hydrodynamic modelling of free water-surface constructed storm water wetlands using a finite volume technique.

    PubMed

    Zounemat-Kermani, Mohammad; Scholz, Miklas; Tondar, Mohammad-Mahdi

    2015-01-01

    One of the key factors in designing free water-surface constructed wetlands (FWS CW) is the hydraulic efficiency (λ), which depends primarily on the retention time of the polluted storm water. Increasing the hydraulic retention time (HRT) at various flow levels will increase λ of the overall constructed wetland (CW). The effects of characteristic geometric features that increase HRT were explored through the use of a two-dimensional depth-average hydrodynamic model. This numerical model was developed to solve the equations of continuity and motions on an unstructured triangular mesh using the Galerkin finite volume formulation and equations of the k-ε turbulence model. Eighty-nine diverse forms of artificial FWS CW with 11 different aspect ratios were numerically simulated and subsequently analysed for four scenarios: rectangular CW, modified rectangular CW with rounded edges, different inlet/outlet configurations of CW, and surface and submerged obstructions in front of the inlet part of the CW. Results from the simulations showed that increasing the aspect ratio has a direct influence on the enhancement of λ in all cases. However, the aspect ratio should be at least 9 in order to achieve an appropriate rate for λ in rectangular CW. Modified rounded rectangular CW improved λ by up to 23%, which allowed for the selection of a reduced aspect ratio. Simulation results showed that CW with low aspect ratios benefited from obstructions and optimized inlet/outlet configurations in terms of improved HRT.

  18. High resolution finite volume methods on arbitrary grids via wave propagation

    NASA Technical Reports Server (NTRS)

    Leveque, Randall J.

    1987-01-01

    A generalization of Godunov's method for systems of conservation laws has been developed and analyzed that can be applied with arbitrary time steps on arbitrary grids in one space dimension. Stability for arbitrary time steps is achieved by allowing waves to propagate through more than one mesh cell in a time step. The method is extended here to second order accuracy and to a finite volume method in two space dimensions. This latter method is based on solving one dimensional normal and tangential Riemann problems at cell interfaces and again propagating waves through one or more mesh cells. By avoiding the usual time step restriction of explicit methods, it is possible to use reasonable time steps on irregular grids where the minimum cell area is much smaller than the average cell. Boundary conditions for the Euler equations are discussed and special attention is given to the case of a Cartesian grid cut by an irregular boundary. In this case small grid cells arise only near the boundary, and it is desirable to use a time step appropriate for the regular interior cells. Numerical results in two dimensions show that this can be achieved.

  19. Impact erosion prediction using the finite volume particle method with improved constitutive models

    NASA Astrophysics Data System (ADS)

    Leguizamón, Sebastián; Jahanbakhsh, Ebrahim; Maertens, Audrey; Vessaz, Christian; Alimirzazadeh, Siamak; Avellan, François

    2016-11-01

    Erosion damage in hydraulic turbines is a common problem caused by the high- velocity impact of small particles entrained in the fluid. In this investigation, the Finite Volume Particle Method is used to simulate the three-dimensional impact of rigid spherical particles on a metallic surface. Three different constitutive models are compared: the linear strainhardening (L-H), Cowper-Symonds (C-S) and Johnson-Cook (J-C) models. They are assessed in terms of the predicted erosion rate and its dependence on impact angle and velocity, as compared to experimental data. It has been shown that a model accounting for strain rate is necessary, since the response of the material is significantly tougher at the very high strain rate regime caused by impacts. High sensitivity to the friction coefficient, which models the cutting wear mechanism, has been noticed. The J-C damage model also shows a high sensitivity to the parameter related to triaxiality, whose calibration appears to be scale-dependent, not exclusively material-determined. After calibration, the J-C model is capable of capturing the material's erosion response to both impact velocity and angle, whereas both C-S and L-H fail.

  20. Development of a Cartesian-grid finite-volume characteristic flux model for marine applications

    NASA Astrophysics Data System (ADS)

    Leroy, C.; Le Touzé, D.; Alessandrini, B.

    2010-06-01

    A Finite Volume method based on Characteristic Fluxes for compressible fluids is developed. An explicit cell-centered resolution is adopted, where second-order accuracy is provided by using a MUSCL scheme with Sweby or Superbee limiters for the hyperbolic part. Resolution is performed on a generic unstructured Cartesian grid, where solid boundaries are handled by a Cut-Cell method. Interfaces are explicitely advected in a non-diffusive way, ensuring local mass conservation of each fluid. An improved cell cutting has been developed to handle boundaries of arbitrary geometrical complexity. The mesh density is locally adapted to provide accuracy along these boundaries, which can be fixed or move inside the mesh. Instead of using a polygon clipping algorithm, we use the Voxel traversal algorithm coupled with a local floodfill scanline to intersect 2D or 3D boundary surface meshes with the fixed Cartesian grid. Small cells stability problem near the boundaries is solved using a fully conservative merging method. Inflow and outflow conditions are also implemented in the model. The solver is validated on 2D academic test cases, such as the flow past a cylinder. The latter test cases are performed both in the frame of the body and in a fixed frame where the body is moving across the mesh. Extension to 3D is presently being implemented and first results will be presented at the conference.

  1. A finite volume method for trace element diffusion and partitioning during crystal growth

    NASA Astrophysics Data System (ADS)

    Hesse, Marc A.

    2012-09-01

    A finite volume method on a uniform grid is presented to compute the polythermal diffusion and partitioning of a trace element during the growth of a porphyroblast crystal in a uniform matrix and in linear, cylindrical and spherical geometry. The motion of the crystal-matrix interface and the thermal evolution are prescribed functions of time. The motion of the interface is discretized and it advances from one cell boundary to next as the prescribed interface position passes the cell center. The appropriate conditions for the flux across the crystal-matrix interface are derived from discrete mass conservation. Numerical results are benchmarked against steady and transient analytic solutions for isothermal diffusion with partitioning and growth. Two applications illustrate the ability of the model to reproduce observed rare-earth element patterns in garnets (Skora et al., 2006) and water concentration profiles around spherulites in obsidian (Watkins et al., 2009). Simulations with diffusion inside the growing crystal show complex concentration evolutions for trace elements with high diffusion coefficients, such as argon or hydrogen, but demonstrate that rare-earth element concentrations in typical metamorphic garnets are not affected by intracrystalline diffusion.

  2. Finite element surface registration incorporating curvature, volume preservation, and statistical model information.

    PubMed

    Albrecht, Thomas; Dedner, Andreas; 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.

  3. 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

  4. 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.

  5. 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

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

    DOE PAGES

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

    2015-03-11

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

  7. 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.

  8. Finite element analysis of the effect of electrodes placement on accurate resistivity measurement in a diamond anvil cell with van der Pauw technique

    NASA Astrophysics Data System (ADS)

    Wu, Baojia; Huang, Xiaowei; Han, Yonghao; Gao, Chunxiao; Peng, Gang; Liu, Cailong; Wang, Yue; Cui, Xiaoyan; Zou, Guangtian

    2010-05-01

    The van der Pauw technique is widely used to determine resistivity of materials. In diamond anvil cell the compressed sample will make the contact placement change under high pressure. Using finite element analysis, we study the effect of contact placement error induced by pressure on the resistivity measurement accuracy of van der Pauw method. The results show the contact placement has a significant effect on determination accuracy. This method can provide accurate determination of sample resistivity when the spacing b between the contact center and sample periphery is less than D/9 (sample diameter). And the effect of contact placement error on accuracy rapidly increases as the contact location is closing to the sample center. For the same contact placement, the contact size error has a more obvious effect on the semiconductor sample.

  9. On the importance of 3D, geometrically accurate, and subject-specific finite element analysis for evaluation of in-vivo soft tissue loads.

    PubMed

    Moerman, Kevin M; van Vijven, Marc; Solis, Leandro R; van Haaften, Eline E; Loenen, Arjan C Y; Mushahwar, Vivian K; Oomens, Cees W J

    2017-04-01

    Pressure ulcers are a type of local soft tissue injury due to sustained mechanical loading and remain a common issue in patient care. People with spinal cord injury (SCI) are especially at risk of pressure ulcers due to impaired mobility and sensory perception. The development of load improving support structures relies on realistic tissue load evaluation e.g. using finite element analysis (FEA). FEA requires realistic subject-specific mechanical properties and geometries. This study focuses on the effect of geometry. MRI is used for the creation of geometrically accurate models of the human buttock for three able-bodied volunteers and three volunteers with SCI. The effect of geometry on observed internal tissue deformations for each subject is studied by comparing FEA findings for equivalent loading conditions. The large variations found between subjects confirms the importance of subject-specific FEA.

  10. Finite element analysis of the effect of electrodes placement on accurate resistivity measurement in a diamond anvil cell with van der Pauw technique

    SciTech Connect

    Wu Baojia; Huang Xiaowei; Han Yonghao; Gao Chunxiao; Peng Gang; Liu Cailong; Wang Yue; Cui Xiaoyan; Zou Guangtian

    2010-05-15

    The van der Pauw technique is widely used to determine resistivity of materials. In diamond anvil cell the compressed sample will make the contact placement change under high pressure. Using finite element analysis, we study the effect of contact placement error induced by pressure on the resistivity measurement accuracy of van der Pauw method. The results show the contact placement has a significant effect on determination accuracy. This method can provide accurate determination of sample resistivity when the spacing b between the contact center and sample periphery is less than D/9 (sample diameter). And the effect of contact placement error on accuracy rapidly increases as the contact location is closing to the sample center. For the same contact placement, the contact size error has a more obvious effect on the semiconductor sample.

  11. 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.

  12. 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

  13. A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

    SciTech Connect

    Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; Rossi, Simone

    2015-11-12

    Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.

  14. A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

    DOE PAGES

    Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

    2015-11-12

    Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

  15. A new Control Volume Finite Element Method with Discontinuous Pressure Representation for Multi-phase Flow with Implicit Adaptive time Integration and Dynamic Unstructured mesh Optimization

    NASA Astrophysics Data System (ADS)

    Salinas, Pablo; Pavlidis, Dimitrios; Percival, James; Adam, Alexander; Xie, Zhihua; Pain, Christopher; Jackson, Matthew

    2015-11-01

    We present a new, high-order, control-volume-finite-element (CVFE) method with discontinuous representation for pressure and velocity to simulate multiphase flow in heterogeneous porous media. Time is discretized using an adaptive, fully implicit method. Heterogeneous geologic features are represented as volumes bounded by surfaces. Our approach conserves mass and does not require the use of CVs that span domain boundaries. Computational efficiency is increased by use of dynamic mesh optimization. We demonstrate that the approach, amongst other features, accurately preserves sharp saturation changes associated with high aspect ratio geologic domains, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at lower cost than an equivalent fine, fixed mesh and conventional CVFE methods. The use of implicit time integration allows the method to efficiently converge using highly anisotropic meshes without having to reduce the time-step. The work is significant for two key reasons. First, it resolves a long-standing problem associated with the use of classical CVFE methods. Second, it reduces computational cost/increases solution accuracy through the use of dynamic mesh optimization and time-stepping with large Courant number. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged.

  16. 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

  17. 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

  18. 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

  19. 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.

  20. An implicit block LU-SGS finite-volume lattice-Boltzmann scheme for steady flows on arbitrary unstructured meshes

    NASA Astrophysics Data System (ADS)

    Li, Weidong; Luo, Li-Shi

    2016-12-01

    This work proposes a fully implicit lattice Boltzmann (LB) scheme based on finite-volume (FV) discretization on arbitrary unstructured meshes. The linear system derived from the finite-volume lattice Boltzmann equation (LBE) is solved by the block lower-upper (BLU) symmetric-Gauss-Seidel (SGS) algorithm. The proposed implicit FV-LB scheme is efficient and robust, and has a low-storage requirement. The effectiveness and efficiency of the proposed implicit FV-LB scheme are validated and verified by the simulations of three test cases in two dimensions: (a) the laminar Blasius flow over a flat plate with Re =105; (b) the steady viscous flow past a circular cylinder with Re = 10, 20, and 40; and (c) the inviscid flow past a circular cylinder. The proposed implicit FV-LB scheme is shown to be not only effective and efficient for simulations of steady viscous flows, but also robust and efficient for simulations of inviscid flows in particular.

  1. Hybrid Multiscale Finite Volume Method for Advection-Diffusion Equations Subject to Heterogeneous Reactive Boundary Conditions

    SciTech Connect

    Barajas-Solano, David A.; Tartakovsky, A. M.

    2016-10-13

    We present a hybrid scheme for the coupling of macro and microscale continuum models for reactive contaminant transport in fractured and porous media. The transport model considered is the advection-dispersion equation, subject to linear heterogeneous reactive boundary conditions. The Multiscale Finite Volume method (MsFV) is employed to define an approximation to the microscale concentration field defined in terms of macroscopic or \\emph{global} degrees of freedom, together with local interpolator and corrector functions capturing microscopic spatial variability. The macroscopic mass balance relations for the MsFV global degrees of freedom are coupled with the macroscopic model, resulting in a global problem for the simultaneous time-stepping of all macroscopic degrees of freedom throughout the domain. In order to perform the hybrid coupling, the micro and macroscale models are applied over overlapping subdomains of the simulation domain, with the overlap denoted as the handshake subdomain $\\Omega^{hs}$, over which continuity of concentration and transport fluxes between models is enforced. Continuity of concentration is enforced by posing a restriction relation between models over $\\Omega^{hs}$. Continuity of fluxes is enforced by prolongating the macroscopic model fluxes across the boundary of $\\Omega^{hs}$ to microscopic resolution. The microscopic interpolator and corrector functions are solutions to local microscopic advection-diffusion problems decoupled from the global degrees of freedom and from each other by virtue of the MsFV decoupling ansatz. The error introduced by the decoupling ansatz is reduced iteratively by the preconditioned GMRES algorithm, with the hybrid MsFV operator serving as the preconditioner.

  2. Tsunami wave propagation using a high-order well-balanced finite volume scheme

    NASA Astrophysics Data System (ADS)

    Castro, Cristóbal E.

    2010-05-01

    In this work we present a new numerical tool suitable for tsunami wave propagation simulations. We developed a finite volume high-order well-balanced numerical method on unstructured meshes based on the ADER-FV scheme [1]. We use the ADER-FV[2,3] scheme to solve with arbitrary accuracy in space and time the shallow water equation with non-constant bathymetry. In order to properly simulate a tsunami wave propagation we introduce the well-balanced or C-property[4] in the high-order numerical solution. In this presentation we address two important issues that appear when one tries to solve a tsunami propagation problem. First, when small gravity waves are propagated for hundred of wave-lengths, the accuracy in space and time of the numerical method is fundamental to preserve the amplitude. In this presentation we study the propagation of small perturbations over long distances, relating the order of accuracy, the mesh dimension and the wave amplitude. Second, as we deal with high-order schemes we can naturally use polynomial representation of the bathymetry. Here we try to understand the influence of the bathymetry representation in the final solution. [1] C. E. Castro et al. "ADER scheme on unstructured meshes for shallow water: simulation of tsunami waves", submitted [2] E. F. Toro et al. "Towards very high order godunov schemes". In E. F. Toro, editor, Godunov methods; Theory and applications, pages 907--940, Oxford, 2001. Kluwer Academic Plenum Publishers. [3] E. F. Toro and V. A. Titarev. "Solution of the generalized Riemann problem for advection-reaction equations". Proc. Roy. Soc. London, pages 271--281, 2002. [4] A. Bermúdez and M. E. Vázquez. "Upwind methods for hyperbolic conservation laws with source terms". Computer and Fluids, 23(8):1049--1071, 1994.

  3. High-order finite-volume methods for the shallow-water equations on the sphere

    NASA Astrophysics Data System (ADS)

    Ullrich, Paul A.; Jablonowski, Christiane; van Leer, Bram

    2010-08-01

    This paper presents a third-order and fourth-order finite-volume method for solving the shallow-water equations on a non-orthogonal equiangular cubed-sphere grid. Such a grid is built upon an inflated cube placed inside a sphere and provides an almost uniform grid point distribution. The numerical schemes are based on a high-order variant of the Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) pioneered by van Leer. In each cell the reconstructed left and right states are either obtained via a dimension-split piecewise-parabolic method or a piecewise-cubic reconstruction. The reconstructed states then serve as input to an approximate Riemann solver that determines the numerical fluxes at two Gaussian quadrature points along the cell boundary. The use of multiple quadrature points renders the resulting flux high-order. Three types of approximate Riemann solvers are compared, including the widely used solver of Rusanov, the solver of Roe and the new AUSM +-up solver of Liou that has been designed for low-Mach number flows. Spatial discretizations are paired with either a third-order or fourth-order total-variation-diminishing Runge-Kutta timestepping scheme to match the order of the spatial discretization. The numerical schemes are evaluated with several standard shallow-water test cases that emphasize accuracy and conservation properties. These tests show that the AUSM +-up flux provides the best overall accuracy, followed closely by the Roe solver. The Rusanov flux, with its simplicity, provides significantly larger errors by comparison. A brief discussion on extending the method to arbitrary order-of-accuracy is included.

  4. 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.

  5. An implicit finite volume scheme for a scalar hyperbolic problem with measure data related to piecewise deterministic Markov processes

    NASA Astrophysics Data System (ADS)

    Eymard, Robert; Mercier, Sophie; Prignet, Alain

    2008-12-01

    We are interested here in the numerical approximation of a family of probability measures, solution of the Chapman-Kolmogorov equation associated to some non-diffusion Markov process with uncountable state space. Such an equation contains a transport term and another term, which implies redistribution of the probability mass on the whole space. An implicit finite volume scheme is proposed, which is intermediate between an upstream weighting scheme and a modified Lax-Friedrichs one. Due to the seemingly unusual probability framework, a new weak bounded variation inequality had to be developed, in order to prove the convergence of the discretised transport term. Such an inequality may be used in other contexts, such as for the study of finite volume approximations of scalar linear or nonlinear hyperbolic equations with initial data in L1. Also, due to the redistribution term, the tightness of the family of approximate probability measures had to be proven. Numerical examples are provided, showing the efficiency of the implicit finite volume scheme and its potentiality to be helpful in an industrial reliability context.

  6. The Moving Boundary Node Method: A level set-based, finite volume algorithm with applications to cell motility

    PubMed Central

    Wolgemuth, Charles W.; Zajac, Mark

    2010-01-01

    Eukaryotic cell crawling is a highly complex biophysical and biochemical process, where deformation and motion of a cell are driven by internal, biochemical regulation of a poroelastic cytoskeleton. One challenge to building quantitative models that describe crawling cells is solving the reaction-diffusion-advection dynamics for the biochemical and cytoskeletal components of the cell inside its moving and deforming geometry. Here we develop an algorithm that uses the level set method to move the cell boundary and uses information stored in the distance map to construct a finite volume representation of the cell. Our method preserves Cartesian connectivity of nodes in the finite volume representation while resolving the distorted cell geometry. Derivatives approximated using a Taylor series expansion at finite volume interfaces lead to second order accuracy even on highly distorted quadrilateral elements. A modified, Laplacian-based interpolation scheme is developed that conserves mass while interpolating values onto nodes that join the cell interior as the boundary moves. An implicit time-stepping algorithm is used to maintain stability. We use the algoirthm to simulate two simple models for cellular crawling. The first model uses depolymerization of the cytoskeleton to drive cell motility and suggests that the shape of a steady crawling cell is strongly dependent on the adhesion between the cell and the substrate. In the second model, we use a model for chemical signalling during chemotaxis to determine the shape of a crawling cell in a constant gradient and to show cellular response upon gradient reversal. PMID:20689723

  7. A σ-coordinate model for 3D free-surface flows using an unstructured finite-volume technique

    NASA Astrophysics Data System (ADS)

    Uh Zapata, Miguel

    2016-11-01

    The aim of this work is to develop a numerical solution of three-dimensional free-surface flows using a σ-coordinate model, a projection method and an unstructured finite-volume technique. The coordinate transformation is used in order to overcome difficulties arising from free surface elevation and irregular geometry. The projection method consists to combine the momentum and continuity equations in order to establish a Poisson-type equation for the non-hydrostatic pressure. A cell-centered finite volume method with a triangular mesh in the horizontal direction is used to simulate the flows with free-surfaces, in which the average values of conserved variables are stored at the centre of each element. A parallel algorithm is also presented for the finite volume discretization of the 3D Navier-Stokes equations. The proposed parallel method is formulated by using a multi-color SOR method, a block domain decomposition and interprocessor data communication techniques with Message Passing Interface. The model has been validated by several benchmarks which numerical simulations are in good agreement with the corresponding analytical and existing experimental results.

  8. A bronchoscopic navigation system using bronchoscope center calibration for accurate registration of electromagnetic tracker and CT volume without markers

    SciTech Connect

    Luo, Xiongbiao

    2014-06-15

    electromagnetically navigated bronchoscopy system was constructed with accurate registration of an electromagnetic tracker and the CT volume on the basis of an improved marker-free registration approach that uses the bronchial centerlines and bronchoscope tip center information. The fiducial and target registration errors of our electromagnetic navigation system were about 6.6 and 4.5 mm in dynamic bronchial phantom validation.

  9. A cut-cell finite volumefinite element coupling approach for fluid–structure interaction in compressible flow

    SciTech Connect

    Pasquariello, Vito; Hammerl, Georg; Örley, Felix; Hickel, Stefan; Danowski, Caroline; Popp, Alexander; Wall, Wolfgang A.; Adams, Nikolaus A.

    2016-02-15

    We present a loosely coupled approach for the solution of fluid–structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet–Neumann partitioning. The interface motion in the Eulerian frame is accounted for by a conservative cut-cell Immersed Boundary method. The present approach enables sub-cell resolution by considering individual cut-elements within a single fluid cell, which guarantees an accurate representation of the time-varying solid interface. The cut-cell procedure inevitably leads to non-matching interfaces, demanding for a special treatment. A Mortar method is chosen in order to obtain a conservative and consistent load transfer. We validate our method by investigating two-dimensional test cases comprising a shock-loaded rigid cylinder and a deformable panel. Moreover, the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset. Finally, we propose a three-dimensional fluid–structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations.

  10. 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.

  11. Improved Simulation of Subsurface Flow in Heterogeneous Reservoirs Using a Fully Discontinuous Control-Volume-Finite-Element Method, Implicit Timestepping and Dynamic Unstructured Mesh Optimization

    NASA Astrophysics Data System (ADS)

    Salinas, P.; Jackson, M.; Pavlidis, D.; Pain, C.; Adam, A.; Xie, Z.; Percival, J. R.

    2015-12-01

    We present a new, high-order, control-volume-finite-element (CVFE) method with discontinuous representation for pressure and velocity to simulate multiphase flow in heterogeneous porous media. Time is discretized using an adaptive, fully implicit method. Heterogeneous geologic features are represented as volumes bounded by surfaces. Within these volumes, termed geologic domains, the material properties are constant. A given model typically contains numerous such geologic domains. Our approach conserves mass and does not require the use of CVs that span domain boundaries. Computational efficiency is increased by use of dynamic mesh optimization, in which an unstructured mesh adapts in space and time to key solution fields, such as pressure, velocity or saturation, whilst preserving the geometry of the geologic domains. Up-, cross- or down-scaling of material properties during mesh optimization is not required, as the properties are uniform within each geologic domain. We demonstrate that the approach, amongst other features, accurately preserves sharp saturation changes associated with high aspect ratio geologic domains such as fractures and mudstones, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than an equivalent fine, fixed mesh and conventional CVFE methods. The use of implicit time integration allows the method to efficiently converge using highly anisotropic meshes without having to reduce the time-step. The work is significant for two key reasons. First, it resolves a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media, in which CVs span boundaries between domains of contrasting material properties. Second, it reduces computational cost/increases solution accuracy through the use of dynamic mesh optimization and time-stepping with large Courant number.

  12. 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.

  13. Lagrangian ADER-WENO finite volume schemes on unstructured triangular meshes based on genuinely multidimensional HLL Riemann solvers

    NASA Astrophysics Data System (ADS)

    Boscheri, Walter; Balsara, Dinshaw S.; Dumbser, Michael

    2014-06-01

    In this paper we use the genuinely multidimensional HLL Riemann solvers recently developed by Balsara et al. in [13] to construct a new class of computationally efficient high order Lagrangian ADER-WENO one-step ALE finite volume schemes on unstructured triangular meshes. A nonlinear WENO reconstruction operator allows the algorithm to achieve high order of accuracy in space, while high order of accuracy in time is obtained by the use of an ADER time-stepping technique based on a local space-time Galerkin predictor. The multidimensional HLL and HLLC Riemann solvers operate at each vertex of the grid, considering the entire Voronoi neighborhood of each node and allow for larger time steps than conventional one-dimensional Riemann solvers. The results produced by the multidimensional Riemann solver are then used twice in our one-step ALE algorithm: first, as a node solver that assigns a unique velocity vector to each vertex, in order to preserve the continuity of the computational mesh; second, as a building block for genuinely multidimensional numerical flux evaluation that allows the scheme to run with larger time steps compared to conventional finite volume schemes that use classical one-dimensional Riemann solvers in normal direction. The space-time flux integral computation is carried out at the boundaries of each triangular space-time control volume using the Simpson quadrature rule in space and Gauss-Legendre quadrature in time. A rezoning step may be necessary in order to overcome element overlapping or crossing-over. Since our one-step ALE finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, the remapping stage is not needed, making our algorithm a so-called direct ALE method.

  14. Nonlinear finite element analysis of solids and structures. Volume 1: Essentials

    SciTech Connect

    Crisfield, M.A.

    1991-12-31

    This book is written for the practicing engineer. It is an attempt to bring together various strands of work on nonlinear finite elements. The developments in the book are related to computer applications; there are a number of Fortran listings, and many flow charts, for solving parts of nonlinear finite element problems. (Floppy disks with the Fortran source and data files are available from the publisher). This book takes an engineering rather than a mathematical approach to nonlinear finite elements. The first three chapters deal with truss elements. The author introduces basic concepts of nonlinear finite element analysis for simple truss systems with one degree of freedom. The solution schemes considered include an incremental (Euler), an iterative (Newton-Raphson), and a combined incremental and iteration approach (full or modified Newton-Raphson or the initial stress method). In chapter 2, the author introduces the shallow truss theory of chapter 1 to derive the finite element equations for a shallow truss slement with four degrees of freedom. A set of Fortran subroutines is given to solve simple bar-spring problems; some flowcharts are also provided. This chapter also contains data and solutions from a number of bar-spring problems.

  15. 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.

  16. A hybrid pressure-density-based Mach uniform algorithm for 2D Euler equations on unstructured grids by using multi-moment finite volume method

    NASA Astrophysics Data System (ADS)

    Xie, Bin; Deng, Xi; Sun, Ziyao; Xiao, Feng

    2017-04-01

    We propose a novel Mach-uniform numerical model for 2D Euler equations on unstructured grids by using multi-moment finite volume method. The model integrates two key components newly developed to solve compressible flows on unstructured grids with improved accuracy and robustness. A new variant of AUSM scheme, so-called AUSM+-pcp (AUSM+ with pressure-correction projection), has been devised including a pressure-correction projection to the AUSM+ flux splitting, which maintains the exact numerical conservativeness and works well for all Mach numbers. A novel 3th-order, non-oscillatory and less-dissipative reconstruction has been proposed by introducing a multi-dimensional limiting and a BVD (boundary variation diminishing) treatment to the VPM (volume integrated average (VIA) and point value (PV) based multi-moment) reconstruction. The resulting reconstruction scheme, the limited VPM-BVD formulation, is able to resolve both smooth and non-smooth solutions with high fidelity. Benchmark tests have been used to verify the present model. The numerical results substantiate the present model as an accurate and robust unstructured-grid formulation for flows of all Mach numbers.

  17. 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

  18. 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.

  19. 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.)

  20. 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.

  1. A simple method for accurate liver volume estimation by use of curve-fitting: a pilot study.

    PubMed

    Aoyama, Masahito; Nakayama, Yoshiharu; Awai, Kazuo; Inomata, Yukihiro; Yamashita, Yasuyuki

    2013-01-01

    In this paper, we describe the effectiveness of our curve-fitting method by comparing liver volumes estimated by our new technique to volumes obtained with the standard manual contour-tracing method. Hepatic parenchymal-phase images of 13 patients were obtained with multi-detector CT scanners after intravenous bolus administration of 120-150 mL of contrast material (300 mgI/mL). The liver contours of all sections were traced manually by an abdominal radiologist, and the liver volume was computed by summing of the volumes inside the contours. The section number between the first and last slice was then divided into 100 equal parts, and each volume was re-sampled by use of linear interpolation. We generated 13 model profile curves by averaging 12 cases, leaving out one case, and we estimated the profile curve for each patient by fitting the volume values at 4 points using a scale and translation transform. Finally, we determined the liver volume by integrating the sampling points of the profile curve. We used Bland-Altman analysis to evaluate the agreement between the volumes estimated with our curve-fitting method and the volumes measured by the manual contour-tracing method. The correlation between the volume measured by manual tracing and that estimated with our curve-fitting method was relatively high (r = 0.98; slope 0.97; p < 0.001). The mean difference between the manual tracing and our method was -22.9 cm(3) (SD of the difference, 46.2 cm(3)). Our volume-estimating technique that requires the tracing of only 4 images exhibited a relatively high linear correlation with the manual tracing technique.

  2. Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. Part I: Finite Volume Methods

    NASA Astrophysics Data System (ADS)

    Valori, Gherardo; Pariat, Etienne; Anfinogentov, Sergey; Chen, Feng; Georgoulis, Manolis K.; Guo, Yang; Liu, Yang; Moraitis, Kostas; Thalmann, Julia K.; Yang, Shangbin

    2016-11-01

    Magnetic helicity is a conserved quantity of ideal magneto-hydrodynamics characterized by an inverse turbulent cascade. Accordingly, it is often invoked as one of the basic physical quantities driving the generation and structuring of magnetic fields in a variety of astrophysical and laboratory plasmas. We provide here the first systematic comparison of six existing methods for the estimation of the helicity of magnetic fields known in a finite volume. All such methods are reviewed, benchmarked, and compared with each other, and specifically tested for accuracy and sensitivity to errors. To that purpose, we consider four groups of numerical tests, ranging from solutions of the three-dimensional, force-free equilibrium, to magneto-hydrodynamical numerical simulations. Almost all methods are found to produce the same value of magnetic helicity within few percent in all tests. In the more solar-relevant and realistic of the tests employed here, the simulation of an eruptive flux rope, the spread in the computed values obtained by all but one method is only 3 %, indicating the reliability and mutual consistency of such methods in appropriate parameter ranges. However, methods show differences in the sensitivity to numerical resolution and to errors in the solenoidal property of the input fields. In addition to finite volume methods, we also briefly discuss a method that estimates helicity from the field lines' twist, and one that exploits the field's value at one boundary and a coronal minimal connectivity instead of a pre-defined three-dimensional magnetic-field solution.

  3. A General-Purpose Finite-Volume Advection Scheme for Continuous and Discontinuous Fields on Unstructured Grids

    NASA Astrophysics Data System (ADS)

    Dendy, E. D.; Padial-Collins, N. T.; VanderHeyden, W. B.

    2002-08-01

    We present a new general-purpose advection scheme for unstructured meshes based on the use of a variation of the interface-tracking flux formulation recently put forward by O. Ubbink and R. I. Issa ( J. Comput. Phys.153, 26 (1999)), in combination with an extended version of the flux-limited advection scheme of J. Thuburn ( J. Comput. Phys.123, 74 (1996)), for continuous fields. Thus, along with a high-order mode for continuous fields, the new scheme presented here includes optional integrated interface-tracking modes for discontinuous fields. In all modes, the method is conservative, monotonic, and compatible. It is also highly shape preserving. The scheme works on unstructured meshes composed of any kind of connectivity element, including triangular and quadrilateral elements in two dimensions and tetrahedral and hexahedral elements in three dimensions. The scheme is finite-volume based and is applicable to control-volume finite-element and edge-based node-centered computations. An explicit-implicit extension to the continuous-field scheme is provided only to allow for computations in which the local Courant number exceeds unity. The transition from the explicit mode to the implicit mode is performed locally and in a continuous fashion, providing a smooth hybrid explicit-implicit calculation. Results for a variety of test problems utilizing the continuous and discontinuous advection schemes are presented.

  4. 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.

  5. Multichannel 0→2 and 1→2 transition amplitudes for arbitrary spin particles in a finite volume

    DOE PAGES

    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

  6. Stability analysis of unstructured finite volume methods for linear shallow water flows using pseudospectra and singular value decomposition

    NASA Astrophysics Data System (ADS)

    Beljadid, Abdelaziz; Mohammadian, Abdolmajid; Qiblawey, Hazim

    2016-10-01

    The discretization of the shallow water system on unstructured grids can lead to spurious modes which usually can affect accuracy and/or cause stability problems. This paper introduces a new approach for stability analysis of unstructured linear finite volume schemes for linear shallow water equations with the Coriolis Effect using spectra, pseudospectra, and singular value decomposition. The discrete operator of the scheme is the principal parameter used in the analysis. It is shown that unstructured grids have a large influence on operator normality. In some cases the eigenvectors of the operator can be far from orthogonal, which leads to amplification of solutions and/or stability problems. Large amplifications of the solution can be observed, even for discrete operators which respect the condition of asymptotic stability, and in some cases even for Lax-Richtmyer stable methods. The pseudospectra are shown to be efficient for the verification of stability of finite volume methods for linear shallow water equations. In some cases, the singular value decomposition is employed for further analysis in order to provide more information about the existence of unstable modes. The results of the analysis can be helpful in choosing the type of mesh, the appropriate placements of the variables of the system on the grid, and the suitable discretization method which is stable for a wide range of modes.

  7. 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.

  8. Implicit finite volume and discontinuous Galerkin methods for multicomponent flow in unstructured 3D fractured porous media

    NASA Astrophysics Data System (ADS)

    Moortgat, Joachim; Amooie, Mohammad Amin; Soltanian, Mohamad Reza

    2016-10-01

    We present a new implicit higher-order finite element (FE) approach to efficiently model compressible multicomponent fluid flow on unstructured grids and in fractured porous subsurface formations. The scheme is sequential implicit: pressures and fluxes are updated with an implicit Mixed Hybrid Finite Element (MHFE) method, and the transport of each species is approximated with an implicit second-order Discontinuous Galerkin (DG) FE method. Discrete fractures are incorporated with a cross-flow equilibrium approach. This is the first investigation of all-implicit higher-order MHFE-DG for unstructured triangular, quadrilateral (2D), and hexahedral (3D) grids and discrete fractures. A lowest-order implicit finite volume (FV) transport update is also developed for the same grid types. The implicit methods are compared to an Implicit-Pressure-Explicit-Composition (IMPEC) scheme. For fractured domains, the unconditionally stable implicit transport update is shown to increase computational efficiency by orders of magnitude as compared to IMPEC, which has a time-step constraint proportional to the pore volume of discrete fracture grid cells. However, when lowest-order Euler time-discretizations are used, numerical errors increase linearly with the larger implicit time-steps, resulting in high numerical dispersion. Second-order Crank-Nicolson implicit MHFE-DG and MHFE-FV are therefore presented as well. Convergence analyses show twice the convergence rate for the DG methods as compared to FV, resulting in two to three orders of magnitude higher computational efficiency. Numerical experiments demonstrate the efficiency and robustness in modeling compressible multicomponent flow on irregular and fractured 2D and 3D grids, even in the presence of fingering instabilities.

  9. High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms

    SciTech Connect

    Xing Yulong . E-mail: xing@dam.brown.edu; Shu Chiwang . E-mail: shu@dam.brown.edu

    2006-05-20

    Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) 206-227; J. Sci. Comput., accepted], we designed a well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which at the same time maintains genuine high order accuracy for general solutions, to a class of hyperbolic systems with separable source terms including the shallow water equations, the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. In this paper, we generalize high order finite volume WENO schemes and Runge-Kutta discontinuous Galerkin (RKDG) finite element methods to the same class of hyperbolic systems to maintain a well-balanced property. Finite volume and discontinuous Galerkin finite element schemes are more flexible than finite difference schemes to treat complicated geometry and adaptivity. However, because of a different computational framework, the maintenance of the well-balanced property requires different technical approaches. After the description of our well-balanced high order finite volume WENO and RKDG schemes, we perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions.

  10. Rapid jetting status inspection and accurate droplet volume measurement for a piezo drop-on-demand inkjet print head using a scanning mirror for display applications

    NASA Astrophysics Data System (ADS)

    Shin, Dong-Youn; Kim, Minsung

    2017-02-01

    Despite the inherent fabrication simplicity of piezo drop-on-demand inkjet printing, the non-uniform deposition of colourants or electroluminescent organic materials leads to faulty display products, and hence, the importance of rapid jetting status inspection and accurate droplet volume measurement increases from a process perspective. In this work, various jetting status inspections and droplet volume measurement methods are reviewed by discussing their advantages and disadvantages, and then, the opportunities for the developed prototype with a scanning mirror are explored. This work demonstrates that jetting status inspection of 384 fictitious droplets can be performed within 17 s with maximum and minimum measurement accuracies of 0.2 ± 0.5 μ m for the fictitious droplets of 50 μ m in diameter and -1.2 ± 0.3 μ m for the fictitious droplets of 30 μ m in diameter, respectively. In addition to the new design of an inkjet monitoring instrument with a scanning mirror, two novel methods to accurately measure the droplet volume by amplifying a minute droplet volume difference and then converting to other physical properties are suggested and the droplet volume difference of ±0.3% is demonstrated to be discernible using numerical simulations, even with the low measurement accuracy of 1 μ m . When the fact is considered that the conventional vision-based method with a CCD camera requires the optical measurement accuracy less than 25 nm to measure the volume of an in-flight droplet in the nominal diameter of 50 μ m at the same volume measurement accuracy, the suggested method with the developed prototype offers a whole new opportunity to inkjet printing for display applications.

  11. Rapid jetting status inspection and accurate droplet volume measurement for a piezo drop-on-demand inkjet print head using a scanning mirror for display applications.

    PubMed

    Shin, Dong-Youn; Kim, Minsung

    2017-02-01

    Despite the inherent fabrication simplicity of piezo drop-on-demand inkjet printing, the non-uniform deposition of colourants or electroluminescent organic materials leads to faulty display products, and hence, the importance of rapid jetting status inspection and accurate droplet volume measurement increases from a process perspective. In this work, various jetting status inspections and droplet volume measurement methods are reviewed by discussing their advantages and disadvantages, and then, the opportunities for the developed prototype with a scanning mirror are explored. This work demonstrates that jetting status inspection of 384 fictitious droplets can be performed within 17 s with maximum and minimum measurement accuracies of 0.2 ± 0.5 μm for the fictitious droplets of 50 μm in diameter and -1.2 ± 0.3 μm for the fictitious droplets of 30 μm in diameter, respectively. In addition to the new design of an inkjet monitoring instrument with a scanning mirror, two novel methods to accurately measure the droplet volume by amplifying a minute droplet volume difference and then converting to other physical properties are suggested and the droplet volume difference of ±0.3% is demonstrated to be discernible using numerical simulations, even with the low measurement accuracy of 1 μm. When the fact is considered that the conventional vision-based method with a CCD camera requires the optical measurement accuracy less than 25 nm to measure the volume of an in-flight droplet in the nominal diameter of 50 μm at the same volume measurement accuracy, the suggested method with the developed prototype offers a whole new opportunity to inkjet printing for display applications.

  12. Composite Grid and Finite-Volume LU (Lower-Upper) Implicit Scheme for Turbine Flow Analysis.

    DTIC Science & Technology

    1987-06-01

    is tive and those of "-" matrices are nonpositive. aw aF aG - + - (4) A + =1 - at ax ay- 2 (A + rAL), A = 2 (A - rA1) where W is the vector of...or 0 type) grid in the immedi- aF aG ate vicinity of the turbine blade, provides a good A = ;w B= boundary layer resolution around the leading-edge...FUEL-TURBOPUMP TURBINE. C. I ROTATION FIUE7 OPST RDFRFRTSTG vSM SLTROUPT IE em8 (A) GRID NODES TO BE USED IN FINITE-DIFFERENCE SCHEME. %y WI (B -EL ETEST

  13. On the determination of Ω - Ω scattering amplitudes from finite volume spectra

    NASA Astrophysics Data System (ADS)

    Li, Ning; Wu, Ya-Jie

    2016-12-01

    The elastic scattering phase shifts to the two-particle energy levels in a finite cubic box is related by the Lüscher’s formula. In this paper, based on the nonrelativistic quantum mechanics model which is usually assumed to be the low energy scattering case in lattice simulations, we confirmed the generalized Lüscher’s formula for the case of two-particle scattering with arbitrary spin in Ref. 1. In particular, Lüscher’s formula is synthesized for two-spin-3/2-particle scattering, i.e. Ω - Ω scattering on lattice that may help us study the promising dibaryon states.

  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. 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

  16. Adaptive finite volume methods with well-balanced Riemann solvers for modeling floods in rugged terrain: Application to the Malpasset dam-break flood (France, 1959)

    USGS Publications Warehouse

    George, D.L.

    2011-01-01

    The simulation of advancing flood waves over rugged topography, by solving the shallow-water equations with well-balanced high-resolution finite volume methods and block-structured dynamic adaptive mesh refinement (AMR), is described and validated in this paper. The efficiency of block-structured AMR makes large-scale problems tractable, and allows the use of accurate and stable methods developed for solving general hyperbolic problems on quadrilateral grids. Features indicative of flooding in rugged terrain, such as advancing wet-dry fronts and non-stationary steady states due to balanced source terms from variable topography, present unique challenges and require modifications such as special Riemann solvers. A well-balanced Riemann solver for inundation and general (non-stationary) flow over topography is tested in this context. The difficulties of modeling floods in rugged terrain, and the rationale for and efficacy of using AMR and well-balanced methods, are presented. The algorithms are validated by simulating the Malpasset dam-break flood (France, 1959), which has served as a benchmark problem previously. Historical field data, laboratory model data and other numerical simulation results (computed on static fitted meshes) are shown for comparison. The methods are implemented in GEOCLAW, a subset of the open-source CLAWPACK software. All the software is freely available at. Published in 2010 by John Wiley & Sons, Ltd.

  17. Accuracy and convergence of coupled finite-volume/Monte Carlo codes for plasma edge simulations of nuclear fusion reactors

    SciTech Connect

    Ghoos, K.; Dekeyser, W.; Samaey, G.; Börner, P.; Baelmans, M.

    2016-10-01

    The plasma and neutral transport in the plasma edge of a nuclear fusion reactor is usually simulated using coupled finite volume (FV)/Monte Carlo (MC) codes. However, under conditions of future reactors like ITER and DEMO, convergence issues become apparent. This paper examines the convergence behaviour and the numerical error contributions with a simplified FV/MC model for three coupling techniques: Correlated Sampling, Random Noise and Robbins Monro. Also, practical procedures to estimate the errors in complex codes are proposed. Moreover, first results with more complex models show that an order of magnitude speedup can be achieved without any loss in accuracy by making use of averaging in the Random Noise coupling technique.

  18. 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.

  19. Numerical study of a finite volume scheme for incompressible Navier-Stokes equations based on SIMPLE-family algorithms

    NASA Astrophysics Data System (ADS)

    Alahyane, M.; Hakim, A.; Raghay, S.

    2017-01-01

    In this work, we present a numerical study of a finite volume scheme based on SIMPLE algorithm for incompressible Navier-Stokes problem. However, this algorithm still not applicable to a large category of problems this could be understood from its stability and convergence, which depends strongly on the parameter of relaxation, in some cases this algorithm could have an unexpected behavior. Therefore, in our work we focus on this particular point to overcome this respected choice of relaxation parameter and to find a sufficient condition for the convergence of the algorithm in general cases. This will be followed by numerical applications in image processing variety of fluid flow problems described by incompressible Navier-Stokes equations.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. Finite-volume Euler and Navier-Stokes solvers for three-dimensional and conical vortex flows over delta wings

    NASA Technical Reports Server (NTRS)

    Kandil, Osama A.; Chuang, Andrew H.; Shifflette, James M.

    1987-01-01

    A unified central-difference finite-volume Euler and Navier-Stokes solver with four-stage Runge-Kutta time stepping is presented. The computer code developed for this purpose is capable of solving the standard set and nonstandard sets (zero-total-pressure loss) of Euler equations and the thin-layer and full Navier-Stokes equations. Applications are presented for conical supersonic flows with weak shocks using the standard and nonstandard sets of Euler equations, and the thin-layer and full Navier-Stokes equations for sharp and round-edged delta wings. Applications are also presented for three-dimensional transonic and subsonic flows using the standard set of Euler equations for sharp-edged delta wings. The computational results of the different sets of equations are compared with each other and with the experimental results and conclusions on the validity of these sets to these applications, are presented.

  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. Parametric investigation of a thermally driven QCD Deconfining Phase Transition in a finite volume at zero chemical potential

    NASA Astrophysics Data System (ADS)

    Bensalem, S.; Ait El Djoudi, A.

    2016-10-01

    This work deals with a statistical description of a thermally driven deconfining phase transition (DPT) from a hadronic gas consisting of massless pions to a color-singlet Quark- Gluon Plasma (QGP), in a finite volume. The thermodynamical approach, within a coexistence model is used to investigate the Quantum Chromo-Dynamics DPT occurring between the two phases, at vanishing chemical potential. Considering the color singletness condition for the QGP phase, with massless up and down quarks, the exact total partition function of the studied system is obtained and then employed to calculate mean values of physical quantities, well characterizing the system near the transition. The finite-size effects on the DPT have been investigated through the study of the thermal behavior of the order parameter, the susceptibility and the second cumulant of the probability density. The similarity between the susceptibility and the second cumulant representing the variance is probed for the studied DPT and a parameterization of the variance is proposed for the first time.

  7. 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.

  8. A coupled phase-field and volume-of-fluid method for accurate representation of limiting water wave deformation

    NASA Astrophysics Data System (ADS)

    Liu, Yu; Yu, Xiping

    2016-09-01

    A coupled phase-field and volume-of-fluid method is developed to study the sensitive behavior of water waves during breaking. The THINC model is employed to solve the volume-of-fluid function over the entire domain covered by a relatively coarse grid while the phase-field model based on Allen-Cahn equation is applied over the fine grid. A special algorithm that takes into account the sharpness of the diffuse-interface is introduced to correlate the order parameter obtained on the fine grid and the volume-of-fluid function obtained on the coarse grid. The coupled model is then applied to the study of water waves generated by moving pressures on the free surface. The deformation process of the wave crest during the initial stage of breaking is discussed in details. It is shown that there is a significant variation of the free nappe developed at the front side of the wave crest as the wave steepness differs. It is of a plunging type at large wave steepness while of a spilling type at small wave steepness. The numerical results also indicate that breaking occurs later and the duration of breaking is shorter for waves of smaller steepness and vice versa. Neglecting the capillary effect leads to wave breaking with a sharper nappe and a more dynamic plunging process. The surface tension also has an effect to prevent the formation of a free nappe at the front side of the wave crest in some cases.

  9. A comparison of finite volume flux vector splittings for the Euler equations

    NASA Technical Reports Server (NTRS)

    Anderson, W. K.; Thomas, J. L.; Van Leer, B.

    1985-01-01

    A comparison is made between the computational results of the Steger-Warming (1981) and van Leer (1982) flux splitting methods, which have been applied in generalized coordinates to quasi-one-dimensional transonic flow in a nozzle and two-dimensional subsonic, transonic, and supersonic flow over airfoils. The latter splitting method leads to higher convergence rates and a sharper representation of shocks in the transition region. The second-order accurate, one-sided-difference model is extended to a third-order, upwind-biased model with only small additional computational effort.

  10. CAM-SE-CSLAM: Consistent finite-volume transport with spectral-element dynamics

    NASA Astrophysics Data System (ADS)

    Lauritzen, P. H.; Taylor, M.; Ullrich, P. A.; Overfelt, J.; Goldhaber, S.; Nair, R. D.

    2015-12-01

    For the development of CAM-SE-CSLAM (= basically CAM-SE with accelerated tracer transport), the coupling between two distinct numerical methods is necessary with strict requirements for consistency. Taylor, Overfelt and Ullrich have derived a method to calculate implied spectral element air mass fluxes through CSLAM control volume edges. A new CSLAM algorithm has been developed that through an iterative algorithm finds swept areas that exactly (to round-off) match the spectral element fluxes thereby ensuring strict consistency between the two methods. Acronyms: CAM-SE: NCAR's Community Atmosphere Model using the spectral-element dynamical core CSLAM: Conservative Semi-Lagrangian Multi-tracer transport scheme

  11. Simulation and Analysis of Finite Volume of Hot Forging Process of Nut

    NASA Astrophysics Data System (ADS)

    Maarefdoust, M.; Hosseyni, M.

    2011-08-01

    In this study the forging operations of nut has been modeled. This nut is a part which is manufactured with the help of hot forging. The aim of this research is utilizing computers in designing forming process, and in particular, modeling of hot forging in the nut and to inquire the stresses appeared on the mold. For this purpose Pro/Engineer software for modeling, and SuperForge2004 software for analyzing the process have been used. This part is formed in two stages. To enrich the results coming out of the use of the software, the findings achieved from the modeling of the first stage are compared with its analytic dissolving. In the second stage modeling of metal forming the effect of rake on increasing the stresses imposed to the die mold is studied. The aim of this research is to correct the molds and the volume of the raw materials so that we can produce high qualified parts in spite of raw material low volume and low pressure on the molds.

  12. 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.

  13. Finite-Element Electromagnetic Simulation of a Volume Coil with Slotted End-Rings for Magnetic Resonance Imaging

    NASA Astrophysics Data System (ADS)

    Vazquez, J. F.; Rodriguez, A. O.

    2008-08-01

    Radiofrequency volume coils are still a vital part to detect the magnetic resonance signal. This is mainly due to its highly uniform field over large regions of interest at expense of a relatively low signal-to-noise ratio. In this work, a new volume coil design with slotted end-rings is proposed for high field magnetic resonance imaging applications and, its electromagnetic properties studied via a numerical study. The slotted end-rings avoid breaking the coil structure into small segments degrading the coil performance and, improving the poor signal at the end-rings usually found in the traditional birdcage coil. Numerical simulations were evaluated by solving Maxwell's equations with the finite element method. Hence, both the electric and magnetic fields were evaluated and presented in the form of bi-dimensional images for the slotted end-ring coil and the birdcage coil for comparison purposes. From the magnetic field images of both coil designs, uniformity profiles were calculated at the midsection and the end-rings of the coil and compared. A substantial improvement can be appreciated at the end-rings for the slotted end-ring coil whereas for the midsection it had an acceptable enhancement. These encouraging results suggest that the slotted end-ring coil have an improved performance compared to the birdcage coil.

  14. Solving Two-Mode Shallow Water Equations Using Finite Volume Methods

    NASA Astrophysics Data System (ADS)

    Cheng, Y.

    2015-12-01

    We develop and study numerical methods for the two-mode shallow water equations recently proposed in [S. STECHMANN, A. MAJDA, and B. KHOUIDER, Theor. Comput. Fluid Dynamics, 22 (2008), pp. 407-432]. Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms. We present several numerical approaches — two operator splitting methods (based on either Roe-type upwind or central-upwind scheme), a central-upwind scheme and a path-conservative central-upwind scheme — and test their performance in a number of numerical experiments. The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method. This is a joint work with M. J. Castro Díaz, A. Chertock and A. Kurganov.

  15. 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.

  16. 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.

  17. A 3D assessment tool for accurate volume measurement for monitoring the evolution of cutaneous leishmaniasis wounds.

    PubMed

    Zvietcovich, Fernando; Castañeda, Benjamin; Valencia, Braulio; Llanos-Cuentas, Alejandro

    2012-01-01

    Clinical assessment and outcome metrics are serious weaknesses identified on the systematic reviews of cutaneous Leishmaniasis wounds. Methods with high accuracy and low-variability are required to standarize study outcomes in clinical trials. This work presents a precise, complete and noncontact 3D assessment tool for monitoring the evolution of cutaneous Leishmaniasis (CL) wounds based on a 3D laser scanner and computer vision algorithms. A 3D mesh of the wound is obtained by a commercial 3D laser scanner. Then, a semi-automatic segmentation using active contours is performed to separate the ulcer from the healthy skin. Finally, metrics of volume, area, perimeter and depth are obtained from the mesh. Traditional manual 3D and 3D measurements are obtained as a gold standard. Experiments applied to phantoms and real CL wounds suggest that the proposed 3D assessment tool provides higher accuracy (error <2%) and precision rates (error <4%) than conventional manual methods (precision error < 35%). This 3D assessment tool provides high accuracy metrics which deserve more formal prospective study.

  18. Baroclinic waves and gravity waves in a finite-volume model of the differentially heated rotating annulus

    NASA Astrophysics Data System (ADS)

    Borchert, Sebastian; Achatz, Ulrich; Fruman, Mark D.; Harlander, Uwe; Vincze, Miklos

    2014-05-01

    The differentially heated rotating annulus is a classical experiment for the investigation of baroclinic flows and can be regarded as a strongly simplified laboratory model of the atmosphere in mid-latitudes. Data measured at the BTU Cottbus-Senftenberg (Harlander et al, 2011) are used to validate a new numerical finite-volume model (cylFloit). The model employs the Adaptive Local Deconvolution Method (ALDM) (Hickel et al, 2006) to parameterize unresolved subgrid-scale turbulence. The validation compares the azimuthal mode numbers of the dominant baroclinic waves and does a principal component analysis of time series of the temperature field observed in the experiment and the model simulation. One part of the laboratory procedure that is commonly neglected in simulations is the annulus spin-up, during which the annulus is accelerated from a state of rest to a desired angular velocity. We investigate whether including the spin-up phase in the simulation improves the agreement with the experiment. In addition we use the model to investigate gravity waves (GWs) in the rotating annulus. These waves play an important role in atmospheric dynamics by transporting momentum over large distances, affecting daily weather as well as the climate. Our focus is on GWs spontaneously emitted by the baroclinic waves. By simulating a wide and shallow annulus with relatively large temperature difference between inner and outer cylinder walls, we are able to explore a more atmosphere-like regime where the Brunt-Vaisala frequency is larger than the inertial frequency. Various analyses suggest there is distinct GW activity in these simulations, as well as indications of spontaneous GW emission. Harlander, U., von Larcher, T., Wang, Y., Egbers, C., 2011: PIV- and LDV- measurements of baroclinic wave interactions in a thermally driven rotating annulus. Exp. Fluids, 51(1), 37-49. Hickel, S., Adams, N. A., Domaradzki, J. A., 2006: An adaptive local deconvolution method for implicit LES. J

  19. Accurate discrimination of Alzheimer's disease from other dementia and/or normal subjects using SPECT specific volume analysis

    NASA Astrophysics Data System (ADS)

    Iyatomi, Hitoshi; Hashimoto, Jun; Yoshii, Fumuhito; Kazama, Toshiki; Kawada, Shuichi; Imai, Yutaka

    2014-03-01

    Discrimination between Alzheimer's disease and other dementia is clinically significant, however it is often difficult. In this study, we developed classification models among Alzheimer's disease (AD), other dementia (OD) and/or normal subjects (NC) using patient factors and indices obtained by brain perfusion SPECT. SPECT is commonly used to assess cerebral blood flow (CBF) and allows the evaluation of the severity of hypoperfusion by introducing statistical parametric mapping (SPM). We investigated a total of 150 cases (50 cases each for AD, OD, and NC) from Tokai University Hospital, Japan. In each case, we obtained a total of 127 candidate parameters from: (A) 2 patient factors (age and sex), (B) 12 CBF parameters and 113 SPM parameters including (C) 3 from specific volume analysis (SVA), and (D) 110 from voxel-based analysis stereotactic extraction estimation (vbSEE). We built linear classifiers with a statistical stepwise feature selection and evaluated the performance with the leave-one-out cross validation strategy. Our classifiers achieved very high classification performances with reasonable number of selected parameters. In the most significant discrimination in clinical, namely those of AD from OD, our classifier achieved both sensitivity (SE) and specificity (SP) of 96%. In a similar way, our classifiers achieved a SE of 90% and a SP of 98% in AD from NC, as well as a SE of 88% and a SP of 86% in AD from OD and NC cases. Introducing SPM indices such as SVA and vbSEE, classification performances improved around 7-15%. We confirmed that these SPM factors are quite important for diagnosing Alzheimer's disease.

  20. Stabilized Finite Elements in FUN3D

    NASA Technical Reports Server (NTRS)

    Anderson, W. Kyle; Newman, James C.; Karman, Steve L.

    2017-01-01

    A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

  1. Simulation of dissolution in porous media in three dimensions with lattice Boltzmann, finite-volume, and surface-rescaling methods

    NASA Astrophysics Data System (ADS)

    Gray, F.; Cen, J.; Boek, E. S.

    2016-10-01

    We present a pore-scale dissolution model for the simulation of reactive transport in complex porous media such as those encountered in carbon-storage injection processes. We couple a lattice Boltzmann model for flow calculation with a finite-volume method for solving chemical transport equations, and allow the computational grid to change as mineral surfaces are dissolved according to first-order reaction kinetics. We appraise this scheme for use with high Péclet number flows in three-dimensional geometries and show how the popular first-order convection scheme is affected by severe numerical diffusion when grid Péclet numbers exceed unity, and confirm that this can be overcome relatively easily by using a second-order method in conjunction with a flux-limiter function. We then propose a surface rescaling method which uses parabolic elements to counteract errors in surface area exposed by the Cartesian grid and avoid the use of more complex embedded surface methods when surface reaction kinetics are incorporated. Finally, we compute dissolution in an image of a real porous limestone rock sample injected with HCl for different Péclet numbers and obtain dissolution patterns in concordance with theory and experimental observation. A low injection flow rate was shown to lead to erosion of the pore space concentrated at the face of the rock, whereas a high flow rate leads to wormhole formation.

  2. 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.

  3. 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.

  4. 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.

  5. XTROEM-FV: a new code for computational astrophysics based on very high order finite-volume methods - II. Relativistic hydro- and magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Núñez-de la Rosa, Jonatan; Munz, Claus-Dieter

    2016-07-01

    In this work, we discuss the extension of the XTROEM-FV code to relativistic hydrodynamics and magnetohydrodynamics. XTROEM-FV is a simulation package for computational astrophysics based on very high order finite-volume methods on Cartesian coordinates. Arbitrary spatial high order of accuracy is achieved with a weighted essentially non-oscillatory (WENO) reconstruction operator, and the time evolution is carried out with a strong stability preserving Runge-Kutta scheme. In XTROEM-FV has been implemented a cheap, robust, and accurate shock-capturing strategy for handling complex shock waves problems, typical in an astrophysical environment. The divergence constraint of the magnetic field is tackled with the generalized Lagrange multiplier divergence cleaning approach. Numerical computations of smooth flows for the relativistic hydrodynamics and magnetohydrodynamics equations are performed and confirm the high-order accuracy of the main reconstruction algorithm for such kind of flows. XTROEM-FV has been subject to a comprehensive numerical benchmark, especially for complex flows configurations within an astrophysical context. Computations of problems with shocks with very high order reconstruction operators up to seventh order are reported. For instance, one-dimensional shock tubes problems for relativistic hydrodynamics and magnetohydrodynamics, as well as two-dimensional flows like the relativistic double Mach reflection problem, the interaction of a shock wave with a bubble, the relativistic Orszag-Tang vortex, the cylindrical blast wave problem, the rotor problem, the Kelvin-Helmholtz instability, and an astrophysical slab jet. XTROEM-FV represents a new attempt to simulate astrophysical flow phenomena with very high order numerical methods.

  6. 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.

  7. 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.

  8. 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.

  9. 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).

  10. High order accurate, one-sided finite-difference approximations to concentration gradients at the boundaries, for the simulation of electrochemical reaction-diffusion problems in one-dimensional space geometry.

    PubMed

    Bieniasz, L K

    2003-07-01

    Accurate calculation of concentration gradients at the boundaries is crucial in electrochemical kinetic simulations, owing to the frequent occurrence of gradient-dependent boundary conditions, and the importance of the gradient-dependent electric current. By using the information about higher spatial derivatives of the concentrations, contained in the time-dependent, kinetic reaction-diffusion partial differential equation(s) in one-dimensional space geometry, under appropriate assumptions it is possible to increase the accuracy orders of the conventional, one-sided n-point finite-difference formulae for the concentration gradients at the boundaries, without increasing n. In this way a new class of high order accurate gradient approximations is derived, and tested in simulations of potential-step chronoamperometric and current-step chronopotentiometric transients for the Reinert-Berg system. The new formulae possess advantages over the conventional gradient approximations. For example, they allow one to obtain a third order accuracy by using two space points only, or fourth order accuracy by using three points, and yet they yield smaller errors than the conventional four-point, or five-point formulae, respectively. Needing fewer points, for approximating the gradients with a given accuracy, simplifies also the solution of the linear algebraic equations arising from the application of implicit time integration schemes.

  11. Accurate assessment of breast volume: a study comparing the volumetric gold standard (direct water displacement measurement of mastectomy specimen) with a 3D laser scanning technique.

    PubMed

    Yip, Jia Miin; Mouratova, Naila; Jeffery, Rebecca M; Veitch, Daisy E; Woodman, Richard J; Dean, Nicola R

    2012-02-01

    Preoperative assessment of breast volume could contribute significantly to the planning of breast-related procedures. The availability of 3D scanning technology provides us with an innovative method for doing this. We performed this study to compare measurements by this technology with breast volume measurement by water displacement. A total of 30 patients undergoing 39 mastectomies were recruited from our center. The volume of each patient's breast(s) was determined with a preoperative 3D laser scan. The volume of the mastectomy specimen was then measured in the operating theater by water displacement. There was a strong linear association between breast volumes measured using the 2 different methods when using a Pearson correlation (r = 0.95, P < 0.001). The mastectomy mean volume was defined by the equation: mastectomy mean volume = (scan mean volume × 1.03) -70.6. This close correlation validates the Cyberware WBX Scanner as a tool for assessment of breast volume.

  12. A novel fully-implicit finite volume method applied to the lid-driven cavity problem - Part II: Linear stability analysis

    NASA Astrophysics Data System (ADS)

    Sahin, Mehmet; Owens, Robert G.

    2003-05-01

    A novel finite volume method, described in Part I of this paper (Sahin and Owens, Int. J. Numer. Meth. Fluids 2003; 42:57-77), is applied in the linear stability analysis of a lid-driven cavity flow in a square enclosure. A combination of Arnoldi's method and extrapolation to zero mesh size allows us to determine the first critical Reynolds number at which Hopf bifurcation takes place. The extreme sensitivity of the predicted critical Reynolds number to the accuracy of the method and to the treatment of the singularity points is noted. Results are compared with those in the literature and are in very good agreement.

  13. The Finite Analytic Method and its Applications. Laminar and Turbulent Flows Past Two Dimensional and Axisymmetric Bodies. Volume 1

    DTIC Science & Technology

    1990-03-01

    analytic method. My thanks also go to Dr. Oscar P. Manley of the U.S. Department of Energy for his support of the application of the finite analytic...Shyy, S. S. Tong and S. M. Correa , " Numerical Recirculating Flow calculation Using a Body-Fitted Coordinate System," Numerical heat transfer, Vol.8, pp

  14. Finite Element Heat & Mass Transfer Code

    SciTech Connect

    Trease, Lynn

    1996-10-10

    FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; and double porosity and double porosity/double permeability capabilities.

  15. A comparison of two formulations for high-order accurate essentially non-oscillatory schemes

    NASA Technical Reports Server (NTRS)

    Casper, Jay; Shu, Chi-Wang; Atkins, H. L.

    1993-01-01

    The finite-volume and finite-difference implementations of high-order accurate essentially non-oscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined for accuracy, sensitivity to grid irregularities, resolution of waves that are oblique to the mesh, and computational efficiency. Some algorithm modifications that may be required for a given application are suggested. Conclusions that pertain to the relative merits of both formulations are drawn, and some circumstances for which each might be useful are noted.

  16. High order finite volume methods on wavelet-adapted grids with local time-stepping on multicore architectures for the simulation of shock-bubble interactions

    NASA Astrophysics Data System (ADS)

    Hejazialhosseini, Babak; Rossinelli, Diego; Bergdorf, Michael; Koumoutsakos, Petros

    2010-11-01

    We present a space-time adaptive solver for single- and multi-phase compressible flows that couples average interpolating wavelets with high-order finite volume schemes. The solver introduces the concept of wavelet blocks, handles large jumps in resolution and employs local time-stepping for efficient time integration. We demonstrate that the inherently sequential wavelet-based adaptivity can be implemented efficiently in multicore computer architectures using task-based parallelism and introducing the concept of wavelet blocks. We validate our computational method on a number of benchmark problems and we present simulations of shock-bubble interaction at different Mach numbers, demonstrating the accuracy and computational performance of the method.

  17. The 0.125 degree finite-volume General Circulation Model on the NASA Columbia Supercomputer: Preliminary Simulations of Mesoscale Vortices

    NASA Technical Reports Server (NTRS)

    Shen, B.-W.; Atlas, R.; Chern, J.-D.; Reale, O.; Lin, S.-J.; Lee, T.; Chang, J.

    2005-01-01

    The NASA Columbia supercomputer was ranked second on the TOP500 List in November, 2004. Such a quantum jump in computing power provides unprecedented opportunities to conduct ultra-high resolution simulations with the finite-volume General Circulation Model (fvGCM). During 2004, the model was run in realtime experimentally at 0.25 degree resolution producing remarkable hurricane forecasts [Atlas et al., 2005]. In 2005, the horizontal resolution was further doubled, which makes the fvGCM comparable to the first mesoscale resolving General Circulation Model at the Earth Simulator Center [Ohfuchi et al., 2004]. Nine 5-day 0.125 degree simulations of three hurricanes in 2004 are presented first for model validation. Then it is shown how the model can simulate the formation of the Catalina eddies and Hawaiian lee vortices, which are generated by the interaction of the synoptic-scale flow with surface forcing, and have never been reproduced in a GCM before.)

  18. 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.

  19. A system for accurate and automated injection of hyperpolarized substrate with minimal dead time and scalable volumes over a large range.

    PubMed

    Reynolds, Steven; Bucur, Adriana; Port, Michael; Alizadeh, Tooba; Kazan, Samira M; Tozer, Gillian M; Paley, Martyn N J

    2014-02-01

    Over recent years hyperpolarization by dissolution dynamic nuclear polarization has become an established technique for studying metabolism in vivo in animal models. Temporal signal plots obtained from the injected metabolite and daughter products, e.g. pyruvate and lactate, can be fitted to compartmental models to estimate kinetic rate constants. Modeling and physiological parameter estimation can be made more robust by consistent and reproducible injections through automation. An injection system previously developed by us was limited in the injectable volume to between 0.6 and 2.4ml and injection was delayed due to a required syringe filling step. An improved MR-compatible injector system has been developed that measures the pH of injected substrate, uses flow control to reduce dead volume within the injection cannula and can be operated over a larger volume range. The delay time to injection has been minimized by removing the syringe filling step by use of a peristaltic pump. For 100μl to 10.000ml, the volume range typically used for mice to rabbits, the average delivered volume was 97.8% of the demand volume. The standard deviation of delivered volumes was 7μl for 100μl and 20μl for 10.000ml demand volumes (mean S.D. was 9 ul in this range). In three repeat injections through a fixed 0.96mm O.D. tube the coefficient of variation for the area under the curve was 2%. For in vivo injections of hyperpolarized pyruvate in tumor-bearing rats, signal was first detected in the input femoral vein cannula at 3-4s post-injection trigger signal and at 9-12s in tumor tissue. The pH of the injected pyruvate was 7.1±0.3 (mean±S.D., n=10). For small injection volumes, e.g. less than 100μl, the internal diameter of the tubing contained within the peristaltic pump could be reduced to improve accuracy. Larger injection volumes are limited only by the size of the receiving vessel connected to the pump.

  20. A system for accurate and automated injection of hyperpolarized substrate with minimal dead time and scalable volumes over a large range☆

    PubMed Central

    Reynolds, Steven; Bucur, Adriana; Port, Michael; Alizadeh, Tooba; Kazan, Samira M.; Tozer, Gillian M.; Paley, Martyn N.J.

    2014-01-01

    Over recent years hyperpolarization by dissolution dynamic nuclear polarization has become an established technique for studying metabolism in vivo in animal models. Temporal signal plots obtained from the injected metabolite and daughter products, e.g. pyruvate and lactate, can be fitted to compartmental models to estimate kinetic rate constants. Modeling and physiological parameter estimation can be made more robust by consistent and reproducible injections through automation. An injection system previously developed by us was limited in the injectable volume to between 0.6 and 2.4 ml and injection was delayed due to a required syringe filling step. An improved MR-compatible injector system has been developed that measures the pH of injected substrate, uses flow control to reduce dead volume within the injection cannula and can be operated over a larger volume range. The delay time to injection has been minimized by removing the syringe filling step by use of a peristaltic pump. For 100 μl to 10.000 ml, the volume range typically used for mice to rabbits, the average delivered volume was 97.8% of the demand volume. The standard deviation of delivered volumes was 7 μl for 100 μl and 20 μl for 10.000 ml demand volumes (mean S.D. was 9 ul in this range). In three repeat injections through a fixed 0.96 mm O.D. tube the coefficient of variation for the area under the curve was 2%. For in vivo injections of hyperpolarized pyruvate in tumor-bearing rats, signal was first detected in the input femoral vein cannula at 3–4 s post-injection trigger signal and at 9–12 s in tumor tissue. The pH of the injected pyruvate was 7.1 ± 0.3 (mean ± S.D., n = 10). For small injection volumes, e.g. less than 100 μl, the internal diameter of the tubing contained within the peristaltic pump could be reduced to improve accuracy. Larger injection volumes are limited only by the size of the receiving vessel connected to the pump. PMID:24355621

  1. A system for accurate and automated injection of hyperpolarized substrate with minimal dead time and scalable volumes over a large range

    NASA Astrophysics Data System (ADS)

    Reynolds, Steven; Bucur, Adriana; Port, Michael; Alizadeh, Tooba; Kazan, Samira M.; Tozer, Gillian M.; Paley, Martyn N. J.

    2014-02-01

    Over recent years hyperpolarization by dissolution dynamic nuclear polarization has become an established technique for studying metabolism in vivo in animal models. Temporal signal plots obtained from the injected metabolite and daughter products, e.g. pyruvate and lactate, can be fitted to compartmental models to estimate kinetic rate constants. Modeling and physiological parameter estimation can be made more robust by consistent and reproducible injections through automation. An injection system previously developed by us was limited in the injectable volume to between 0.6 and 2.4 ml and injection was delayed due to a required syringe filling step. An improved MR-compatible injector system has been developed that measures the pH of injected substrate, uses flow control to reduce dead volume within the injection cannula and can be operated over a larger volume range. The delay time to injection has been minimized by removing the syringe filling step by use of a peristaltic pump. For 100 μl to 10.000 ml, the volume range typically used for mice to rabbits, the average delivered volume was 97.8% of the demand volume. The standard deviation of delivered volumes was 7 μl for 100 μl and 20 μl for 10.000 ml demand volumes (mean S.D. was 9 ul in this range). In three repeat injections through a fixed 0.96 mm O.D. tube the coefficient of variation for the area under the curve was 2%. For in vivo injections of hyperpolarized pyruvate in tumor-bearing rats, signal was first detected in the input femoral vein cannula at 3-4 s post-injection trigger signal and at 9-12 s in tumor tissue. The pH of the injected pyruvate was 7.1 ± 0.3 (mean ± S.D., n = 10). For small injection volumes, e.g. less than 100 μl, the internal diameter of the tubing contained within the peristaltic pump could be reduced to improve accuracy. Larger injection volumes are limited only by the size of the receiving vessel connected to the pump.

  2. 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.

  3. Finite amplitude method for measuring the nonlinearity parameter BA in small-volume samples using focused ultrasound.

    PubMed

    Saito, Shigemi

    2010-01-01

    On the basis of finite amplitude and comparative methods, the acoustic nonlinearity parameter BA of a liquid sample of as small as 0.1 ml is measured using an 18.6-MHz focused Gaussian beam. The sample fills the space between a polystyrene plate and a tungsten reflector set about 1 mm apart from each other within the focal region. The sound speed c and attenuation coefficient alpha are determined using the time of flight and the insertion loss of the sound passing through the sample, respectively. The density rho is estimated from the reflection coefficient at the interface between the polystyrene plate and the sample, where the transformation from longitudinal to transverse waves is considered. To compensate for the effect of velocity dispersion on the second harmonic generation, the relative phase of the second harmonic sound is also measured using dual-frequency sound. By summarizing all the linear properties and amplitude data of the second harmonic component in the sound transmitted through the sample, the BA value is finally determined. The measurement is validated through the experiments on nondispersive liquids and weakly dispersive biological samples with known BA values.

  4. 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.

  5. Relativistic, model-independent, multichannel 22 transition amplitudes in a finite volume

    SciTech Connect

    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 the $\\rho$-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.

  6. Accurate Evaluation of Quantum Integrals

    NASA Technical Reports Server (NTRS)

    Galant, D. C.; Goorvitch, D.; Witteborn, Fred C. (Technical Monitor)

    1995-01-01

    Combining an appropriate finite difference method with Richardson's extrapolation results in a simple, highly accurate numerical method for solving a Schrodinger's equation. Important results are that error estimates are provided, and that one can extrapolate expectation values rather than the wavefunctions to obtain highly accurate expectation values. We discuss the eigenvalues, the error growth in repeated Richardson's extrapolation, and show that the expectation values calculated on a crude mesh can be extrapolated to obtain expectation values of high accuracy.

  7. Development of a semi-implicit fluid modeling code using finite-volume method based on Cartesian grids

    NASA Astrophysics Data System (ADS)

    Smith, Matthew R.; Hung, Chieh-Tsan; Lin, Kun-Mo; Wu, Jong-Shinn; Yu, Jen-Perng

    2011-01-01

    Presented is the HLLG (Harten, Lax and van Leer with Gradient inclusion) method for application to the numerical solution of general Partial Differential Equations (PDEs) in conservation form. The HLLG method is based on the traditional HLL method with formal mathematical inclusion of gradients of conserved properties across the control volume employed for flux derivation. The simple extension demonstrates that conventional higher extensions of the HLL method are mathematically inconsistent and produce various numerical instabilities. The HLLG method, with higher order extensions consistent with the flux derivation, is absent of (or less affected by) the said numerical instabilities. The HLLG method is then applied to solutions of the Euler Equations and the simulation of 1D argon RF plasma simulation.

  8. Pore-scale simulations of drainage in granular materials: Finite size effects and the representative elementary volume

    NASA Astrophysics Data System (ADS)

    Yuan, Chao; Chareyre, Bruno; Darve, Félix

    2016-09-01

    A pore-scale model is introduced for two-phase flow in dense packings of polydisperse spheres. The model is developed as a component of a more general hydromechanical coupling framework based on the discrete element method, which will be elaborated in future papers and will apply to various processes of interest in soil science, in geomechanics and in oil and gas production. Here the emphasis is on the generation of a network of pores mapping the void space between spherical grains, and the definition of local criteria governing the primary drainage process. The pore space is decomposed by Regular Triangulation, from which a set of pores connected by throats are identified. A local entry capillary pressure is evaluated for each throat, based on the balance of capillary pressure and surface tension at equilibrium. The model reflects the possible entrapment of disconnected patches of the receding wetting phase. It is validated by a comparison with drainage experiments. In the last part of the paper, a series of simulations are reported to illustrate size and boundary effects, key questions when studying small samples made of spherical particles be it in simulations or experiments. Repeated tests on samples of different sizes give evolution of water content which are not only scattered but also strongly biased for small sample sizes. More than 20,000 spheres are needed to reduce the bias on saturation below 0.02. Additional statistics are generated by subsampling a large sample of 64,000 spheres. They suggest that the minimal sampling volume for evaluating saturation is one hundred times greater that the sampling volume needed for measuring porosity with the same accuracy. This requirement in terms of sample size induces a need for efficient computer codes. The method described herein has a low algorithmic complexity in order to satisfy this requirement. It will be well suited to further developments toward coupled flow-deformation problems in which evolution of the

  9. Practical aspects of spatially high accurate methods

    NASA Technical Reports Server (NTRS)

    Godfrey, Andrew G.; Mitchell, Curtis R.; Walters, Robert W.

    1992-01-01

    The computational qualities of high order spatially accurate methods for the finite volume solution of the Euler equations are presented. Two dimensional essentially non-oscillatory (ENO), k-exact, and 'dimension by dimension' ENO reconstruction operators are discussed and compared in terms of reconstruction and solution accuracy, computational cost and oscillatory behavior in supersonic flows with shocks. Inherent steady state convergence difficulties are demonstrated for adaptive stencil algorithms. An exact solution to the heat equation is used to determine reconstruction error, and the computational intensity is reflected in operation counts. Standard MUSCL differencing is included for comparison. Numerical experiments presented include the Ringleb flow for numerical accuracy and a shock reflection problem. A vortex-shock interaction demonstrates the ability of the ENO scheme to excel in simulating unsteady high-frequency flow physics.

  10. A three-dimensional finite-volume Eulerian-Lagrangian Localized Adjoint Method (ELLAM) for solute-transport modeling

    USGS Publications Warehouse

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

    2000-01-01

    This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.

  11. The effect of local bending on gating of MscL using a representative volume element and finite element simulation

    PubMed Central

    Bavi, Omid; Vossoughi, Manouchehr; Naghdabadi, Reza; Jamali, Yousef

    2014-01-01

    Many physiological processes such as cell division, endocytosis and exocytosis cause severe local curvature of the cell membrane. Local curvature has been shown experimentally to modulate numerous mechanosensitive (MS) ion channels. In order to quantify the effects of local curvature we introduced a coarse grain representative volume element for the bacterial mechanosensitive ion channel of large conductance (MscL) using continuum elasticity. Our model is designed to be consistent with the channel conformation in the closed and open states to capture its major continuum rheological behavior in response to the local membrane curvature. Herein we show that change in the local curvature of the lipid bilayer can modulate MscL activity considerably by changing both bilayer thickness and lateral pressure profile. Intriguingly, although bending in any direction results in almost the same free-energy cost, inward (cytoplasmic) bending favors channel opening, whereas outward (periplasmic) bending facilitates closing of the narrowest part of the MscL pore. This quantitative study using MscL as a model channel may have wide reaching consequences for the effect of local curvature on the physiological function of other types of prokaryotic and eukaryotic membrane proteins. PMID:25478623

  12. The Relation of Finite Element and Finite Difference Methods

    NASA Technical Reports Server (NTRS)

    Vinokur, M.

    1976-01-01

    Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

  13. 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 as git

  14. A primal-dual mimetic finite element scheme for the rotating shallow water equations on polygonal spherical meshes

    NASA Astrophysics Data System (ADS)

    Thuburn, John; Cotter, Colin J.

    2015-06-01

    A new numerical method is presented for solving the shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical properties of the continuous equations and thereby capture several desirable physical properties related to balance and conservation. The method relies on two novel features. The first is the use of compound finite elements to provide suitable finite element spaces on general polygonal meshes. The second is the use of dual finite element spaces on the dual of the original mesh, along with suitably defined discrete Hodge star operators to map between the primal and dual meshes, enabling the use of a finite volume scheme on the dual mesh to compute potential vorticity fluxes. The resulting method has the same mimetic properties as a finite volume method presented previously, but is more accurate on a number of standard test cases.

  15. Investigation of the spreading and dilution of domestic waste water inputs into a tidal bay using the finite-volume model FVCOM

    NASA Astrophysics Data System (ADS)

    Lettmann, Karsten; Wolff, Jörg-Olaf; Liebezeit, Gerd; Meier, Georg

    2010-05-01

    The 'Jade Bay' is a tidal bay located in the western part of the German Wadden Sea, southern North-Sea coast. During particularly heavy rain falls, rain water mixed with domestic waste water is discharged into the bay due to the limited capacities of the waste water treatment plant of the city of Wilhelmshaven. As the discharge point is located only a few hundred meters from a public bathing beach it is important to know spreading and dilution of the waste waters by tidal and wind-driven mixing. To model the behaviour of the waste water plumes, the unstructured mesh finite-volume model FVCOM (Chen and al., 2003) is used, which allows to cover the large area of the Jade and the nearby North Sea with a relatively high resolution near the point of discharge and a coarser resolution at the outer edges of the study side. We adapted the included sediment module of FVCOM to handle the sedimentation, decay and evolution in the bottom sediments of the discharged waste water particles, especially with respect to bacteria. Furthermore, alternative discharge points located in the interior of the Jade bay were tested, which might be more suited for a faster dilution and a smaller residence time of the waste water particles in the tidal bay.

  16. Simulations of Hurricane Katrina (2005) with the 0.125 degree finite-volume General Circulation Model on the NASA Columbia Supercomputer

    NASA Technical Reports Server (NTRS)

    Shen, B.-W.; Atlas, R.; Reale, O.; Lin, S.-J.; Chern, J.-D.; Chang, J.; Henze, C.

    2006-01-01

    Hurricane Katrina was the sixth most intense hurricane in the Atlantic. Katrina's forecast poses major challenges, the most important of which is its rapid intensification. Hurricane intensity forecast with General Circulation Models (GCMs) is difficult because of their coarse resolution. In this article, six 5-day simulations with the ultra-high resolution finite-volume GCM are conducted on the NASA Columbia supercomputer to show the effects of increased resolution on the intensity predictions of Katrina. It is found that the 0.125 degree runs give comparable tracks to the 0.25 degree, but provide better intensity forecasts, bringing the center pressure much closer to observations with differences of only plus or minus 12 hPa. In the runs initialized at 1200 UTC 25 AUG, the 0.125 degree simulates a more realistic intensification rate and better near-eye wind distributions. Moreover, the first global 0.125 degree simulation without convection parameterization (CP) produces even better intensity evolution and near-eye winds than the control run with CP.

  17. Is it possible to design a portable power generator based on micro-solid oxide fuel cells? A finite volume analysis

    NASA Astrophysics Data System (ADS)

    Pla, D.; Sánchez-González, A.; Garbayo, I.; Salleras, M.; Morata, A.; Tarancón, A.

    2015-10-01

    The inherent limited capacity of current battery technology is not sufficient for covering the increasing power requirements of widely extended portable devices. Among other promising alternatives, recent advances in the field of micro-Solid Oxide Fuel Cells (μ-SOFCs) converted this disruptive technology into a serious candidate to power next generations of portable devices. However, the implementation of single cells in real devices, i.e. μ-SOFC stacks coupled to the required balance-of-plant elements like fuel reformers or post combustors, still remains unexplored. This work aims addressing this system-level research by proposing a new compact design of a vertically stacked device fuelled with ethanol. The feasibility and design optimization for achieving a thermally self-sustained regime and a rapid and low-power consuming start-up is studied by finite volume analysis. An optimal thermal insulation strategy is defined to maintain the steady-state operation temperature of the μ-SOFC at 973 K and an external temperature lower than 323 K. A hybrid start-up procedure, based on heaters embedded in the μ-SOFCs and heat released by chemical reactions in the post-combustion unit, is analyzed allowing start-up times below 1 min and energy consumption under 500 J. These results clearly demonstrate the feasibility of high temperature μ-SOFC power systems fuelled with hydrocarbons for portable applications, therefore, anticipating a new family of mobile and uninterrupted power generators.

  18. Finite volume scheme for double convection-diffusion exchange of solutes in bicarbonate high-flux hollow-fiber dialyzer therapy.

    PubMed

    Annan, Kodwo

    2012-01-01

    The efficiency of a high-flux dialyzer in terms of buffering and toxic solute removal largely depends on the ability to use convection-diffusion mechanism inside the membrane. A two-dimensional transient convection-diffusion model coupled with acid-base correction term was developed. A finite volume technique was used to discretize the model and to numerically simulate it using MATLAB software tool. We observed that small solute concentration gradients peaked and were large enough to activate solute diffusion process in the membrane. While CO(2) concentration gradients diminished from their maxima and shifted toward the end of the membrane, HCO(3)(-) concentration gradients peaked at the same position. Also, CO(2) concentration decreased rapidly within the first 47 minutes while optimal HCO(3)(-) concentration was achieved within 30 minutes of the therapy. Abnormally high diffusion fluxes were observed near the blood-membrane interface that increased diffusion driving force and enhanced the overall diffusive process. While convective flux dominated total flux during the dialysis session, there was a continuous interference between convection and diffusion fluxes that call for the need to seek minimal interference between these two mechanisms. This is critical for the effective design and operation of high-flux dialyzers.

  19. Finite volume modeling of laser assisted friction stir welding of 2017A-T451 aluminum alloy for enhanced sustainability of welded joints

    NASA Astrophysics Data System (ADS)

    Mimouni, Oussama; Badji, Riad; Hadji, Mohamed; Kouadri-Henni, Afia

    2016-10-01

    This study focuses on a new welding modification friction stir welding, using a preheating during the welding phase. This method utilizes laser energy to pre-heat the workpiece to a localized area at the front of the FSW tool, thereby reducing the temperature gradient over a localized area in advance of the tool. The amount of heat generated during welding determines the quality of the weld. Therefore the understanding of the temperature distribution is required to determine the optimal method of welding parameters. In this study, a two-dimensional model of an aluminum alloy plate coupled to a circular laser source is developed, using FLUENT software that is based on the finite volume method, also the geometry of the pin of the FSW tool was modified in several configurations to highlight the effect of the geometry of the tool on the temperature distribution in the welded plate. The model developed can be used to better understand the process, predict process performance and to determine the optimal parameters of the process.

  20. Finite Volume Scheme for Double Convection-Diffusion Exchange of Solutes in Bicarbonate High-Flux Hollow-Fiber Dialyzer Therapy

    PubMed Central

    Annan, Kodwo

    2012-01-01

    The efficiency of a high-flux dialyzer in terms of buffering and toxic solute removal largely depends on the ability to use convection-diffusion mechanism inside the membrane. A two-dimensional transient convection-diffusion model coupled with acid-base correction term was developed. A finite volume technique was used to discretize the model and to numerically simulate it using MATLAB software tool. We observed that small solute concentration gradients peaked and were large enough to activate solute diffusion process in the membrane. While CO2 concentration gradients diminished from their maxima and shifted toward the end of the membrane, HCO3 − concentration gradients peaked at the same position. Also, CO2 concentration decreased rapidly within the first 47 minutes while optimal HCO3 − concentration was achieved within 30 minutes of the therapy. Abnormally high diffusion fluxes were observed near the blood-membrane interface that increased diffusion driving force and enhanced the overall diffusive process. While convective flux dominated total flux during the dialysis session, there was a continuous interference between convection and diffusion fluxes that call for the need to seek minimal interference between these two mechanisms. This is critical for the effective design and operation of high-flux dialyzers. PMID:23197994

  1. A WENO-Limited, ADER-DT, Finite-Volume Scheme for Efficient, Robust, and Communication-Avoiding Multi-Dimensional Transport

    SciTech Connect

    Norman, Matthew R

    2014-01-01

    The novel ADER-DT time discretization is applied to two-dimensional transport in a quadrature-free, WENO- and FCT-limited, Finite-Volume context. Emphasis is placed on (1) the serial and parallel computational properties of ADER-DT and this framework and (2) the flexibility of ADER-DT and this framework in efficiently balancing accuracy with other constraints important to transport applications. This study demonstrates a range of choices for the user when approaching their specific application while maintaining good parallel properties. In this method, genuine multi-dimensionality, single-step and single-stage time stepping, strict positivity, and a flexible range of limiting are all achieved with only one parallel synchronization and data exchange per time step. In terms of parallel data transfers per simulated time interval, this improves upon multi-stage time stepping and post-hoc filtering techniques such as hyperdiffusion. This method is evaluated with standard transport test cases over a range of limiting options to demonstrate quantitatively and qualitatively what a user should expect when employing this method in their application.

  2. A WENO-limited, ADER-DT, finite-volume scheme for efficient, robust, and communication-avoiding multi-dimensional transport

    NASA Astrophysics Data System (ADS)

    Norman, Matthew R.

    2014-10-01

    The novel ADER-DT time discretization is applied to two-dimensional transport in a quadrature-free, WENO- and FCT-limited, Finite-Volume context. Emphasis is placed on (1) the serial and parallel computational properties of ADER-DT and this framework and (2) the flexibility of ADER-DT and this framework in efficiently balancing accuracy with other constraints important to transport applications. This study demonstrates a range of choices for the user when approaching their specific application while maintaining good parallel properties. In this method, genuine multi-dimensionality, single-step and single-stage time stepping, strict positivity, and a flexible range of limiting are all achieved with only one parallel synchronization and data exchange per time step. In terms of parallel data transfers per simulated time interval, this improves upon multi-stage time stepping and post-hoc filtering techniques such as hyperdiffusion. This method is evaluated with standard transport test cases over a range of limiting options to demonstrate quantitatively and qualitatively what a user should expect when employing this method in their application.

  3. Production of Volume Wave Plasma with Internally Mounted Cylindrical Planar Microwave Launcher and Two-Dimensional Field Analysis Using Finite Difference Time Domain Method

    NASA Astrophysics Data System (ADS)

    Ogino, Akihisa; Naito, Katsutoshi; Terashita, Fumie; Nanko, Shohei; Nagatsu, Masaaki

    2005-02-01

    In this paper, we presented experimental results on the production of volume wave plasma (VWP) using an internally mounted cylindrical planar microwave launcher, for application to novel plasma processings, such as inner wall coating, impurity-free etching or internal sterilization of medical instruments using VWP. It was demonstrated that the ellipsoidal VWP is produced in front of a microwave launcher in He or Ar gas atmosphere. Numerical analyses of microwave fields radiated from a planar launcher have been carried out using the two-dimensional finite difference time domain (FDTD) method to determine the mechanism of VWP production in middle of the chamber. It was shown that the calculation results showed fairly good agreements with the experimental results measured using a dipole antenna probe. The spatial distributions of plasma density and the temperature of VWP were also measured using a double probe. It was found that the electron density is comparable to or slightly less than cutoff density of 7.4 × 1010 cm-3 corresponding to the microwave frequency of fm=2.45 GHz, and that the electron temperature is approximately 6 eV at the plasma center.

  4. Accurate quantitative measurements of brachial artery cross-sectional vascular area and vascular volume elastic modulus using automated oscillometric measurements: comparison with brachial artery ultrasound

    PubMed Central

    Tomiyama, Yuuki; Yoshinaga, Keiichiro; Fujii, Satoshi; Ochi, Noriki; Inoue, Mamiko; Nishida, Mutumi; Aziki, Kumi; Horie, Tatsunori; Katoh, Chietsugu; Tamaki, Nagara

    2015-01-01

    Increasing vascular diameter and attenuated vascular elasticity may be reliable markers for atherosclerotic risk assessment. However, previous measurements have been complex, operator-dependent or invasive. Recently, we developed a new automated oscillometric method to measure a brachial artery's estimated area (eA) and volume elastic modulus (VE). The aim of this study was to investigate the reliability of new automated oscillometric measurement of eA and VE. Rest eA and VE were measured using the recently developed automated detector with the oscillometric method. eA was estimated using pressure/volume curves and VE was defined as follows (VE=Δ pressure/ (100 × Δ area/area) mm Hg/%). Sixteen volunteers (age 35.2±13.1 years) underwent the oscillometric measurements and brachial ultrasound at rest and under nitroglycerin (NTG) administration. Oscillometric measurement was performed twice on different days. The rest eA correlated with ultrasound-measured brachial artery area (r=0.77, P<0.001). Rest eA and VE measurement showed good reproducibility (eA: intraclass correlation coefficient (ICC)=0.88, VE: ICC=0.78). Under NTG stress, eA was significantly increased (12.3±3.0 vs. 17.1±4.6 mm2, P<0.001), and this was similar to the case with ultrasound evaluation (4.46±0.72 vs. 4.73±0.75 mm, P<0.001). VE was also decreased (0.81±0.16 vs. 0.65±0.11 mm Hg/%, P<0.001) after NTG. Cross-sectional vascular area calculated using this automated oscillometric measurement correlated with ultrasound measurement and showed good reproducibility. Therefore, this is a reliable approach and this modality may have practical application to automatically assess muscular artery diameter and elasticity in clinical or epidemiological settings. PMID:25693851

  5. More Accurate Definition of Clinical Target Volume Based on the Measurement of Microscopic Extensions of the Primary Tumor Toward the Uterus Body in International Federation of Gynecology and Obstetrics Ib-IIa Squamous Cell Carcinoma of the Cervix

    SciTech Connect

    Xie, Wen-Jia; Wu, Xiao; Xue, Ren-Liang; Lin, Xiang-Ying; Kidd, Elizabeth A.; Yan, Shu-Mei; Zhang, Yao-Hong; Zhai, Tian-Tian; Lu, Jia-Yang; Wu, Li-Li; Zhang, Hao; Huang, Hai-Hua; Chen, Zhi-Jian; Li, De-Rui; Xie, Liang-Xi

    2015-01-01

    Purpose: To more accurately define clinical target volume for cervical cancer radiation treatment planning by evaluating tumor microscopic extension toward the uterus body (METU) in International Federation of Gynecology and Obstetrics stage Ib-IIa squamous cell carcinoma of the cervix (SCCC). Patients and Methods: In this multicenter study, surgical resection specimens from 318 cases of stage Ib-IIa SCCC that underwent radical hysterectomy were included. Patients who had undergone preoperative chemotherapy, radiation, or both were excluded from this study. Microscopic extension of primary tumor toward the uterus body was measured. The association between other pathologic factors and METU was analyzed. Results: Microscopic extension toward the uterus body was not common, with only 12.3% of patients (39 of 318) demonstrating METU. The mean (±SD) distance of METU was 0.32 ± 1.079 mm (range, 0-10 mm). Lymphovascular space invasion was associated with METU distance and occurrence rate. A margin of 5 mm added to gross tumor would adequately cover 99.4% and 99% of the METU in the whole group and in patients with lymphovascular space invasion, respectively. Conclusion: According to our analysis of 318 SCCC specimens for METU, using a 5-mm gross tumor volume to clinical target volume margin in the direction of the uterus should be adequate for International Federation of Gynecology and Obstetrics stage Ib-IIa SCCC. Considering the discrepancy between imaging and pathologic methods in determining gross tumor volume extent, we recommend a safer 10-mm margin in the uterine direction as the standard for clinical practice when using MRI for contouring tumor volume.

  6. Hermite WENO limiting for multi-moment finite-volume methods using the ADER-DT time discretization for 1-D systems of conservation laws

    DOE PAGES

    Norman, Matthew R.

    2014-11-24

    New Hermite Weighted Essentially Non-Oscillatory (HWENO) interpolants are developed and investigated within the Multi-Moment Finite-Volume (MMFV) formulation using the ADER-DT time discretization. Whereas traditional WENO methods interpolate pointwise, function-based WENO methods explicitly form a non-oscillatory, high-order polynomial over the cell in question. This study chooses a function-based approach and details how fast convergence to optimal weights for smooth flow is ensured. Methods of sixth-, eighth-, and tenth-order accuracy are developed. We compare these against traditional single-moment WENO methods of fifth-, seventh-, ninth-, and eleventh-order accuracy to compare against more familiar methods from literature. The new HWENO methods improve upon existingmore » HWENO methods (1) by giving a better resolution of unreinforced contact discontinuities and (2) by only needing a single HWENO polynomial to update both the cell mean value and cell mean derivative. Test cases to validate and assess these methods include 1-D linear transport, the 1-D inviscid Burger's equation, and the 1-D inviscid Euler equations. Smooth and non-smooth flows are used for evaluation. These HWENO methods performed better than comparable literature-standard WENO methods for all regimes of discontinuity and smoothness in all tests herein. They exhibit improved optimal accuracy due to the use of derivatives, and they collapse to solutions similar to typical WENO methods when limiting is required. The study concludes that the new HWENO methods are robust and effective when used in the ADER-DT MMFV framework. Finally, these results are intended to demonstrate capability rather than exhaust all possible implementations.« less

  7. Hermite WENO limiting for multi-moment finite-volume methods using the ADER-DT time discretization for 1-D systems of conservation laws

    SciTech Connect

    Norman, Matthew R.

    2014-11-24

    New Hermite Weighted Essentially Non-Oscillatory (HWENO) interpolants are developed and investigated within the Multi-Moment Finite-Volume (MMFV) formulation using the ADER-DT time discretization. Whereas traditional WENO methods interpolate pointwise, function-based WENO methods explicitly form a non-oscillatory, high-order polynomial over the cell in question. This study chooses a function-based approach and details how fast convergence to optimal weights for smooth flow is ensured. Methods of sixth-, eighth-, and tenth-order accuracy are developed. We compare these against traditional single-moment WENO methods of fifth-, seventh-, ninth-, and eleventh-order accuracy to compare against more familiar methods from literature. The new HWENO methods improve upon existing HWENO methods (1) by giving a better resolution of unreinforced contact discontinuities and (2) by only needing a single HWENO polynomial to update both the cell mean value and cell mean derivative. Test cases to validate and assess these methods include 1-D linear transport, the 1-D inviscid Burger's equation, and the 1-D inviscid Euler equations. Smooth and non-smooth flows are used for evaluation. These HWENO methods performed better than comparable literature-standard WENO methods for all regimes of discontinuity and smoothness in all tests herein. They exhibit improved optimal accuracy due to the use of derivatives, and they collapse to solutions similar to typical WENO methods when limiting is required. The study concludes that the new HWENO methods are robust and effective when used in the ADER-DT MMFV framework. Finally, these results are intended to demonstrate capability rather than exhaust all possible implementations.

  8. A new development of the dynamic procedure in large-eddy simulation based on a Finite Volume integral approach. Application to stratified turbulence

    NASA Astrophysics Data System (ADS)

    Denaro, Filippo Maria; de Stefano, Giuliano

    2011-10-01

    A Finite Volume-based large-eddy simulation method is proposed along with a suitable extension of the dynamic modelling procedure that takes into account for the integral formulation of the governing filtered equations. Discussion about the misleading interpretation of FV in some literature is addressed. Then, the classical Germano identity is congruently rewritten in such a way that the determination of the modelling parameters does not require any arbitrary averaging procedure and thus retains a fully local character. The numerical modelling of stratified turbulence is the specific problem considered in this study, as an archetypal of simple geophysical flows. The original scaling formulation of the dynamic sub-grid scale model proposed by Wong and Lilly (Phys. Fluids 6(6), 1994) is suitably extended to the present integral formulation. This approach is preferred with respect to traditional ones since the eddy coefficients can be independently computed by avoiding the addition of unjustified buoyancy production terms in the constitutive equations. Simple scaling arguments allow us not to use the equilibrium hypothesis according to which the dissipation rate should equal the sub-grid scale energy production. A careful a priori analysis of the relevance of the test filter shape as well as the filter-to-grid ratio is reported. Large-eddy simulation results are a posteriori compared with a reference pseudo-spectral direct numerical solution that is suitably post-filtered in order to have a meaningful comparison. In particular, the spectral distribution of kinetic and thermal energy as well as the viscosity and diffusivity sub-grid scale profiles are illustrated. The good performances of the proposed method, in terms of both evolutions of global quantities and statistics, are very promising for the future development and application of the method.

  9. MODFLOW–USG version 1: An unstructured grid version of MODFLOW for simulating groundwater flow and tightly coupled processes using a control volume finite-difference formulation

    USGS Publications Warehouse

    Panday, Sorab; Langevin, Christian D.; Niswonger, Richard G.; Ibaraki, Motomu; Hughes, Joseph D.

    2013-01-01

    A new version of MODFLOW, called MODFLOW–USG (for UnStructured Grid), was developed to support a wide variety of structured and unstructured grid types, including nested grids and grids based on prismatic triangles, rectangles, hexagons, and other cell shapes. Flexibility in grid design can be used to focus resolution along rivers and around wells, for example, or to subdiscretize individual layers to better represent hydrostratigraphic units. MODFLOW–USG is based on an underlying control volume finite difference (CVFD) formulation in which a cell can be connected to an arbitrary number of adjacent cells. To improve accuracy of the CVFD formulation for irregular grid-cell geometries or nested grids, a generalized Ghost Node Correction (GNC) Package was developed, which uses interpolated heads in the flow calculation between adjacent connected cells. MODFLOW–USG includes a Groundwater Flow (GWF) Process, based on the GWF Process in MODFLOW–2005, as well as a new Connected Linear Network (CLN) Process to simulate the effects of multi-node wells, karst conduits, and tile drains, for example. The CLN Process is tightly coupled with the GWF Process in that the equations from both processes are formulated into one matrix equation and solved simultaneously. This robustness results from using an unstructured grid with unstructured matrix storage and solution schemes. MODFLOW–USG also contains an optional Newton-Raphson formulation, based on the formulation in MODFLOW–NWT, for improving solution convergence and avoiding problems with the drying and rewetting of cells. Because the existing MODFLOW solvers were developed for structured and symmetric matrices, they were replaced with a new Sparse Matrix Solver (SMS) Package developed specifically for MODFLOW–USG. The SMS Package provides several methods for resolving nonlinearities and multiple symmetric and asymmetric linear solution schemes to solve the matrix arising from the flow equations and the Newton

  10. Hermite WENO limiting for multi-moment finite-volume methods using the ADER-DT time discretization for 1-D systems of conservation laws

    NASA Astrophysics Data System (ADS)

    Norman, Matthew R.

    2015-02-01

    New Hermite Weighted Essentially Non-Oscillatory (HWENO) interpolants are developed and investigated within the Multi-Moment Finite-Volume (MMFV) formulation using the ADER-DT time discretization. Whereas traditional WENO methods interpolate pointwise, function-based WENO methods explicitly form a non-oscillatory, high-order polynomial over the cell in question. This study chooses a function-based approach and details how fast convergence to optimal weights for smooth flow is ensured. Methods of sixth-, eighth-, and tenth-order accuracy are developed. These are compared against traditional single-moment WENO methods of fifth-, seventh-, ninth-, and eleventh-order accuracy to compare against more familiar methods from literature. The new HWENO methods improve upon existing HWENO methods (1) by giving a better resolution of unreinforced contact discontinuities and (2) by only needing a single HWENO polynomial to update both the cell mean value and cell mean derivative. Test cases to validate and assess these methods include 1-D linear transport, the 1-D inviscid Burger's equation, and the 1-D inviscid Euler equations. Smooth and non-smooth flows are used for evaluation. These HWENO methods performed better than comparable literature-standard WENO methods for all regimes of discontinuity and smoothness in all tests herein. They exhibit improved optimal accuracy due to the use of derivatives, and they collapse to solutions similar to typical WENO methods when limiting is required. The study concludes that the new HWENO methods are robust and effective when used in the ADER-DT MMFV framework. These results are intended to demonstrate capability rather than exhaust all possible implementations.

  11. Can a partial volume edge effect reduction algorithm improve the repeatability of subject-specific finite element models of femurs obtained from CT data?

    PubMed

    Peleg, Eran; Herblum, Ryan; Beek, Maarten; Joskowicz, Leo; Liebergall, Meir; Mosheiff, Rami; Whyne, Cari

    2014-01-01

    The reliability of patient-specific finite element (FE) modelling is dependent on the ability to provide repeatable analyses. Differences of inter-operator generated grids can produce variability in strain and stress readings at a desired location, which are magnified at the surface of the model as a result of the partial volume edge effects (PVEEs). In this study, a new approach is introduced based on an in-house developed algorithm which adjusts the location of the model's surface nodes to a consistent predefined threshold Hounsfield unit value. Three cadaveric human femora specimens were CT scanned, and surface models were created after a semi-automatic segmentation by three different experienced operators. A FE analysis was conducted for each model, with and without applying the surface-adjustment algorithm (a total of 18 models), implementing identical boundary conditions. Maximum principal strain and stress and spatial coordinates were probed at six equivalent surface nodes from the six generated models for each of the three specimens at locations commonly utilised for experimental strain guage measurement validation. A Wilcoxon signed-ranks test was conducted to determine inter-operator variability and the impact of the PVEE-adjustment algorithm. The average inter-operator difference in stress values was significantly reduced after applying the adjustment algorithm (before: 3.32 ± 4.35 MPa, after: 1.47 ± 1.77 MPa, p = 0.025). Strain values were found to be less sensitive to inter-operative variability (p = 0.286). In summary, the new approach as presented in this study may provide a means to improve the repeatability of subject-specific FE models of bone obtained from CT data.

  12. A numerical study of the barotropic tides and tidal energy distribution in the Indonesian seas with the assimilated finite volume coastal ocean model

    NASA Astrophysics Data System (ADS)

    Ding, Yang; Bao, Xianwen; Yu, Huaming; Kuang, Liang

    2012-04-01

    The tides and tidal energetics in the Indonesian seas are simulated using a three-dimensional finite volume coastal ocean model. The high-resolution coastline-fitted model is configured to better resolve the hydrodynamic processes around the numerous barrier islands. A large model domain is adopted to minimize the uncertainty adjacent to open boundaries. The model results with elevation assimilation based on a simple nudge scheme faithfully reproduced the general features of the barotropic tides in the Indonesian Seas. The mean root-mean-square errors between the observed and simulated tidal constants are 2.3, 1.1, 2.4, and 1.5 cm for M2, S2, K1, and O1, respectively. Analysis of the model solutions indicates that the semidiurnal tides in the Indonesian Seas are primarily dominated by the Indian Ocean, whereas the diurnal tides in this region are mainly influenced by the Pacific Ocean, which is consistent with previous studies. Examinations of tidal energy transport reveal that the tidal energy for both of the simulated tidal constituents are transported from the Indian Ocean into the IS mainly through the Lombok Strait and the Timor Sea, whereas only M2 energy enters the Banda Sea and continues northward. The tidal energy dissipates the most in the passages on both sides of Timor Island, with the maximum M2 and K1 tidal energy transport reaching about 750 and 650 kW m-1, respectively. The total energy losses of the four dominant constituents in the IS are nearly 338 GW, with the M2 constituent dissipating 240.8 GW. It is also shown that the bottom dissipation rate for the M2 tide is about 1-2 order of magnitudes larger than that of the other three tidal components in the Indonesian seas.

  13. Component mode synthesis and large deflection vibration of complex structures. Volume 3: Multiple-mode nonlinear free and forced vibrations of beams using finite element method

    NASA Technical Reports Server (NTRS)

    Mei, Chuh; Shen, Mo-How

    1987-01-01

    Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.

  14. Accurate modelling of unsteady flows in collapsible tubes.

    PubMed

    Marchandise, Emilie; Flaud, Patrice

    2010-01-01

    The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.

  15. Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

    SciTech Connect

    Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.

    2013-11-14

    The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges −5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol{sup −1}) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non

  16. Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

    PubMed Central

    Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.

    2013-01-01

    The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges −5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol−1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB

  17. LaRC design analysis report for National Transonic Facility for 304 stainless steel tunnel shell. Volume 1S: Finite difference analysis of cone/cylinder junction

    NASA Technical Reports Server (NTRS)

    Ramsey, J. W., Jr.; Taylor, J. T.; Wilson, J. F.; Gray, C. E., Jr.; Leatherman, A. D.; Rooker, J. R.; Allred, J. W.

    1976-01-01

    The results of extensive computer (finite element, finite difference and numerical integration), thermal, fatigue, and special analyses of critical portions of a large pressurized, cryogenic wind tunnel (National Transonic Facility) are presented. The computer models, loading and boundary conditions are described. Graphic capability was used to display model geometry, section properties, and stress results. A stress criteria is presented for evaluation of the results of the analyses. Thermal analyses were performed for major critical and typical areas. Fatigue analyses of the entire tunnel circuit are presented.

  18. Finite Element Method for Capturing Ultra-relativistic Shocks

    NASA Technical Reports Server (NTRS)

    Richardson, G. A.; Chung, T. J.

    2003-01-01

    While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.

  19. Mapping methods for computationally efficient and accurate structural reliability

    NASA Technical Reports Server (NTRS)

    Shiao, Michael C.; Chamis, Christos C.

    1992-01-01

    Mapping methods are developed to improve the accuracy and efficiency of probabilistic structural analyses with coarse finite element meshes. The mapping methods consist of: (1) deterministic structural analyses with fine (convergent) finite element meshes, (2) probabilistic structural analyses with coarse finite element meshes, (3) the relationship between the probabilistic structural responses from the coarse and fine finite element meshes, and (4) a probabilistic mapping. The results show that the scatter of the probabilistic structural responses and structural reliability can be accurately predicted using a coarse finite element model with proper mapping methods. Therefore, large structures can be analyzed probabilistically using finite element methods.

  20. Accurate derivative evaluation for any Grad–Shafranov solver

    SciTech Connect

    Ricketson, L.F.; Cerfon, A.J.; Rachh, M.; Freidberg, J.P.

    2016-01-15

    We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad–Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of convergence as the solution itself. At the heart of our scheme is an efficient and accurate computation of the Dirichlet to Neumann map through the evaluation of a singular volume integral and the solution to a Fredholm integral equation of the second kind. Our numerical method is particularly useful for magnetic confinement fusion simulations, since it allows the evaluation of quantities such as the magnetic field, the parallel current density and the magnetic curvature with much higher accuracy than has been previously feasible on the affordable coarse grids that are usually implemented.

  1. Accurate, meshless methods for magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Hopkins, Philip F.; Raives, Matthias J.

    2016-01-01

    Recently, we explored new meshless finite-volume Lagrangian methods for hydrodynamics: the `meshless finite mass' (MFM) and `meshless finite volume' (MFV) methods; these capture advantages of both smoothed particle hydrodynamics (SPH) and adaptive mesh refinement (AMR) schemes. We extend these to include ideal magnetohydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains nabla \\cdot B≈ 0. We implement these in the code GIZMO, together with state-of-the-art SPH MHD. We consider a large test suite, and show that on all problems the new methods are competitive with AMR using constrained transport (CT) to ensure nabla \\cdot B=0. They correctly capture the growth/structure of the magnetorotational instability, MHD turbulence, and launching of magnetic jets, in some cases converging more rapidly than state-of-the-art AMR. Compared to SPH, the MFM/MFV methods exhibit convergence at fixed neighbour number, sharp shock-capturing, and dramatically reduced noise, divergence errors, and diffusion. Still, `modern' SPH can handle most test problems, at the cost of larger kernels and `by hand' adjustment of artificial diffusion. Compared to non-moving meshes, the new methods exhibit enhanced `grid noise' but reduced advection errors and diffusion, easily include self-gravity, and feature velocity-independent errors and superior angular momentum conservation. They converge more slowly on some problems (smooth, slow-moving flows), but more rapidly on others (involving advection/rotation). In all cases, we show divergence control beyond the Powell 8-wave approach is necessary, or all methods can converge to unphysical answers even at high resolution.

  2. 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.

  3. Simulation of fluid-solid coexistence in finite volumes: a method to study the properties of wall-attached crystalline nuclei.

    PubMed

    Deb, Debabrata; Winkler, Alexander; Virnau, Peter; Binder, Kurt

    2012-04-07

    The Asakura-Oosawa model for colloid-polymer mixtures is studied by Monte Carlo simulations at densities inside the two-phase coexistence region of fluid and solid. Choosing a geometry where the system is confined between two flat walls, and a wall-colloid potential that leads to incomplete wetting of the crystal at the wall, conditions can be created where a single nanoscopic wall-attached crystalline cluster coexists with fluid in the remainder of the simulation box. Following related ideas that have been useful to study heterogeneous nucleation of liquid droplets at the vapor-liquid coexistence, we estimate the contact angles from observations of the crystalline clusters in thermal equilibrium. We find fair agreement with a prediction based on Young's equation, using estimates of interface and wall tension from the study of flat surfaces. It is shown that the pressure versus density curve of the finite system exhibits a loop, but the pressure maximum signifies the "droplet evaporation-condensation" transition and thus has nothing in common with a van der Waals-like loop. Preparing systems where the packing fraction is deep inside the two-phase coexistence region, the system spontaneously forms a "slab state," with two wall-attached crystalline domains separated by (flat) interfaces from liquid in full equilibrium with the crystal in between; analysis of such states allows a precise estimation of the bulk equilibrium properties at phase coexistence.

  4. Investigation of difficult component effects on finite element model vibration prediction for the Bell AH-1G helicopter. Volume 1: Ground vibration test results

    NASA Technical Reports Server (NTRS)

    Dompka, R. V.

    1989-01-01

    Under the NASA-sponsored Design Analysis Methods for VIBrationS (DAMVIBS) program, a series of ground vibration tests and NASTRAN finite element model (FEM) correlations were conducted on the Bell AH-1G helicopter gunship to investigate the effects of difficult components on the vibration response of the airframe. Previous correlations of the AH-1G showed good agreement between NASTRAN and tests through 15 to 20 Hz, but poor agreement in the higher frequency range of 20 to 30 Hz. Thus, this effort emphasized the higher frequency airframe vibration response correlations and identified areas that need further R and T work. To conduct the investigations, selected difficult components (main rotor pylon, secondary structure, nonstructural doors/panels, landing gear, engine, fuel, etc.) were systematically removed to quantify their effects on overall vibratory response of the airframe. The entire effort was planned and documented, and the results reviewed by NASA and industry experts in order to ensure scientific control of the testing, analysis, and correlation exercise. In particular, secondary structure and damping had significant effects on the frequency response of the airframe above 15 Hz. Also, the nonlinear effects of thrust stiffening and elastomer mounts were significant on the low frequency pylon modes below main rotor 1p (5.4 Hz). The results of the ground vibration testing are presented.

  5. Investigation of difficult component effects on finite element model vibration prediction for the Bell AG-1G helicopter. Volume 2: Correlation results

    NASA Technical Reports Server (NTRS)

    Dompka, R. V.

    1989-01-01

    Under the NASA-sponsored DAMVIBS (Design Analysis Methods for VIBrationS) program, a series of ground vibration tests and NASTRAN finite element model (FEM) correlations were conducted on the Bell AH-1G helicopter gunship to investigate the effects of difficult components on the vibration response of the airframe. Previous correlations of the AG-1G showed good agreement between NASTRAN and tests through 15 to 20 Hz, but poor agreement in the higher frequency range of 20 to 30 Hz. Thus, this effort emphasized the higher frequency airframe vibration response correlations and identified areas that need further R and T work. To conduct the investigations, selected difficult components (main rotor pylon, secondary structure, nonstructural doors/panels, landing gear, engine, furl, etc.) were systematically removed to quantify their effects on overall vibratory response of the airframe. The entire effort was planned and documented, and the results reviewed by NASA and industry experts in order to ensure scientific control of the testing, analysis, and correlation exercise. In particular, secondary structure and damping had significant effects on the frequency response of the airframe above 15 Hz. Also, the nonlinear effects of thrust stiffening and elastomer mounts were significant on the low frequency pylon modes below main rotor 1p (5.4 Hz). The results of the NASTRAN FEM correlations are given.

  6. 3D mechanical analysis of aeronautical plain bearings: Validation of a finite element model from measurement of displacement fields by digital volume correlation and optical scanning tomography

    NASA Astrophysics Data System (ADS)

    Germaneau, A.; Peyruseigt, F.; Mistou, S.; Doumalin, P.; Dupré, J.-C.

    2010-06-01

    On Airbus aircraft, spherical plain bearings are used on many components; in particular to link engine to pylon or pylon to wing. Design of bearings is based on contact pressure distribution on spherical surfaces. To determine this distribution, a 3D analysis of the mechanical behaviour of aeronautical plain bearing is presented in this paper. A numerical model has been built and validated from a comparison with 3D experimental measurements of kinematic components. For that, digital volume correlation (DVC) coupled with optical scanning tomography (OST) is employed to study the mechanical response of a plain bearing model made in epoxy resin. Experimental results have been compared with the ones obtained from the simulated model. This comparison enables us to study the influence of various boundary conditions to build the FE model. Some factors have been highlighted like the fitting behaviour which can radically change contact pressure distribution. This work shows the contribution of a representative mechanical environment to study precisely mechanical response of aeronautical plain bearings.

  7. DebrisInterMixing-2.3: a finite volume solver for three-dimensional debris-flow simulations with two calibration parameters - Part 1: Model description

    NASA Astrophysics Data System (ADS)

    von Boetticher, Albrecht; Turowski, Jens M.; McArdell, Brian W.; Rickenmann, Dieter; Kirchner, James W.

    2016-08-01

    Here, we present a three-dimensional fluid dynamic solver that simulates debris flows as a mixture of two fluids (a Coulomb viscoplastic model of the gravel mixed with a Herschel-Bulkley representation of the fine material suspension) in combination with an additional unmixed phase representing the air and the free surface. We link all rheological parameters to the material composition, i.e., to water content, clay content, and mineral composition, content of sand and gravel, and the gravel's friction angle; the user must specify only two free model parameters. The volume-of-fluid (VoF) approach is used to combine the mixed phase and the air phase into a single cell-averaged Navier-Stokes equation for incompressible flow, based on code adapted from standard solvers of the open-source CFD software OpenFOAM. This effectively single-phase mixture VoF method saves computational costs compared to the more sophisticated drag-force-based multiphase models. Thus, complex three-dimensional flow structures can be simulated while accounting for the pressure- and shear-rate-dependent rheology.

  8. The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements.

    PubMed

    Daszkiewicz, Karol; Maquer, Ghislain; Zysset, Philippe K

    2016-10-26

    Boundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from [Formula: see text] scans of femoral heads and vertebral bodies. They were converted into [Formula: see text] models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs- and KUBCs-based tensors were determined for each sample. "In situ" stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset-Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors, and model parameters [Formula: see text] (Poisson's ratio) [Formula: see text] and [Formula: see text] (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on [Formula: see text]. However, KUBCs- and PMUBCs-based [Formula: see text] and [Formula: see text], respectively, decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.

  9. Numerical implementation of energy-based models in finite element analysis

    NASA Astrophysics Data System (ADS)

    Chattonjai, Piyachat

    2016-06-01

    Soil is one of the most complex materials including several characteristics which are not only effect on stress-strain relationship but also volume changed such as contraction and dilation. Those characteristics depend on so many factors such as stress history, drained condition, current effective stress state, stress paths as well as void ratio, etc. In finite element analysis, the relevant constitutive model which includes relevant factors as mentioned above is one of the main key that will provide the accurate predicting of strength and deformation characteristic of geotechnical structure. For modern finite element program, the user-defined material subroutines have been provided when the material models included in the material library could not accurately predict the rather complex behavior of material. The objective of this study is to implement the elasto-plastic work-hardening-softening constitutive model into ABAQUS via VUMAT subroutine. The simulated results were verified by the experimental results of Toyoura sand under plane strain condition.

  10. Implementation of the NCAR Community Land Model (CLM) in the NASA/NCAR finite-volume Global Climate Model (fvGCM)

    NASA Technical Reports Server (NTRS)

    Radakovich, Jon D.; Wang, Guiling; Chern, Jiundar; Bosilovich, Michael G.; Lin, Shian-Jiann; Nebuda, Sharon; Shen, Bo-Wen

    2002-01-01

    In this study, the NCAR CLM version 2.0 land-surface model was integrated into the NASA/NCAR fvGCM. The CLM was developed collaboratively by an open interagency/university group of scientists and based on well-proven physical parameterizations and numerical schemes that combine the best features of BATS, NCAR-LSM, and IAP94. The CLM design is a one-dimensional point model with 1 vegetation layer, along with sub-grid scale tiles. The features of the CLM include 10-uneven soil layers with water, ice, and temperature states in each soil layer, and five snow layers, with water flow, refreezing, compaction, and aging allowed. In addition, the CLM utilizes two-stream canopy radiative transfer, the Bonan lake model and topographic enhanced streamflow based on TOPMODEL. The DAO fvGCM uses a genuinely conservative Flux-Form Semi-Lagrangian transport algorithm along with terrain- following Lagrangian control-volume vertical coordinates. The physical parameterizations are based on the NCAR Community Atmosphere Model (CAM-2). For our purposes, the fvGCM was run at 2 deg x 2.5 deg horizontal resolution with 55 vertical levels. The 10-year climate from the fvGCM with CLM2 was intercompared with the climate from fvGCM with LSM, ECMWF and NCEP. We concluded that the incorporation of CLM2 did not significantly impact the fvGCM climate from that of LSM. The most striking difference was the warm bias in the CLM2 surface skin temperature over desert regions. We determined that the warm bias can be partially attributed to the value of the drag coefficient for the soil under the canopy, which was too small resulting in a decoupling between the ground surface and the canopy. We also discovered that the canopy interception was high compared to observations in the Amazon region. A number of experiments were then performed focused on implementing model improvements. In order to correct the warm bias, the drag coefficient for the soil under the canopy was considered a function of LAI (Leaf

  11. 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

  12. Acoustic Treatment Design Scaling Methods. Volume 4; Numerical Simulation of the Nonlinear Acoustic Impedance of a Perforated Plate Single-Degree-of-Freedom Resonator Using a Time-Domain Finite Difference Method

    NASA Technical Reports Server (NTRS)

    Kraft, R. E.

    1999-01-01

    Single-degree-of-freedom resonators consisting of honeycomb cells covered by perforated facesheets are widely used as acoustic noise suppression liners in aircraft engine ducts. The acoustic resistance and mass reactance of such liners are known to vary with the intensity of the sound incident upon the panel. Since the pressure drop across a perforated liner facesheet increases quadratically with the flow velocity through the facesheet, this is known as the nonlinear resistance effect. In the past, two different empirical frequency domain models have been used to predict the Sound Pressure Level effect of the incident wave on the perforated liner impedance, one that uses the incident particle velocity in isolated narrowbands, and one that models the particle velocity as the overall velocity. In the absence of grazing flow, neither frequency domain model is entirely accurate in predicting the nonlinear effect that is measured for typical perforated sheets. The time domain model is developed in an attempt to understand and improve the model for the effect of spectral shape and amplitude of multi-frequency incident sound pressure on the liner impedance. A computer code for the time-domain finite difference model is developed and predictions using the models are compared to current frequency-domain models.

  13. A balanced-force finite-element method for surface-tension-driven interfacial flows using interface-capturing approaches

    NASA Astrophysics Data System (ADS)

    Xie, Zhihua; Pavlidis, Dimitrios; Percival, James; Gomes, Jefferson; Pain, Christopher; Matar, Omar

    2013-11-01

    Interfacial flows with surface tension are often found in industrial and practical engineering applications, including bubbles, droplets, liquid film and jets. Accurate modelling of such flows is challenging due to their highly complex dynamics, which often involve changes of interfacial topology. We present a balanced-force finite-element method with adaptive unstructured meshes for interfacial flows. The method uses a mixed control-volume and finite element formulation, which ensures the surface tension forces, and the resulting pressure gradients, are exactly balanced, minimising the spurious velocities often found in numerical simulations of such flows. A volume-of-fluid-type method is employed for interface capturing based on a compressive control-volume advection method, and second-order finite element methods. A distance function is reconstructed from the volume fraction on the unstructured meshes, which provides accurate estimation of the curvature. Numerical examples of an equilibrium drop and dynamics of bubbles (droplets) are presented to demonstrate the capability of this method.

  14. Accurate monotone cubic interpolation

    NASA Technical Reports Server (NTRS)

    Huynh, Hung T.

    1991-01-01

    Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.

  15. ANSYS duplicate finite-element checker routine

    NASA Technical Reports Server (NTRS)

    Ortega, R.

    1995-01-01

    An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.

  16. Translation Invariant Extensions of Finite Volume Measures

    NASA Astrophysics Data System (ADS)

    Goldstein, S.; Kuna, T.; Lebowitz, J. L.; Speer, E. R.

    2017-02-01

    We investigate the following questions: Given a measure μ _Λ on configurations on a subset Λ of a lattice L, where a configuration is an element of Ω ^Λ for some fixed set Ω , does there exist a measure μ on configurations on all of L, invariant under some specified symmetry group of L, such that μ _Λ is its marginal on configurations on Λ ? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which L=Z^d and the symmetries are the translations. For the case in which Λ is an interval in Z we give a simple necessary and sufficient condition, local translation invariance ( LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which L is the Bethe lattice. On Z we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When Λ subset Z is not an interval, or when Λ subset Z^d with d>1, the LTI condition is necessary but not sufficient for extendibility. For Z^d with d>1, extendibility is in some sense undecidable.

  17. Finite Volume Algorithms for Heat Conduction

    DTIC Science & Technology

    2010-05-01

    2010. TABLE OF CONTENTS Section Page 1.0 INTRODUCTION ...4 1.0 INTRODUCTION The transfer of heat has been of great interest within the engineering and scientific communities for...31 REFERENCES 1. Shames, Irving, Introduction to Solid Mechanics, Prentice Hall, Englewood Cliffs, N.J., 1975, pp.69-71

  18. Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer

    NASA Astrophysics Data System (ADS)

    Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian

    2015-10-01

    Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.

  19. Performance of Two Cloud-Radiation Parameterization Schemes in the Finite Volume General Circulation Model for Anomalously Wet May and June 2003 Over the Continental United States and Amazonia

    NASA Technical Reports Server (NTRS)

    Sud, Y. C.; Mocko, David M.; Lin, S. J.

    2006-01-01

    An objective assessment of the impact of a new cloud scheme, called Microphysics of Clouds with Relaxed Arakawa-Schubert Scheme (McRAS) (together with its radiation modules), on the finite volume general circulation model (fvGCM) was made with a set of ensemble forecasts that invoke performance evaluation over both weather and climate timescales. The performance of McRAS (and its radiation modules) was compared with that of the National Center for Atmospheric Research Community Climate Model (NCAR CCM3) cloud scheme (with its NCAR physics radiation). We specifically chose the boreal summer months of May and June 2003, which were characterized by an anomalously wet eastern half of the continental United States as well as northern regions of Amazonia. The evaluation employed an ensemble of 70 daily 10-day forecasts covering the 61 days of the study period. Each forecast was started from the analyzed initial state of the atmosphere and spun-up soil moisture from the first-day forecasts with the model. Monthly statistics of these forecasts with up to 10-day lead time provided a robust estimate of the behavior of the simulated monthly rainfall anomalies. Patterns of simulated versus observed rainfall, 500-hPa heights, and top-of-the-atmosphere net radiation were recast into regional anomaly correlations. The correlations were compared among the simulations with each of the schemes. The results show that fvGCM with McRAS and its radiation package performed discernibly better than the original fvGCM with CCM3 cloud physics plus its radiation package. The McRAS cloud scheme also showed a reasonably positive response to the observed sea surface temperature on mean monthly rainfall fields at different time leads. This analysis represents a method for helpful systematic evaluation prior to selection of a new scheme in a global model.

  20. Accurate quantum chemical calculations

    NASA Technical Reports Server (NTRS)

    Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.; Taylor, Peter R.

    1989-01-01

    An important goal of quantum chemical calculations is to provide an understanding of chemical bonding and molecular electronic structure. A second goal, the prediction of energy differences to chemical accuracy, has been much harder to attain. First, the computational resources required to achieve such accuracy are very large, and second, it is not straightforward to demonstrate that an apparently accurate result, in terms of agreement with experiment, does not result from a cancellation of errors. Recent advances in electronic structure methodology, coupled with the power of vector supercomputers, have made it possible to solve a number of electronic structure problems exactly using the full configuration interaction (FCI) method within a subspace of the complete Hilbert space. These exact results can be used to benchmark approximate techniques that are applicable to a wider range of chemical and physical problems. The methodology of many-electron quantum chemistry is reviewed. Methods are considered in detail for performing FCI calculations. The application of FCI methods to several three-electron problems in molecular physics are discussed. A number of benchmark applications of FCI wave functions are described. Atomic basis sets and the development of improved methods for handling very large basis sets are discussed: these are then applied to a number of chemical and spectroscopic problems; to transition metals; and to problems involving potential energy surfaces. Although the experiences described give considerable grounds for optimism about the general ability to perform accurate calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.

  1. Keeping the edge: an accurate numerical method to solve the stream power law

    NASA Astrophysics Data System (ADS)

    Campforts, B.; Govers, G.

    2015-12-01

    Bedrock rivers set the base level of surrounding hill slopes and mediate the dynamic interplay between mountain building and denudation. The propensity of rivers to preserve pulses of increased tectonic uplift also allows to reconstruct long term uplift histories from longitudinal river profiles. An accurate reconstruction of river profile development at different timescales is therefore essential. Long term river development is typically modeled by means of the stream power law. Under specific conditions this equation can be solved analytically but numerical Finite Difference Methods (FDMs) are most frequently used. Nonetheless, FDMs suffer from numerical smearing, especially at knickpoint zones which are key to understand transient landscapes. Here, we solve the stream power law by means of a Finite Volume Method (FVM) which is Total Variation Diminishing (TVD). Total volume methods are designed to simulate sharp discontinuities making them very suitable to model river incision. In contrast to FDMs, the TVD_FVM is well capable of preserving knickpoints as illustrated for the fast propagating Niagara falls. Moreover, we show that the TVD_FVM performs much better when reconstructing uplift at timescales exceeding 100 Myr, using Eastern Australia as an example. Finally, uncertainty associated with parameter calibration is dramatically reduced when the TVD_FVM is applied. Therefore, the use of a TVD_FVM to understand long term landscape evolution is an important addition to the toolbox at the disposition of geomorphologists.

  2. BIOACCESSIBILITY TESTS ACCURATELY ESTIMATE ...

    EPA Pesticide Factsheets

    Hazards of soil-borne Pb to wild birds may be more accurately quantified if the bioavailability of that Pb is known. To better understand the bioavailability of Pb to birds, we measured blood Pb concentrations in Japanese quail (Coturnix japonica) fed diets containing Pb-contaminated soils. Relative bioavailabilities were expressed by comparison with blood Pb concentrations in quail fed a Pb acetate reference diet. Diets containing soil from five Pb-contaminated Superfund sites had relative bioavailabilities from 33%-63%, with a mean of about 50%. Treatment of two of the soils with P significantly reduced the bioavailability of Pb. The bioaccessibility of the Pb in the test soils was then measured in six in vitro tests and regressed on bioavailability. They were: the “Relative Bioavailability Leaching Procedure” (RBALP) at pH 1.5, the same test conducted at pH 2.5, the “Ohio State University In vitro Gastrointestinal” method (OSU IVG), the “Urban Soil Bioaccessible Lead Test”, the modified “Physiologically Based Extraction Test” and the “Waterfowl Physiologically Based Extraction Test.” All regressions had positive slopes. Based on criteria of slope and coefficient of determination, the RBALP pH 2.5 and OSU IVG tests performed very well. Speciation by X-ray absorption spectroscopy demonstrated that, on average, most of the Pb in the sampled soils was sorbed to minerals (30%), bound to organic matter 24%, or present as Pb sulfate 18%. Ad

  3. A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

    NASA Astrophysics Data System (ADS)

    Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

    2015-12-01

    Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties

  4. Monte Carlo Computation of the Finite-Size Scaling Function: an Alternative Approach

    NASA Astrophysics Data System (ADS)

    Kim, Jae-Kwon; de Souza, Adauto J. F.; Landau, D. P.

    1996-03-01

    We show how to compute numerically a finite-size-scaling function which is particularly effective in extracting accurate infinite- volume -limit values (bulk values) of certain physical quantities^1. We illustrate our procedure for the two and three dimensional Ising models, and report our bulk values for the correlation lenth, magnetic susceptibility, and renormalized four-point coupling constant. Based on these bulk values we extract the values of various critical parameters. ^1 J.-K. Kim, Euro. Phys. Lett. 28, 211 (1994) Research supported in part by the NSF ^Permanent address: Departmento de Fisica e Matematica, Universidade Federal Rural de Pernambuco, 52171-900, Recife, Pernambuco, Brazil

  5. Accurate spectral color measurements

    NASA Astrophysics Data System (ADS)

    Hiltunen, Jouni; Jaeaeskelaeinen, Timo; Parkkinen, Jussi P. S.

    1999-08-01

    Surface color measurement is of importance in a very wide range of industrial applications including paint, paper, printing, photography, textiles, plastics and so on. For a demanding color measurements spectral approach is often needed. One can measure a color spectrum with a spectrophotometer using calibrated standard samples as a reference. Because it is impossible to define absolute color values of a sample, we always work with approximations. The human eye can perceive color difference as small as 0.5 CIELAB units and thus distinguish millions of colors. This 0.5 unit difference should be a goal for the precise color measurements. This limit is not a problem if we only want to measure the color difference of two samples, but if we want to know in a same time exact color coordinate values accuracy problems arise. The values of two instruments can be astonishingly different. The accuracy of the instrument used in color measurement may depend on various errors such as photometric non-linearity, wavelength error, integrating sphere dark level error, integrating sphere error in both specular included and specular excluded modes. Thus the correction formulas should be used to get more accurate results. Another question is how many channels i.e. wavelengths we are using to measure a spectrum. It is obvious that the sampling interval should be short to get more precise results. Furthermore, the result we get is always compromise of measuring time, conditions and cost. Sometimes we have to use portable syste or the shape and the size of samples makes it impossible to use sensitive equipment. In this study a small set of calibrated color tiles measured with the Perkin Elmer Lamda 18 and the Minolta CM-2002 spectrophotometers are compared. In the paper we explain the typical error sources of spectral color measurements, and show which are the accuracy demands a good colorimeter should have.

  6. Accurate shear measurement with faint sources

    SciTech Connect

    Zhang, Jun; Foucaud, Sebastien; Luo, Wentao E-mail: walt@shao.ac.cn

    2015-01-01

    For cosmic shear to become an accurate cosmological probe, systematic errors in the shear measurement method must be unambiguously identified and corrected for. Previous work of this series has demonstrated that cosmic shears can be measured accurately in Fourier space in the presence of background noise and finite pixel size, without assumptions on the morphologies of galaxy and PSF. The remaining major source of error is source Poisson noise, due to the finiteness of source photon number. This problem is particularly important for faint galaxies in space-based weak lensing measurements, and for ground-based images of short exposure times. In this work, we propose a simple and rigorous way of removing the shear bias from the source Poisson noise. Our noise treatment can be generalized for images made of multiple exposures through MultiDrizzle. This is demonstrated with the SDSS and COSMOS/ACS data. With a large ensemble of mock galaxy images of unrestricted morphologies, we show that our shear measurement method can achieve sub-percent level accuracy even for images of signal-to-noise ratio less than 5 in general, making it the most promising technique for cosmic shear measurement in the ongoing and upcoming large scale galaxy surveys.

  7. Second-order accurate nonoscillatory schemes for scalar conservation laws

    NASA Technical Reports Server (NTRS)

    Huynh, Hung T.

    1989-01-01

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

  8. A highly accurate dynamic contact angle algorithm for drops on inclined surface based on ellipse-fitting.

    PubMed

    Xu, Z N; Wang, S Y

    2015-02-01

    To improve the accuracy in the calculation of dynamic contact angle for drops on the inclined surface, a significant number of numerical drop profiles on the inclined surface with different inclination angles, drop volumes, and contact angles are generated based on the finite difference method, a least-squares ellipse-fitting algorithm is used to calculate the dynamic contact angle. The influences of the above three factors are systematically investigated. The results reveal that the dynamic contact angle errors, including the errors of the left and right contact angles, evaluated by the ellipse-fitting algorithm tend to increase with inclination angle/drop volume/contact angle. If the drop volume and the solid substrate are fixed, the errors of the left and right contact angles increase with inclination angle. After performing a tremendous amount of computation, the critical dimensionless drop volumes corresponding to the critical contact angle error are obtained. Based on the values of the critical volumes, a highly accurate dynamic contact angle algorithm is proposed and fully validated. Within nearly the whole hydrophobicity range, it can decrease the dynamic contact angle error in the inclined plane method to less than a certain value even for different types of liquids.

  9. Multichannel 02 and 12 transition amplitudes for arbitrary spin particles in a finite volume

    SciTech Connect

    Hansen, Maxwell; Briceno, Raul

    2015-10-01

    We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volume $\\textbf{0}\\rightarrow\\textbf{2}$ 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.

  10. Accurate Determination of the Volume of an Irregular Helium Balloon

    ERIC Educational Resources Information Center

    Blumenthal, Jack; Bradvica, Rafaela; Karl, Katherine

    2013-01-01

    In a recent paper, Zable described an experiment with a near-spherical balloon filled with impure helium. Measuring the temperature and the pressure inside and outside the balloon, the lift of the balloon, and the mass of the balloon materials, he described how to use the ideal gas laws and Archimedes' principal to compute the average molecular…

  11. Towards an accurate volume reconstruction in atom probe tomography.

    PubMed

    Beinke, Daniel; Oberdorfer, Christian; Schmitz, Guido

    2016-06-01

    An alternative concept for the reconstruction of atom probe data is outlined. It is based on the calculation of realistic trajectories of the evaporated ions in a recursive refinement process. To this end, the electrostatic problem is solved on a Delaunay tessellation. To enable the trajectory calculation, the order of reconstruction is inverted with respect to previous reconstruction schemes: the last atom detected is reconstructed first. In this way, the emitter shape, which controls the trajectory, can be defined throughout the duration of the reconstruction. A proof of concept is presented for 3D model tips, containing spherical precipitates or embedded layers of strongly contrasting evaporation thresholds. While the traditional method following Bas et al. generates serious distortions in these cases, a reconstruction with the proposed electrostatically informed approach improves the geometry of layers and particles significantly.

  12. Hybrid finite element-finite difference method for thermal analysis of blood vessels.

    PubMed

    Blanchard, C H; Gutierrez, G; White, J A; Roemer, R B

    2000-01-01

    A hybrid finite-difference/finite-element technique for the thermal analysis of blood vessels embedded in perfused tissue has been developed and evaluated. This method provides efficient and accurate solutions to the conjugated heat transfer problem of convection by blood coupled to conduction in the tissue. The technique uses a previously developed 3D automatic meshing method for creating a finite element mesh in the tissue surrounding the vessels, coupled iteratively with a 1-D marching finite difference method for the interior of the vessels. This hybrid technique retains the flexibility and ease of automated finite-element meshing techniques for modelling the complex geometry of blood vessels and irregularly shaped tissues, and speeds the solution time by using a simple finite-difference method to calculate the bulk mean temperatures within all blood vessels. The use of the 1D finite-difference technique in the blood vessels also eliminates the large computer memory requirements needed to accurately solve large vessel network problems when fine FE meshes are used in the interior of vessels. The accuracy of the hybrid technique has been verified against previously verified numerical solutions. In summary, the hybrid technique combines the accuracy and flexibility found in automated finite-element techniques, with the speed and reduction of computational memory requirements associated with the 1D finite-difference technique, something which has not been done before. This method, thus, has the potential to provide accurate, flexible and relatively fast solutions for the thermal analysis of coupled perfusion/blood vessel problems, and large vessel network problems.

  13. Modeling anisotropic flow and heat transport by using mimetic finite differences

    NASA Astrophysics Data System (ADS)

    Chen, Tao; Clauser, Christoph; Marquart, Gabriele; Willbrand, Karen; Büsing, Henrik

    2016-08-01

    Modeling anisotropic flow in porous or fractured rock often assumes that the permeability tensor is diagonal, which means that its principle directions are always aligned with the coordinate axes. However, the permeability of a heterogeneous anisotropic medium usually is a full tensor. For overcoming this shortcoming, we use the mimetic finite difference method (mFD) for discretizing the flow equation in a hydrothermal reservoir simulation code, SHEMAT-Suite, which couples this equation with the heat transport equation. We verify SHEMAT-Suite-mFD against analytical solutions of pumping tests, using both diagonal and full permeability tensors. We compare results from three benchmarks for testing the capability of SHEMAT-Suite-mFD to handle anisotropic flow in porous and fractured media. The benchmarks include coupled flow and heat transport problems, three-dimensional problems and flow through a fractured porous medium with full equivalent permeability tensor. It shows firstly that the mimetic finite difference method can model anisotropic flow both in porous and in fractured media accurately and its results are better than those obtained by the multi-point flux approximation method in highly anisotropic models, secondly that the asymmetric permeability tensor can be included and leads to improved results compared the symmetric permeability tensor in the equivalent fracture models, and thirdly that the method can be easily implemented in existing finite volume or finite difference codes, which has been demonstrated successfully for SHEMAT-Suite.

  14. Accurate source location from waves scattered by surface topography

    NASA Astrophysics Data System (ADS)

    Wang, Nian; Shen, Yang; Flinders, Ashton; Zhang, Wei

    2016-06-01

    Accurate source locations of earthquakes and other seismic events are fundamental in seismology. The location accuracy is limited by several factors, including velocity models, which are often poorly known. In contrast, surface topography, the largest velocity contrast in the Earth, is often precisely mapped at the seismic wavelength (>100 m). In this study, we explore the use of P coda waves generated by scattering at surface topography to obtain high-resolution locations of near-surface seismic events. The Pacific Northwest region is chosen as an example to provide realistic topography. A grid search algorithm is combined with the 3-D strain Green's tensor database to improve search efficiency as well as the quality of hypocenter solutions. The strain Green's tensor is calculated using a 3-D collocated-grid finite difference method on curvilinear grids. Solutions in the search volume are obtained based on the least squares misfit between the "observed" and predicted P and P coda waves. The 95% confidence interval of the solution is provided as an a posteriori error estimation. For shallow events tested in the study, scattering is mainly due to topography in comparison with stochastic lateral velocity heterogeneity. The incorporation of P coda significantly improves solution accuracy and reduces solution uncertainty. The solution remains robust with wide ranges of random noises in data, unmodeled random velocity heterogeneities, and uncertainties in moment tensors. The method can be extended to locate pairs of sources in close proximity by differential waveforms using source-receiver reciprocity, further reducing errors caused by unmodeled velocity structures.

  15. Finite Element Interface to Linear Solvers

    SciTech Connect

    Williams, Alan

    2005-03-18

    Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on the problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.

  16. Accurate and precise determination of critical properties from Gibbs ensemble Monte Carlo simulations

    SciTech Connect

    Dinpajooh, Mohammadhasan; Bai, Peng; Allan, Douglas A.; Siepmann, J. Ilja

    2015-09-21

    Since the seminal paper by Panagiotopoulos [Mol. Phys. 61, 813 (1997)], the Gibbs ensemble Monte Carlo (GEMC) method has been the most popular particle-based simulation approach for the computation of vapor–liquid phase equilibria. However, the validity of GEMC simulations in the near-critical region has been questioned because rigorous finite-size scaling approaches cannot be applied to simulations with fluctuating volume. Valleau [Mol. Simul. 29, 627 (2003)] has argued that GEMC simulations would lead to a spurious overestimation of the critical temperature. More recently, Patel et al. [J. Chem. Phys. 134, 024101 (2011)] opined that the use of analytical tail corrections would be problematic in the near-critical region. To address these issues, we perform extensive GEMC simulations for Lennard-Jones particles in the near-critical region varying the system size, the overall system density, and the cutoff distance. For a system with N = 5500 particles, potential truncation at 8σ and analytical tail corrections, an extrapolation of GEMC simulation data at temperatures in the range from 1.27 to 1.305 yields T{sub c} = 1.3128 ± 0.0016, ρ{sub c} = 0.316 ± 0.004, and p{sub c} = 0.1274 ± 0.0013 in excellent agreement with the thermodynamic limit determined by Potoff and Panagiotopoulos [J. Chem. Phys. 109, 10914 (1998)] using grand canonical Monte Carlo simulations and finite-size scaling. Critical properties estimated using GEMC simulations with different overall system densities (0.296 ≤ ρ{sub t} ≤ 0.336) agree to within the statistical uncertainties. For simulations with tail corrections, data obtained using r{sub cut} = 3.5σ yield T{sub c} and p{sub c} that are higher by 0.2% and 1.4% than simulations with r{sub cut} = 5 and 8σ but still with overlapping 95% confidence intervals. In contrast, GEMC simulations with a truncated and shifted potential show that r{sub cut} = 8σ is insufficient to obtain accurate results. Additional GEMC simulations for hard

  17. Partial volume effect modeling for segmentation and tissue classification of brain magnetic resonance images: A review.

    PubMed

    Tohka, Jussi

    2014-11-28

    Quantitative analysis of magnetic resonance (MR) brain images are facilitated by the development of automated segmentation algorithms. A single image voxel may contain of several types of tissues due to the finite spatial resolution of the imaging device. This phenomenon, termed partial volume effect (PVE), complicates the segmentation process, and, due to the complexity of human brain anatomy, the PVE is an important factor for accurate brain structure quantification. Partial volume estimation refers to a generalized segmentation task where the amount of each tissue type within each voxel is solved. This review aims to provide a systematic, tutorial-like overview and categorization of methods for partial volume estimation in brain MRI. The review concentrates on the statistically based approaches for partial volume estimation and also explains differences to other, similar image segmentation approaches.

  18. Monte Carlo method for critical systems in infinite volume: The planar Ising model.

    PubMed

    Herdeiro, Victor; Doyon, Benjamin

    2016-10-01

    In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated to generating critical distributions on finite lattices. It uses the advantage of scale invariance combined with ideas of the renormalization group in order to construct a type of "holographic" boundary condition that encodes the presence of an infinite volume beyond it. We check the quality of the distribution obtained in the case of the planar Ising model by comparing various observables with their infinite-plane prediction. We accurately reproduce planar two-, three-, and four-point of spin and energy operators. We also define a lattice stress-energy tensor, and numerically obtain the associated conformal Ward identities and the Ising central charge.

  19. Direct interval volume visualization.

    PubMed

    Ament, Marco; Weiskopf, Daniel; Carr, Hamish

    2010-01-01

    We extend direct volume rendering with a unified model for generalized isosurfaces, also called interval volumes, allowing a wider spectrum of visual classification. We generalize the concept of scale-invariant opacity—typical for isosurface rendering—to semi-transparent interval volumes. Scale-invariant rendering is independent of physical space dimensions and therefore directly facilitates the analysis of data characteristics. Our model represents sharp isosurfaces as limits of interval volumes and combines them with features of direct volume rendering. Our objective is accurate rendering, guaranteeing that all isosurfaces and interval volumes are visualized in a crack-free way with correct spatial ordering. We achieve simultaneous direct and interval volume rendering by extending preintegration and explicit peak finding with data-driven splitting of ray integration and hybrid computation in physical and data domains. Our algorithm is suitable for efficient parallel processing for interactive applications as demonstrated by our CUDA implementation.

  20. On the accurate simulation of tsunami wave propagation

    NASA Astrophysics Data System (ADS)

    Castro, C. E.; Käser, M.; Toro, E. F.

    2009-04-01

    A very important part of any tsunami early warning system is the numerical simulation of the wave propagation in the open sea and close to geometrically complex coastlines respecting bathymetric variations. Here we are interested in improving the numerical tools available to accurately simulate tsunami wave propagation on a Mediterranean basin scale. To this end, we need to accomplish some targets, such as: high-order numerical simulation in space and time, preserve steady state conditions to avoid spurious oscillations and describe complex geometries due to bathymetry and coastlines. We use the Arbitrary accuracy DERivatives Riemann problem method together with Finite Volume method (ADER-FV) over non-structured triangular meshes. The novelty of this method is the improvement of the ADER-FV scheme, introducing the well-balanced property when geometrical sources are considered for unstructured meshes and arbitrary high-order accuracy. In a previous work from Castro and Toro [1], the authors mention that ADER-FV schemes approach asymptotically the well-balanced condition, which was true for the test case mentioned in [1]. However, new evidence[2] shows that for real scale problems as the Mediterranean basin, and considering realistic bathymetry as ETOPO-2[3], this asymptotic behavior is not enough. Under these realistic conditions the standard ADER-FV scheme fails to accurately describe the propagation of gravity waves without being contaminated with spurious oscillations, also known as numerical waves. The main problem here is that at discrete level, i.e. from a numerical point of view, the numerical scheme does not correctly balance the influence of the fluxes and the sources. Numerical schemes that retain this balance are said to satisfy the well-balanced property or the exact C-property. This unbalance reduces, as we refine the spatial discretization or increase the order of the numerical method. However, the computational cost increases considerably this way

  1. Simple Finite Jordan Pseudoalgebras

    NASA Astrophysics Data System (ADS)

    Kolesnikov, Pavel

    2009-01-01

    We consider the structure of Jordan H-pseudoalgebras which are linearly finitely generated over a Hopf algebra H. There are two cases under consideration: H = U(h) and H = U(h) # C[Γ], where h is a finite-dimensional Lie algebra over C, Γ is an arbitrary group acting on U(h) by automorphisms. We construct an analogue of the Tits-Kantor-Koecher construction for finite Jordan pseudoalgebras and describe all simple ones.

  2. Accurate simulation of transient landscape evolution by eliminating numerical diffusion: the TTLEM 1.0 model

    NASA Astrophysics Data System (ADS)

    Campforts, Benjamin; Schwanghart, Wolfgang; Govers, Gerard

    2017-01-01

    Landscape evolution models (LEMs) allow the study of earth surface responses to changing climatic and tectonic forcings. While much effort has been devoted to the development of LEMs that simulate a wide range of processes, the numerical accuracy of these models has received less attention. Most LEMs use first-order accurate numerical methods that suffer from substantial numerical diffusion. Numerical diffusion particularly affects the solution of the advection equation and thus the simulation of retreating landforms such as cliffs and river knickpoints. This has potential consequences for the integrated response of the simulated landscape. Here we test a higher-order flux-limiting finite volume method that is total variation diminishing (TVD-FVM) to solve the partial differential equations of river incision and tectonic displacement. We show that using the TVD-FVM to simulate river incision significantly influences the evolution of simulated landscapes and the spatial and temporal variability of catchment-wide erosion rates. Furthermore, a two-dimensional TVD-FVM accurately simulates the evolution of landscapes affected by lateral tectonic displacement, a process whose simulation was hitherto largely limited to LEMs with flexible spatial discretization. We implement the scheme in TTLEM (TopoToolbox Landscape Evolution Model), a spatially explicit, raster-based LEM for the study of fluvially eroding landscapes in TopoToolbox 2.

  3. Does a pneumotach accurately characterize voice function?

    NASA Astrophysics Data System (ADS)

    Walters, Gage; Krane, Michael

    2016-11-01

    A study is presented which addresses how a pneumotach might adversely affect clinical measurements of voice function. A pneumotach is a device, typically a mask, worn over the mouth, in order to measure time-varying glottal volume flow. By measuring the time-varying difference in pressure across a known aerodynamic resistance element in the mask, the glottal volume flow waveform is estimated. Because it adds aerodynamic resistance to the vocal system, there is some concern that using a pneumotach may not accurately portray the behavior of the voice. To test this hypothesis, experiments were performed in a simplified airway model with the principal dimensions of an adult human upper airway. A compliant constriction, fabricated from silicone rubber, modeled the vocal folds. Variations of transglottal pressure, time-averaged volume flow, model vocal fold vibration amplitude, and radiated sound with subglottal pressure were performed, with and without the pneumotach in place, and differences noted. Acknowledge support of NIH Grant 2R01DC005642-10A1.

  4. Accurate Biomass Estimation via Bayesian Adaptive Sampling

    NASA Astrophysics Data System (ADS)

    Wheeler, K.; Knuth, K.; Castle, P.

    2005-12-01

    and IKONOS imagery and the 3-D volume estimates. The combination of these then allow for a rapid and hopefully very accurate estimation of biomass.

  5. QUARKONIUM AT FINITE TEMPERATURE.

    SciTech Connect

    UMEDA, T.

    2006-06-09

    Lattice QCD studies on charmonium at finite temperature are presented After a discussion about problems for the Maximum Entropy Method applied to finite temperature lattice QCD, I show several results on charmonium spectral functions. The 'wave function' of charmonium is also discussed to study the spatial correlation between quark and anti-quark in deconfinement phase.

  6. Finite Control in Korean

    ERIC Educational Resources Information Center

    Lee, Kum Young

    2009-01-01

    This thesis explores finite control in Korean. An overview of the previous studies of control shows that the mainstream literature on control has consistently argued that referential dependence between an overt matrix argument and an embedded null subject is characteristic of non-finite clauses which contain a PRO subject. Moreover, although some…

  7. Modeling nuclear volume isotope effects in crystals.

    PubMed

    Schauble, Edwin A

    2013-10-29

    Mass-independent isotope fractionations driven by differences in volumes and shapes of nuclei (the field shift effect) are known in several elements and are likely to be found in more. All-electron relativistic electronic structure calculations can predict this effect but at present are computationally intensive and limited to modeling small gas phase molecules and clusters. Density functional theory, using the projector augmented wave method (DFT-PAW), has advantages in greater speed and compatibility with a three-dimensional periodic boundary condition while preserving information about the effects of chemistry on electron densities within nuclei. These electron density variations determine the volume component of the field shift effect. In this study, DFT-PAW calculations are calibrated against all-electron, relativistic Dirac-Hartree-Fock, and coupled-cluster with single, double (triple) excitation methods for estimating nuclear volume isotope effects. DFT-PAW calculations accurately reproduce changes in electron densities within nuclei in typical molecules, when PAW datasets constructed with finite nuclei are used. Nuclear volume contributions to vapor-crystal isotope fractionation are calculated for elemental cadmium and mercury, showing good agreement with experiments. The nuclear-volume component of mercury and cadmium isotope fractionations between atomic vapor and montroydite (HgO), cinnabar (HgS), calomel (Hg2Cl2), monteponite (CdO), and the CdS polymorphs hawleyite and greenockite are calculated, indicating preferential incorporation of neutron-rich isotopes in more oxidized, ionically bonded phases. Finally, field shift energies are related to Mössbauer isomer shifts, and equilibrium mass-independent fractionations for several tin-bearing crystals are calculated from (119)Sn spectra. Isomer shift data should simplify calculations of mass-independent isotope fractionations in other elements with Mössbauer isotopes, such as platinum and uranium.

  8. Modeling nuclear volume isotope effects in crystals

    NASA Astrophysics Data System (ADS)

    Schauble, Edwin A.

    2013-10-01

    Mass-independent isotope fractionations driven by differences in volumes and shapes of nuclei (the field shift effect) are known in several elements and are likely to be found in more. All-electron relativistic electronic structure calculations can predict this effect but at present are computationally intensive and limited to modeling small gas phase molecules and clusters. Density functional theory, using the projector augmented wave method (DFT-PAW), has advantages in greater speed and compatibility with a three-dimensional periodic boundary condition while preserving information about the effects of chemistry on electron densities within nuclei. These electron density variations determine the volume component of the field shift effect. In this study, DFT-PAW calculations are calibrated against all-electron, relativistic Dirac-Hartree-Fock, and coupled-cluster with single, double (triple) excitation methods for estimating nuclear volume isotope effects. DFT-PAW calculations accurately reproduce changes in electron densities within nuclei in typical molecules, when PAW datasets constructed with finite nuclei are used. Nuclear volume contributions to vapor-crystal isotope fractionation are calculated for elemental cadmium and mercury, showing good agreement with experiments. The nuclear-volume component of mercury and cadmium isotope fractionations between atomic vapor and montroydite (HgO), cinnabar (HgS), calomel (Hg2Cl2), monteponite (CdO), and the CdS polymorphs hawleyite and greenockite are calculated, indicating preferential incorporation of neutron-rich isotopes in more oxidized, ionically bonded phases. Finally, field shift energies are related to Mössbauer isomer shifts, and equilibrium mass-independent fractionations for several tin-bearing crystals are calculated from 119Sn spectra. Isomer shift data should simplify calculations of mass-independent isotope fractionations in other elements with Mössbauer isotopes, such as platinum and uranium.

  9. Modeling nuclear volume isotope effects in crystals

    PubMed Central

    Schauble, Edwin A.

    2013-01-01

    Mass-independent isotope fractionations driven by differences in volumes and shapes of nuclei (the field shift effect) are known in several elements and are likely to be found in more. All-electron relativistic electronic structure calculations can predict this effect but at present are computationally intensive and limited to modeling small gas phase molecules and clusters. Density functional theory, using the projector augmented wave method (DFT-PAW), has advantages in greater speed and compatibility with a three-dimensional periodic boundary condition while preserving information about the effects of chemistry on electron densities within nuclei. These electron density variations determine the volume component of the field shift effect. In this study, DFT-PAW calculations are calibrated against all-electron, relativistic Dirac–Hartree–Fock, and coupled-cluster with single, double (triple) excitation methods for estimating nuclear volume isotope effects. DFT-PAW calculations accurately reproduce changes in electron densities within nuclei in typical molecules, when PAW datasets constructed with finite nuclei are used. Nuclear volume contributions to vapor–crystal isotope fractionation are calculated for elemental cadmium and mercury, showing good agreement with experiments. The nuclear-volume component of mercury and cadmium isotope fractionations between atomic vapor and montroydite (HgO), cinnabar (HgS), calomel (Hg2Cl2), monteponite (CdO), and the CdS polymorphs hawleyite and greenockite are calculated, indicating preferential incorporation of neutron-rich isotopes in more oxidized, ionically bonded phases. Finally, field shift energies are related to Mössbauer isomer shifts, and equilibrium mass-independent fractionations for several tin-bearing crystals are calculated from 119Sn spectra. Isomer shift data should simplify calculations of mass-independent isotope fractionations in other elements with Mössbauer isotopes, such as platinum and uranium

  10. Spray Combustion Modeling with VOF and Finite-Rate Chemistry

    NASA Technical Reports Server (NTRS)

    Chen, Yen-Sen; Shang, Huan-Min; Liaw, Paul; Wang, Ten-See

    1996-01-01

    A spray atomization and combustion model is developed based on the volume-of-fluid (VOF) transport equation with finite-rate chemistry model. The gas-liquid interface mass, momentum and energy conservation laws are modeled by continuum surface force mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed range flows. The objectives of the present study are: (1) to develop and verify the fractional volume-of-fluid (VOF) cell partitioning approach into a predictor-corrector algorithm to deal with multiphase (gas-liquid) free surface flow problems; (2) to implement the developed unified algorithm in a general purpose computational fluid dynamics (CFD) code, Finite Difference Navier-Stokes (FDNS), with droplet dynamics and finite-rate chemistry models; and (3) to demonstrate the effectiveness of the present approach by simulating benchmark problems of jet breakup/spray atomization and combustion. Modeling multiphase fluid flows poses a significant challenge because a required boundary must be applied to a transient, irregular surface that is discontinuous, and the flow regimes considered can range from incompressible to highspeed compressible flows. The flow-process modeling is further complicated by surface tension, interfacial heat and mass transfer, spray formation and turbulence, and their interactions. The major contribution of the present method is to combine the novel feature of the Volume of Fluid (VOF) method and the Eulerian/Lagrangian method into a unified algorithm for efficient noniterative, time-accurate calculations of multiphase free surface flows valid at all speeds. The proposed method reformulated the VOF equation to strongly couple two distinct phases (liquid and gas), and tracks droplets on a Lagrangian frame when spray model is required, using a unified predictor-corrector technique to account for the non-linear linkages through the convective contributions of VOF. The discontinuities within the

  11. Finite scale equations for compressible fluid flow

    SciTech Connect

    Margolin, Len G

    2008-01-01

    Finite-scale equations (FSE) describe the evolution of finite volumes of fluid over time. We discuss the FSE for a one-dimensional compressible fluid, whose every point is governed by the Navier-Stokes equations. The FSE contain new momentum and internal energy transport terms. These are similar to terms added in numerical simulation for high-speed flows (e.g. artificial viscosity) and for turbulent flows (e.g. subgrid scale models). These similarities suggest that the FSE may provide new insight as a basis for computational fluid dynamics. Our analysis of the FS continuity equation leads to a physical interpretation of the new transport terms, and indicates the need to carefully distinguish between volume-averaged and mass-averaged velocities in numerical simulation. We make preliminary connections to the other recent work reformulating Navier-Stokes equations.

  12. Effective thermal conductivity of metal and non-metal particulate composites with interfacial thermal resistance at high volume fraction of nano to macro-sized spheres

    SciTech Connect

    Faroughi, Salah Aldin; Huber, Christian

    2015-02-07

    In this study, we propose a theoretical model to compute the effective thermal conductivity of metal and dielectric spherical particle reinforced composites with interfacial thermal resistance. We consider a wide range of filler volume fraction with sizes ranging from nano- to macro-scale. The model, based on the differential effective medium theory, accounts for particle interactions through two sets of volume fraction corrections. The first correction accounts for a finite volume of composite and the second correction introduces a self-crowding factor that allows us to develop an accurate model for particle interaction even for high volume fraction of fillers. The model is examined to other published models, experiments, and numerical simulations for different types of composites. We observe an excellent agreement between the model and published datasets over a wide range of particle volume fractions and material properties of the composite constituents.

  13. Competition for finite resources

    NASA Astrophysics Data System (ADS)

    Cook, L. Jonathan; Zia, R. K. P.

    2012-05-01

    The resources in a cell are finite, which implies that the various components of the cell must compete for resources. One such resource is the ribosomes used during translation to create proteins. Motivated by this example, we explore this competition by connecting two totally asymmetric simple exclusion processes (TASEPs) to a finite pool of particles. Expanding on our previous work, we focus on the effects on the density and current of having different entry and exit rates.

  14. Electric impedance tomography for monitoring volume and size of the urinary bladder.

    PubMed

    Leonhardt, Steffen; Cordes, Axel; Plewa, Harry; Pikkemaat, Robert; Soljanik, Irina; Moehring, Klaus; Gerner, Hans J; Rupp, Rüdiger

    2011-12-01

    A novel non-invasive technique for monitoring fluid content in the human bladder is described. Specifically, a precommercial electric impedance tomograph (EIT) was applied to measure and visualize impedance changes in the lower torso due to changes in bladder volume. Preliminary measurements were conducted during routine urodynamic tests of nine male paraplegic patients, in whom a contrast agent was slowly infused into the bladder for diagnostic purposes. In some patients, a good correlation between bladder volume and EIT measurements was found, whereas in others the correlation was still good but inverted, presumably due to a poor electrode positioning. These preliminary results indicate that a sufficiently accurate finite element modeling of the impedance distribution in the abdomen, and proper electrode positioning aids, are important prerequisites to enable this technology to be used for routine measurement of bladder volume.

  15. LETTER TO THE EDITOR: Explicit finite inverse Hilbert transforms

    NASA Astrophysics Data System (ADS)

    You, Jiangsheng; Zeng, Gengsheng L.

    2006-06-01

    Recently, Noo and coworkers discovered an explicit inversion formula for the finite Hilbert transform, which is very important to accurate reconstruction from truncated projections. This letter presents two formulae for the finite inverse Hilbert transform using some elementary complex variable analysis. The new formulae do not contain the constant C and the singular endpoints that exist in the formula in Noo et al (2004 Phys. Med. Biol. 49 3903-23).

  16. Extension of the Mass-Conserving Level-Set method to unstructured polyhedral control volumes for two-phase flows

    NASA Astrophysics Data System (ADS)

    Raees, Fahim; van der Heul, Duncan R.; Vuik, Kees

    2013-11-01

    In this research, we present the Mass-Conserving Level-Set method (MCLS) for the simulation of two-dimensional, incompressible, immiscible two-phase flows, using a discretisation scheme that can accurately and efficiently handle domains of arbitrary geometrical complexity. The level set and the volume of fluid fraction are evolved at each time step on unstructured triangular grids. The Higher-Order Discontinuous Galerkin finite element method is used for spatial discretisation of the level set advection equation. The volume of fluid fraction advection is done in geometrical manner using Lagrangian-Eulerian method. This method is accurately mass conserving and easy to implement on unstructured grids. Also, it avoids overlapping regions during the volume of fluid fraction advection. The advected level set is corrected locally to make it mass conserving by the means of an explicit, invertible relation between the local level set and the volume of fluid fraction. This relation is termed as a Volume-of-Fluid function. The results show that proposed method is accurately mass conserving. Also, higher-order convergence is highlighted with this method on unstructured grids for the different test cases.

  17. Peridynamic Multiscale Finite Element Methods

    SciTech Connect

    Costa, Timothy; Bond, Stephen D.; Littlewood, David John; Moore, Stan Gerald

    2015-12-01

    The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the

  18. A free surface capturing discretization for the staggered grid finite difference scheme

    NASA Astrophysics Data System (ADS)

    Duretz, T.; May, D. A.; Yamato, P.

    2016-03-01

    The coupling that exists between surface processes and deformation within both the shallow crust and the deeper mantle-lithosphere has stimulated the development of computational geodynamic models that incorporate a free surface boundary condition. We introduce a treatment of this boundary condition that is suitable for staggered grid, finite difference schemes employing a structured Eulerian mesh. Our interface capturing treatment discretizes the free surface boundary condition via an interface that conforms with the edges of control volumes (e.g. a `staircase' representation) and requires only local stencil modifications to be performed. Comparisons with analytic solutions verify that the method is first-order accurate. Additional intermodel comparisons are performed between known reference models to further validate our free surface approximation. Lastly, we demonstrate the applicability of a multigrid solver to our free surface methodology and demonstrate that the local stencil modifications do not strongly influence the convergence of the iterative solver.

  19. Radiosity algorithms using higher order finite element methods

    SciTech Connect

    Troutman, R.; Max, N.

    1993-08-01

    Many of the current radiosity algorithms create a piecewise constant approximation to the actual radiosity. Through interpolation and extrapolation, a continuous solution is obtained. An accurate solution is found by increasing the number of patches which describe the scene. This has the effect of increasing the computation time as well as the memory requirements. By using techniques found in the finite element method, we can incorporate an interpolation function directly into our form factor computation. We can then use less elements to achieve a more accurate solution. Two algorithms, derived from the finite element method, are described and analyzed.

  20. Direct simulations of turbulent flow using finite-difference schemes

    NASA Technical Reports Server (NTRS)

    Rai, Man Mohan; Moin, Parviz

    1989-01-01

    A high-order accurate finite-difference approach is presented for calculating incompressible turbulent flow. The methods used include a kinetic energy conserving central difference scheme and an upwind difference scheme. The methods are evaluated in test cases for the evolution of small-amplitude disturbances and fully developed turbulent channel flow. It is suggested that the finite-difference approach can be applied to complex geometries more easilty than highly accurate spectral methods. It is concluded that the upwind scheme is a good candidate for direct simulations of turbulent flows over complex geometries.

  1. Finite-Temperature Micromagnetism

    SciTech Connect

    Skomski, R; Kumar, P; Hadjipanayis, GC; Sellmyer, DJ

    2013-07-01

    It is investigated how magnetic hysteresis is affected by finite-temperature excitations, using soft regions in hard-magnetic matrices as model systems. In lowest order, magnetization processes are described by the traditional approach of using finite-temperature materials constants such as K-1(T). Nanoscale excitations are usually small perturbations. For example, a Bloch summation over all magnon wave vectors shows that remanence is slightly enhanced, because long-wavelength excitations are suppressed. However, a reverse magnetic field enhances the effect of thermal excitations and causes a small reduction of the coercivity. To describe such effects, we advocate micromagnetic calculations where finite-temperature fluctuations are treated as small corrections to the traditional approach, as contrasted to full-scale Monte Carlo simulations.

  2. Finite difference time domain analysis of chirped dielectric gratings

    NASA Technical Reports Server (NTRS)

    Hochmuth, Diane H.; Johnson, Eric G.

    1993-01-01

    The finite difference time domain (FDTD) method for solving Maxwell's time-dependent curl equations is accurate, computationally efficient, and straight-forward to implement. Since both time and space derivatives are employed, the propagation of an electromagnetic wave can be treated as an initial-value problem. Second-order central-difference approximations are applied to the space and time derivatives of the electric and magnetic fields providing a discretization of the fields in a volume of space, for a period of time. The solution to this system of equations is stepped through time, thus, simulating the propagation of the incident wave. If the simulation is continued until a steady-state is reached, an appropriate far-field transformation can be applied to the time-domain scattered fields to obtain reflected and transmitted powers. From this information diffraction efficiencies can also be determined. In analyzing the chirped structure, a mesh is applied only to the area immediately around the grating. The size of the mesh is then proportional to the electric size of the grating. Doing this, however, imposes an artificial boundary around the area of interest. An absorbing boundary condition must be applied along the artificial boundary so that the outgoing waves are absorbed as if the boundary were absent. Many such boundary conditions have been developed that give near-perfect absorption. In this analysis, the Mur absorbing boundary conditions are employed. Several grating structures were analyzed using the FDTD method.

  3. Finite-size effects in nanocomposite thin films and fibers

    NASA Astrophysics Data System (ADS)

    Stevens, D. R.; Skau, E. W.; Downen, L. N.; Roman, M. P.; Clarke, L. I.

    2011-08-01

    Monte Carlo simulations of finite-size effects for continuum percolation in three-dimensional, rectangular sample spaces filled with spherical particles were performed. For samples with any dimension less than 10-20 times the particle diameter, finite-size effects were observed. For thin films in the finite-size regime, percolation across the thin direction of the film gave critical volume fraction (pc) values that differed from those along the plane of the film. Simulations perpendicular to the film for very thin samples resulted in pc values lower than the classical limit of ˜29% (for spheres in a three-dimensional matrix) which increased with film thickness. For percolation along thin films, while holding film thickness constant, pc increased with increasing sample size, which is a modification of the finite-sized scaling effect for cubic samples. For samples with a large aspect ratio (fibers) and a finite-sized cross-sectional area, the critical volume fraction increased with sample length, as the sample became quasi-one-dimensional. The results are discussed in the context of adding volume along or perpendicular to the percolation direction. From an experimental perspective, these findings indicate that sample shape, as well as relative size, influences percolation in the finite-size regime.

  4. The LLNL High Accuracy Volume Renderer for Unstructured Data: Capabilities, Current Limits, and Potential for ASCI/VIEWS Deployment

    SciTech Connect

    Williams, P L; Max, N L

    2001-06-04

    This report describes a volume rendering system for unstructured data, especially finite element data, that creates images with very high accuracy. The system will currently handle meshes whose cells are either linear or quadratic tetrahedra, or meshes with mixed cell types: tetrahedra, bricks, prisms, and pyramids. The cells may have nonplanar facets. Whenever possible, exact mathematical solutions for the radiance integrals and for interpolation are used. Accurate semitransparent shaded isosurfaces may be embedded in the volume rendering. For very small cells, subpixel accumulation by splatting is used to avoid sampling error. A new exact and efficient visibility ordering algorithm is described. The most accurate images are generated in software, however, more efficient algorithms utilizing graphics hardware may also be selected. The report describes the parallelization of the system for a distributed-shared memory multiprocessor machine, and concludes by discussing the system's limits, desirable future work, and ways to extend the system so as to be compatible with projected ASCI/VIEWS architectures.

  5. Pink-Beam, Highly-Accurate Compact Water Cooled Slits

    SciTech Connect

    Lyndaker, Aaron; Deyhim, Alex; Jayne, Richard; Waterman, Dave; Caletka, Dave; Steadman, Paul; Dhesi, Sarnjeet

    2007-01-19

    Advanced Design Consulting, Inc. (ADC) has designed accurate compact slits for applications where high precision is required. The system consists of vertical and horizontal slit mechanisms, a vacuum vessel which houses them, water cooling lines with vacuum guards connected to the individual blades, stepper motors with linear encoders, limit (home position) switches and electrical connections including internal wiring for a drain current measurement system. The total slit size is adjustable from 0 to 15 mm both vertically and horizontally. Each of the four blades are individually controlled and motorized. In this paper, a summary of the design and Finite Element Analysis of the system are presented.

  6. Extracting accurate strain measurements in bone mechanics: A critical review of current methods.

    PubMed

    Grassi, Lorenzo; Isaksson, Hanna

    2015-10-01

    Osteoporosis related fractures are a social burden that advocates for more accurate fracture prediction methods. Mechanistic methods, e.g. finite element models, have been proposed as a tool to better predict bone mechanical behaviour and strength. However, there is little consensus about the optimal constitutive law to describe bone as a material. Extracting reliable and relevant strain data from experimental tests is of fundamental importance to better understand bone mechanical properties, and to validate numerical models. Several techniques have been used to measure strain in experimental mechanics, with substantial differences in terms of accuracy, precision, time- and length-scale. Each technique presents upsides and downsides that must be carefully evaluated when designing the experiment. Moreover, additional complexities are often encountered when applying such strain measurement techniques to bone, due to its complex composite structure. This review of literature examined the four most commonly adopted methods for strain measurements (strain gauges, fibre Bragg grating sensors, digital image correlation, and digital volume correlation), with a focus on studies with bone as a substrate material, at the organ and tissue level. For each of them the working principles, a summary of the main applications to bone mechanics at the organ- and tissue-level, and a list of pros and cons are provided.

  7. A sharp interface in-cell-reconstruction method for volume tracking phase interfaces in compressible flows

    NASA Astrophysics Data System (ADS)

    Kedelty, Dominic; Ballesteros, Carlos; Chan, Ronald; Herrmann, Marcus

    2016-11-01

    To accurately predict the interaction of the interface with shocks and rarefaction waves, sharp interface methods maintaining the interface as a discontinuity are preferable to capturing methods that tend to smear the interface. We present a hybrid capturing/tracking method (Smiljanovski et al., 1997) that couples an unsplit geometric volume tracking method (Owkes & Desjardins, 2014) to a finite volume wave propagation scheme (LeVeque, 2010). In cells containing the phase interface, states on either side are reconstructed using the jump conditions across the interface, the geometric information of the volume tracking method, and the cell averages of the finite volume method. Cell face Riemann problems are then solved within each phase separately, resulting in area fraction weighted fluxes that update the cell averages directly. This, together with a linearization of the wave interaction across cell faces avoids the small cut-cell time step limitation of typical tracking methods. However, the interaction of waves with the phase interface cannot be linearized and is solved using either exact or approximate two-phase Riemann solvers with arbitrary jumps in the equation of state. Several test cases highlight the capabilities of the new method. Support by the 2016 CTR Summer program at Stanford University and Taitech, Inc. under subcontract TS15-16-02-005 is gratefully acknowledged.

  8. Accurate adjoint design sensitivities for nano metal optics.

    PubMed

    Hansen, Paul; Hesselink, Lambertus

    2015-09-07

    We present a method for obtaining accurate numerical design sensitivities for metal-optical nanostructures. Adjoint design sensitivity analysis, long used in fluid mechanics and mechanical engineering for both optimization and structural analysis, is beginning to be used for nano-optics design, but it fails for sharp-cornered metal structures because the numerical error in electromagnetic simulations of metal structures is highest at sharp corners. These locations feature strong field enhancement and contribute strongly to design sensitivities. By using high-accuracy FEM calculations and rounding sharp features to a finite radius of curvature we obtain highly-accurate design sensitivities for 3D metal devices. To provide a bridge to the existing literature on adjoint methods in other fields, we derive the sensitivity equations for Maxwell's equations in the PDE framework widely used in fluid mechanics.

  9. Uniformly high order accurate essentially non-oscillatory schemes 3

    NASA Technical Reports Server (NTRS)

    Harten, A.; Engquist, B.; Osher, S.; Chakravarthy, S. R.

    1986-01-01

    In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear.

  10. Simulations of weak gravitational lensing - II. Including finite support effects in cosmic shear covariance matrices

    NASA Astrophysics Data System (ADS)

    Harnois-Déraps, Joachim; van Waerbeke, Ludovic

    2015-07-01

    Numerical N-body simulations play a central role in the assessment of weak gravitational lensing statistics, residual systematics and error analysis. In this paper, we investigate and quantify the impact of finite simulation volume on weak lensing two- and four-point statistics. These finite support (FS) effects are modelled for several estimators, simulation box sizes and source redshifts, and validated against a new large suite of 500 N-body simulations. The comparison reveals that our theoretical model is accurate to better than 5 per cent for the shear correlation function ξ+(θ) and its error. We find that the most important quantities for FS modelling are the ratio between the measured angle θ and the angular size of the simulation box at the source redshift, θbox(zs), or the multipole equivalent ℓ/ℓbox(zs). When this ratio reaches 0.1, independently of the source redshift, the shear correlation function ξ+ is suppressed by 5, 10, 20 and 25 per cent for Lbox = 1000, 500, 250 and 147 h-1 Mpc, respectively. The same effect is observed in ξ-(θ), but at much larger angles. This has important consequences for cosmological analyses using N-body simulations and should not be overlooked. We propose simple semi-analytic correction strategies that account for shape noise and survey masks, generalizable to any weak lensing estimator. From the same simulation suite, we revisit the existing non-Gaussian covariance matrix calibration of the shear correlation function, and propose a new one based on the 9-year Wilkinson Microwave Anisotropy Probe)+baryon acoustic oscillations+supernova cosmology. Our calibration matrix is accurate at 20 per cent down to the arcminute scale, for source redshifts in the range 0 < z < 3, even for the far off-diagonal elements. We propose, for the first time, a parametrization for the full ξ- covariance matrix, also 20 per cent accurate for most elements.

  11. 3D Finite Element Analysis of Particle-Reinforced Aluminum

    NASA Technical Reports Server (NTRS)

    Shen, H.; Lissenden, C. J.

    2002-01-01

    Deformation in particle-reinforced aluminum has been simulated using three distinct types of finite element model: a three-dimensional repeating unit cell, a three-dimensional multi-particle model, and two-dimensional multi-particle models. The repeating unit cell model represents a fictitious periodic cubic array of particles. The 3D multi-particle (3D-MP) model represents randomly placed and oriented particles. The 2D generalized plane strain multi-particle models were obtained from planar sections through the 3D-MP model. These models were used to study the tensile macroscopic stress-strain response and the associated stress and strain distributions in an elastoplastic matrix. The results indicate that the 2D model having a particle area fraction equal to the particle representative volume fraction of the 3D models predicted the same macroscopic stress-strain response as the 3D models. However, there are fluctuations in the particle area fraction in a representative volume element. As expected, predictions from 2D models having different particle area fractions do not agree with predictions from 3D models. More importantly, it was found that the microscopic stress and strain distributions from the 2D models do not agree with those from the 3D-MP model. Specifically, the plastic strain distribution predicted by the 2D model is banded along lines inclined at 45 deg from the loading axis while the 3D model prediction is not. Additionally, the triaxial stress and maximum principal stress distributions predicted by 2D and 3D models do not agree. Thus, it appears necessary to use a multi-particle 3D model to accurately predict material responses that depend on local effects, such as strain-to-failure, fracture toughness, and fatigue life.

  12. Rapid Prototyping Integrated With Nondestructive Evaluation and Finite Element Analysis

    NASA Technical Reports Server (NTRS)

    Abdul-Aziz, Ali; Baaklini, George Y.

    2001-01-01

    Most reverse engineering approaches involve imaging or digitizing an object then creating a computerized reconstruction that can be integrated, in three dimensions, into a particular design environment. Rapid prototyping (RP) refers to the practical ability to build high-quality physical prototypes directly from computer aided design (CAD) files. Using rapid prototyping, full-scale models or patterns can be built using a variety of materials in a fraction of the time required by more traditional prototyping techniques (refs. 1 and 2). Many software packages have been developed and are being designed to tackle the reverse engineering and rapid prototyping issues just mentioned. For example, image processing and three-dimensional reconstruction visualization software such as Velocity2 (ref. 3) are being used to carry out the construction process of three-dimensional volume models and the subsequent generation of a stereolithography file that is suitable for CAD applications. Producing three-dimensional models of objects from computed tomography (CT) scans is becoming a valuable nondestructive evaluation methodology (ref. 4). Real components can be rendered and subjected to temperature and stress tests using structural engineering software codes. For this to be achieved, accurate high-resolution images have to be obtained via CT scans and then processed, converted into a traditional file format, and translated into finite element models. Prototyping a three-dimensional volume of a composite structure by reading in a series of two-dimensional images generated via CT and by using and integrating commercial software (e.g. Velocity2, MSC/PATRAN (ref. 5), and Hypermesh (ref. 6)) is being applied successfully at the NASA Glenn Research Center. The building process from structural modeling to the analysis level is outlined in reference 7. Subsequently, a stress analysis of a composite cooling panel under combined thermomechanical loading conditions was performed to validate

  13. A finite different field solver for dipole modes

    SciTech Connect

    Nelson, E.M.

    1992-08-01

    A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL.

  14. Accurate ab Initio Spin Densities.

    PubMed

    Boguslawski, Katharina; Marti, Konrad H; Legeza, Ors; Reiher, Markus

    2012-06-12

    We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as a basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insight into chemically interesting features of the molecule under study such as the distribution of α and β electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput.2011, 7, 2740].

  15. Accurate thermoplasmonic simulation of metallic nanoparticles

    NASA Astrophysics Data System (ADS)

    Yu, Da-Miao; Liu, Yan-Nan; Tian, Fa-Lin; Pan, Xiao-Min; Sheng, Xin-Qing

    2017-01-01

    Thermoplasmonics leads to enhanced heat generation due to the localized surface plasmon resonances. The measurement of heat generation is fundamentally a complicated task, which necessitates the development of theoretical simulation techniques. In this paper, an efficient and accurate numerical scheme is proposed for applications with complex metallic nanostructures. Light absorption and temperature increase are, respectively, obtained by solving the volume integral equation (VIE) and the steady-state heat diffusion equation through the method of moments (MoM). Previously, methods based on surface integral equations (SIEs) were utilized to obtain light absorption. However, computing light absorption from the equivalent current is as expensive as O(NsNv), where Ns and Nv, respectively, denote the number of surface and volumetric unknowns. Our approach reduces the cost to O(Nv) by using VIE. The accuracy, efficiency and capability of the proposed scheme are validated by multiple simulations. The simulations show that our proposed method is more efficient than the approach based on SIEs under comparable accuracy, especially for the case where many incidents are of interest. The simulations also indicate that the temperature profile can be tuned by several factors, such as the geometry configuration of array, beam direction, and light wavelength.

  16. Finite element modelling of SAW correlator

    NASA Astrophysics Data System (ADS)

    Tikka, Ajay C.; Al-Sarawi, Said F.; Abbott, Derek

    2007-12-01

    Numerical simulations of SAW correlators so far are limited to delta function and equivalent circuit models. These models are not accurate as they do not replicate the actual behaviour of the device. Manufacturing a correlator to specifically realise a different configuration is both expensive and time consuming. With the continuous improvement in computing capacity, switching to finite element modelling would be more appropriate. In this paper a novel way of modelling a SAW correlator using finite element analysis is presented. This modelling approach allows the consideration of different code implementation and device structures. This is demonstrated through simulation results for a 5×2-bit Barker sequence encoded SAW correlator. These results show the effect of both bulk and leaky modes on the device performance at various operating frequencies. Moreover, the ways in which the gain of the correlator can be optimised though variation of design parameters will also be outlined.

  17. Nonlinear, finite deformation, finite element analysis

    NASA Astrophysics Data System (ADS)

    Nguyen, Nhung; Waas, Anthony M.

    2016-06-01

    The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli ( C e ) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated

  18. Extracting Time-Accurate Acceleration Vectors From Nontrivial Accelerometer Arrangements.

    PubMed

    Franck, Jennifer A; Blume, Janet; Crisco, Joseph J; Franck, Christian

    2015-09-01

    Sports-related concussions are of significant concern in many impact sports, and their detection relies on accurate measurements of the head kinematics during impact. Among the most prevalent recording technologies are videography, and more recently, the use of single-axis accelerometers mounted in a helmet, such as the HIT system. Successful extraction of the linear and angular impact accelerations depends on an accurate analysis methodology governed by the equations of motion. Current algorithms are able to estimate the magnitude of acceleration and hit location, but make assumptions about the hit orientation and are often limited in the position and/or orientation of the accelerometers. The newly formulated algorithm presented in this manuscript accurately extracts the full linear and rotational acceleration vectors from a broad arrangement of six single-axis accelerometers directly from the governing set of kinematic equations. The new formulation linearizes the nonlinear centripetal acceleration term with a finite-difference approximation and provides a fast and accurate solution for all six components of acceleration over long time periods (>250 ms). The approximation of the nonlinear centripetal acceleration term provides an accurate computation of the rotational velocity as a function of time and allows for reconstruction of a multiple-impact signal. Furthermore, the algorithm determines the impact location and orientation and can distinguish between glancing, high rotational velocity impacts, or direct impacts through the center of mass. Results are shown for ten simulated impact locations on a headform geometry computed with three different accelerometer configurations in varying degrees of signal noise. Since the algorithm does not require simplifications of the actual impacted geometry, the impact vector, or a specific arrangement of accelerometer orientations, it can be easily applied to many impact investigations in which accurate kinematics need to

  19. Finite element analysis of human joints

    SciTech Connect

    Bossart, P.L.; Hollerbach, K.

    1996-09-01

    Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.

  20. Efficient computation of volume in flow predictions

    NASA Technical Reports Server (NTRS)

    Vinokur, M.; Kordulla, W.

    1983-01-01

    An efficient method for calculating cell volumes for time-dependent three-dimensional flow predictions by finite volume calculations is presented. Eight arbitrary corner points are considered and the shape face is divided into two planar triangles. The volume is then dependent on the orientation of the partitioning. In the case of a hexahedron, it is noted that any open surface with a boundary that is a closed curve possesses a surface vector independent of the surface shape. Expressions are defined for the surface vector, which is independent of the partitioning surface diagonal used to quantify the volume. Using a decomposition of the cell volume involving two corners, with each the vertex of three diagonals and six corners which are vertices of one diagonal, gives portions which are tetrahedra. The resultant mesh is can be used for time-dependent finite volume calculations one requires less computer time than previous methods.