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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. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2015-04-01

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

  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. Time-accurate analysis of nonequilibrium gas-particle mixtures using upwind/implicit finite-volume methodology

    SciTech Connect

    Hosangadi, A.; Sinha, N.; Dash, S.M. )

    1992-01-01

    A new Eulerian particulate solver whose numerical formulation is compatible with the numerics in state-of-the-art finite-volume upwind/implicit gas dynamic computer codes is presented. The heat transfer, drag, thermodynamic, and phase-change procedures in this code are derived from earlier, well established data fits and procedures. Performance for numerous flow problems with one- and two-way coupling is quite good. The solutions are nonoscillatory and robust and conserve flux balances very well. 18 refs.

  6. Stable and accurate hybrid finite volume methods based on pure convexity arguments for hyperbolic systems of conservation law

    NASA Astrophysics Data System (ADS)

    De Vuyst, Florian

    2004-01-01

    This exploratory work tries to present first results of a novel approach for the numerical approximation of solutions of hyperbolic systems of conservation laws. The objective is to define stable and "reasonably" accurate numerical schemes while being free from any upwind process and from any computation of derivatives or mean Jacobian matrices. That means that we only want to perform flux evaluations. This would be useful for "complicated" systems like those of two-phase models where solutions of Riemann problems are hard, see impossible to compute. For Riemann or Roe-like solvers, each fluid model needs the particular computation of the Jacobian matrix of the flux and the hyperbolicity property which can be conditional for some of these models makes the matrices be not R-diagonalizable everywhere in the admissible state space. In this paper, we rather propose some numerical schemes where the stability is obtained using convexity considerations. A certain rate of accuracy is also expected. For that, we propose to build numerical hybrid fluxes that are convex combinations of the second-order Lax-Wendroff scheme flux and the first-order modified Lax-Friedrichs scheme flux with an "optimal" combination rate that ensures both minimal numerical dissipation and good accuracy. The resulting scheme is a central scheme-like method. We will also need and propose a definition of local dissipation by convexity for hyperbolic or elliptic-hyperbolic systems. This convexity argument allows us to overcome the difficulty of nonexistence of classical entropy-flux pairs for certain systems. We emphasize the systematic feature of the method which can be fastly implemented or adapted to any kind of systems, with general analytical or data-tabulated equations of state. The numerical results presented in the paper are not superior to many existing state-of-the-art numerical methods for conservation laws such as ENO, MUSCL or central scheme of Tadmor and coworkers. The interest is rather

  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. 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.

  9. Kirkwood-Buff Integrals for Finite Volumes.

    PubMed

    Krüger, Peter; Schnell, Sondre K; Bedeaux, Dick; Kjelstrup, Signe; Vlugt, Thijs J H; Simon, Jean-Marc

    2013-01-17

    Exact expressions for finite-volume Kirkwood-Buff (KB) integrals are derived for hyperspheres in one, two, and three dimensions. These integrals scale linearly with inverse system size. From this, accurate estimates of KB integrals for infinite systems are obtained, and it is shown that they converge much better than the traditional expressions. We show that this approach is very suitable for the computation of KB integrals from molecular dynamics simulations, as we obtain KB integrals for open systems by simulating closed systems.

  10. Finite volume form factors and correlation functions at finite temperature

    NASA Astrophysics Data System (ADS)

    Pozsgay, Balázs

    2009-07-01

    In this thesis we investigate finite size effects in 1+1 dimensional integrable QFT. In particular we consider matrix elements of local operators (finite volume form factors) and vacuum expectation values and correlation functions at finite temperature. In the first part of the thesis we give a complete description of the finite volume form factors in terms of the infinite volume form factors (solutions of the bootstrap program) and the S-matrix of the theory. The calculations are correct to all orders in the inverse of the volume, only exponentially decaying (residual) finite size effects are neglected. We also consider matrix elements with disconnected pieces and determine the general rule for evaluating such contributions in a finite volume. The analytic results are tested against numerical data obtained by the truncated conformal space approach in the Lee-Yang model and the Ising model in a magnetic field. In a separate section we also evaluate the leading exponential correction (the μ-term) associated to multi-particle energies and matrix elements. In the second part of the thesis we show that finite volume factors can be used to derive a systematic low-temperature expansion for correlation functions at finite temperature. In the case of vacuum expectation values the series is worked out up to the third non-trivial order and a complete agreement with the LeClair-Mussardo formula is observed. A preliminary treatment of the two-point function is also given by considering the first nontrivial contributions.

  11. Finite volume hydromechanical simulation in porous media

    NASA Astrophysics Data System (ADS)

    Nordbotten, Jan Martin

    2014-05-01

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

  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. 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.

  14. 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.

  15. 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.

  16. New simple method for fast and accurate measurement of volumes

    NASA Astrophysics Data System (ADS)

    Frattolillo, Antonio

    2006-04-01

    A new simple method is presented, which allows us to measure in just a few minutes but with reasonable accuracy (less than 1%) the volume confined inside a generic enclosure, regardless of the complexity of its shape. The technique proposed also allows us to measure the volume of any portion of a complex manifold, including, for instance, pipes and pipe fittings, valves, gauge heads, and so on, without disassembling the manifold at all. To this purpose an airtight variable volume is used, whose volume adjustment can be precisely measured; it has an overall capacity larger than that of the unknown volume. Such a variable volume is initially filled with a suitable test gas (for instance, air) at a known pressure, as carefully measured by means of a high precision capacitive gauge. By opening a valve, the test gas is allowed to expand into the previously evacuated unknown volume. A feedback control loop reacts to the resulting finite pressure drop, thus contracting the variable volume until the pressure exactly retrieves its initial value. The overall reduction of the variable volume achieved at the end of this process gives a direct measurement of the unknown volume, and definitively gets rid of the problem of dead spaces. The method proposed actually does not require the test gas to be rigorously held at a constant temperature, thus resulting in a huge simplification as compared to complex arrangements commonly used in metrology (gas expansion method), which can grant extremely accurate measurement but requires rather expensive equipments and results in time consuming methods, being therefore impractical in most applications. A simple theoretical analysis of the thermodynamic cycle and the results of experimental tests are described, which demonstrate that, in spite of its simplicity, the method provides a measurement accuracy within 0.5%. The system requires just a few minutes to complete a single measurement, and is ready immediately at the end of the process. The

  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 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.

  19. Finite volume QCD at fixed topological charge

    SciTech Connect

    Aoki, Sinya; Fukaya, Hidenori; Hashimoto, Shoji; Onogi, Tetsuya

    2007-09-01

    In finite volume the partition function of QCD with a given {theta} is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed topological sector, the result deviates from the true expectation value by an amount proportional to the inverse space-time volume 1/V. Using the saddle point expansion, we derive formulas to express the correction due to the fixed topological charge in terms of a 1/V expansion. Applying this formula, we propose a class of methods to determine the topological susceptibility in QCD from various correlation functions calculated in a fixed topological sector.

  20. Finite volume solution of spherical dynamo problems

    NASA Astrophysics Data System (ADS)

    Harder, H.; Hansen, U.

    2003-04-01

    Presently, all existing numerical models of the geodynamo have been calculated by a spectral approach. Certainly a spectral method is ideally suited for the case of high or moderate Ekman number Ek. However, no solutions have been obtained for the regime of an Ekman number below Ek=10-5 to 10-6, which is relevant for the Earth's outer core. Therefore we are currently developing a finite volume method to simulate the geodynamo. Since a local method, like finite volume, is much better suited for massively parallel computation compared to a spectral method, we expect that we can use higher resolution models than previously possible. In addition, the finite volume approach allows an implicit calculation of the dominant Coriolis term in the low Ekman number regime. The development of the thermal and Navier Stokes solvers has been completed. Therefore we will discuss several test solutions of the magnetic induction equation. In addition, first solutions of a fully coupled dynamo model will be presented and compared to similiar spectral solutions.

  1. 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.

  2. 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.

  3. Use of finite volume schemes for transition simulation

    NASA Technical Reports Server (NTRS)

    Fenno, Charles C., Jr.; Hassan, H. A.; Streett, Craig L.

    1991-01-01

    The use of finite-volume methods in the study of spatially and temporally evolving transitional flows over a flat plate is investigated. Schemes are developed with both central and upwind differencing. The compressible Navier-Stokes equations are solved with a Runge-Kutta time stepping scheme. Disturbances are determined using linear theory and superimposed at the inflow boundary. Time accurate integration is then used to allow temporal and spatial disturbance evolution. Characteristic-based boundary conditions are employed. The requirements of using finite-volume algorithms are studied in detail. Special emphasis is placed on difference schemes, grid resolution, and disturbance amplitudes. Moreover, comparisons are made with linear theory for small amplitude disturbances. Both subsonic and supersonic flows are considered, and it is shown that the locations of branch 1 and branch 2 of the neutral stability curve are well predicted, given sufficient resolution.

  4. 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.

  5. Finite volume form factors in the presence of integrable defects

    NASA Astrophysics Data System (ADS)

    Bajnok, Z.; Buccheri, F.; Hollo, L.; Konczer, J.; Takacs, G.

    2014-05-01

    We developed the theory of finite volume form factors in the presence of integrable defects. These finite volume form factors are expressed in terms of the infinite volume form factors and the finite volume density of states and incorporate all polynomial corrections in the inverse of the volume. We tested our results, in the defect Lee-Yang model, against numerical data obtained by truncated conformal space approach (TCSA), which we improved by renormalization group methods adopted to the defect case. To perform these checks we determined the infinite volume defect form factors in the Lee-Yang model exactly, including their vacuum expectation values. We used these data to calculate the two point functions, which we compared, at short distance, to defect CFT. We also derived explicit expressions for the exact finite volume one point functions, which we checked numerically. In all of these comparisons excellent agreement was found.

  6. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2009-03-01

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

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

    SciTech Connect

    Lin, C.-T. Yeh, J.-Y. Chen, J.-Y.

    2009-03-20

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

  9. 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.

  10. 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

  11. 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.

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

    NASA Astrophysics Data System (ADS)

    Oden, J. T.

    1992-08-01

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

  13. 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.

  14. 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

  15. 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.

  16. 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. PMID:26731454

  17. 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.

  18. 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.

  19. Mixed-finite element and finite volume discretization for heavy brine simulations in groundwater

    NASA Astrophysics Data System (ADS)

    Mazzia, A.; Putti, M.

    2002-10-01

    Recently, a new theory of high-concentration brine transport in groundwater has been developed. This approach is based on two nonlinear mass conservation equations, one for the fluid (flow equation) and one for the salt (transport equation), both having nonlinear diffusion terms. In this paper, we present and analyze a numerical technique for the solution of such a model. The approach is based on the mixed hybrid finite element method for the discretization of the diffusion terms in both the flow and transport equations, and a high-resolution TVD finite volume scheme for the convective term. This latter technique is coupled to the discretized diffusive flux by means of a time-splitting approach. A commonly used benchmark test (Elder problem) is used to verify the robustness and nonoscillatory behavior of the proposed scheme and to test the validity of two different formulations, one based on using pressure head [psi] and concentration c as dependent variables, and one using pressure p and mass fraction [omega] as dependent variables. It is found that the latter formulation gives more accurate and reliable results, in particular, at large times. The numerical model is then compared against a semi-analytical solution and the results of a laboratory test. These tests are used to verify numerically the performance and robustness of the proposed numerical scheme when high-concentration gradients (i.e., the double nonlinearity) are present.

  20. 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.

  1. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  3. Finite volume effects for nucleon and heavy meson masses

    SciTech Connect

    Colangelo, Gilberto; Fuhrer, Andreas; Lanz, Stefan

    2010-08-01

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

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. Finite-time transport in volume-preserving flows.

    PubMed

    Mosovsky, B A; Speetjens, M F M; Meiss, J D

    2013-05-24

    Finite-time transport between distinct flow regions is of great relevance to many scientific applications, yet quantitative studies remain scarce to date. The primary obstacle is computing the evolution of material volumes, which is often infeasible due to extreme interfacial stretching. We present a framework for describing and computing finite-time transport in n-dimensional (chaotic) volume-preserving flows that relies on the reduced dynamics of an (n-2)-dimensional "minimal set" of fundamental trajectories. This approach has essential advantages over existing methods: the regions between which transport is investigated can be arbitrarily specified; no knowledge of the flow outside the finite transport interval is needed; and computational effort is substantially reduced. We demonstrate our framework in 2D for an industrial mixing device.

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

    SciTech Connect

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

    2014-12-10

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

  10. A Posteriori Error Estimation for Finite Volume and Finite Element Approximations Using Broken Space Approximation

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Larson, Mats G.

    2000-01-01

    We consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.

  11. Finite volume Kolmogorov-Johnson-Mehl-Avrami theory.

    PubMed

    Berg, Bernd A; Dubey, Santosh

    2008-04-25

    We study the Kolmogorov-Johnson-Mehl-Avrami theory of phase conversion in finite volumes. For the conversion time we find the relationship tau(con)=tau(nu)[1+f(d)(q)]. Here d is the space dimension, tau(nu) the nucleation time in the volume V, and f(d)(q) a scaling function. Its dimensionless argument is q=tau(ex)/tau(nu), where tau(ex) is an expansion time, defined to be proportional to the diameter of the volume divided by expansion speed. We calculate f(d)(q) in one, two, and three dimensions. The often considered limits of phase conversion via either nucleation or spinodal decomposition are found to be volume-size dependent concepts, governed by simple power laws for f(d)(q).

  12. On positivity preserving finite volume schemes for compressible Euler equations

    NASA Technical Reports Server (NTRS)

    Perthame, Benoit; Shu, Chi-Wang

    1993-01-01

    Positivity preserving property of first and higher order finite volume schemes for one and two dimensional compressible Euler equations of gas dynamics is considered. A general framework is established which shows the positivity of density and pressure whenever the underlying one dimensional first order building block based on exact or approximate Riemann solver and the reconstruction are both positivity preserving. Appropriate limitation to achieve high order positivity preserving reconstruction is described.

  13. 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…

  14. Parametric Finite-Volume Theory for Functionally Graded Materials

    NASA Astrophysics Data System (ADS)

    Cavalcante, Marcio A. A.; Marques, Severino P. C.; Pindera, M.-J.

    2008-02-01

    A parametric formulation of the finite-volume theory for functionally graded materials is presented based on a mapping of a square reference subcell onto a quadrilateral subcell in the actual discretized microstructure. This formulation significantly advances the capability and utility of the theory, enabling modeling of curved boundaries of functionally graded structural components, as well as inclusions employed for grading purposes, without the disadvantage of stress concentrations at the corners of rectangular subcells used in the standard version.

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

    NASA Astrophysics Data System (ADS)

    Mungkasi, Sudi

    2016-06-01

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

  16. 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%.

  17. 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

  18. 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.

  19. A parallel high-order accurate finite element nonlinear Stokes ice sheet model and benchmark experiments

    SciTech Connect

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

    2012-01-01

    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.

  20. 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.

  1. 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

  2. Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers

    NASA Astrophysics Data System (ADS)

    Chen, Duan; Cai, Wei; Zinser, Brian; Cho, Min Hyung

    2016-09-01

    In this paper, we develop an accurate and efficient Nyström volume integral equation (VIE) method for the Maxwell equations for a large number of 3-D scatterers. The Cauchy Principal Values that arise from the VIE are computed accurately using a finite size exclusion volume together with explicit correction integrals consisting of removable singularities. Also, the hyper-singular integrals are computed using interpolated quadrature formulae with tensor-product quadrature nodes for cubes, spheres and cylinders, that are frequently encountered in the design of meta-materials. The resulting Nyström VIE method is shown to have high accuracy with a small number of collocation points and demonstrates p-convergence for computing the electromagnetic scattering of these objects. Numerical calculations of multiple scatterers of cubic, spherical, and cylindrical shapes validate the efficiency and accuracy of the proposed method.

  3. 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.

  4. 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.

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

    DOE PAGES

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

    2015-01-13

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

  6. 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.

  7. The composite finite volume method on unstructured meshes for the two-dimensional shallow water equations

    NASA Astrophysics Data System (ADS)

    Jiwen, Wang; Ruxun, Liu

    2001-12-01

    A composite finite volume method (FVM) is developed on unstructured triangular meshes and tested for the two-dimensional free-surface flow equations. The methodology is based on the theory of the remainder effect of finite difference schemes and the property that the numerical dissipation and dispersion of the schemes are compensated by each other in a composite scheme. The composite FVM is formed by global composition of several Lax-Wendroff-type steps followed by a diffusive Lax-Friedrich-type step, which filters out the oscillations around shocks typical for the Lax-Wendroff scheme. To test the efficiency and reliability of the present method, five typical problems of discontinuous solutions of two-dimensional shallow water are solved. The numerical results show that the proposed method, which needs no use of a limiter function, is easy to implement, is accurate, robust and is highly stable. Copyright

  8. High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics

    NASA Astrophysics Data System (ADS)

    Wu, Kailiang; Tang, Huazhong

    2015-10-01

    The paper develops high-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrichs splitting, the WENO reconstruction, the physical-constraints-preserving flux limiter, and the high-order strong stability preserving time discretization. They are extensions of the positivity-preserving finite difference WENO schemes for the non-relativistic Euler equations [20]. However, developing physical-constraints-preserving methods for the RHD system becomes much more difficult than the non-relativistic case because of the strongly coupling between the RHD equations, no explicit formulas of the primitive variables and the flux vectors with respect to the conservative vector, and one more physical constraint for the fluid velocity in addition to the positivity of the rest-mass density and the pressure. The key is to prove the convexity and other properties of the admissible state set and discover a concave function with respect to the conservative vector instead of the pressure which is an important ingredient to enforce the positivity-preserving property for the non-relativistic case. Several one- and two-dimensional numerical examples are used to demonstrate accuracy, robustness, and effectiveness of the proposed physical-constraints-preserving schemes in solving RHD problems with large Lorentz factor, or strong discontinuities, or low rest-mass density or pressure etc.

  9. Computational finite element bone mechanics accurately predicts mechanical competence in the human radius of an elderly population.

    PubMed

    Mueller, Thomas L; Christen, David; Sandercott, Steve; Boyd, Steven K; van Rietbergen, Bert; Eckstein, Felix; Lochmüller, Eva-Maria; Müller, Ralph; van Lenthe, G Harry

    2011-06-01

    High-resolution peripheral quantitative computed tomography (HR-pQCT) is clinically available today and provides a non-invasive measure of 3D bone geometry and micro-architecture with unprecedented detail. In combination with microarchitectural finite element (μFE) models it can be used to determine bone strength using a strain-based failure criterion. Yet, images from only a relatively small part of the radius are acquired and it is not known whether the region recommended for clinical measurements does predict forearm fracture load best. Furthermore, it is questionable whether the currently used failure criterion is optimal because of improvements in image resolution, changes in the clinically measured volume of interest, and because the failure criterion depends on the amount of bone present. Hence, we hypothesized that bone strength estimates would improve by measuring a region closer to the subchondral plate, and by defining a failure criterion that would be independent of the measured volume of interest. To answer our hypotheses, 20% of the distal forearm length from 100 cadaveric but intact human forearms was measured using HR-pQCT. μFE bone strength was analyzed for different subvolumes, as well as for the entire 20% of the distal radius length. Specifically, failure criteria were developed that provided accurate estimates of bone strength as assessed experimentally. It was shown that distal volumes were better in predicting bone strength than more proximal ones. Clinically speaking, this would argue to move the volume of interest for the HR-pQCT measurements even more distally than currently recommended by the manufacturer. Furthermore, new parameter settings using the strain-based failure criterion are presented providing better accuracy for bone strength estimates.

  10. Finite volume TVD Runge Kutta scheme for Navier Stokes computations

    NASA Astrophysics Data System (ADS)

    Bassi, F.; Grasso, F.; Savini, M.

    A numerical procedure for the solution of the Navier-Stokes equations for compressible flows is described and demonstrated. In this finite-volume approach, an upwind-biased second-order TVD scheme based on the method of Harten (1983) is employed for the inviscid (Euler) part of the flow; the viscous contribution is obtained by central differencing; and time integration of the resulting system of ODEs is achieved using a Runge-Kutta algorithm. Results are presented graphically for (1) laminar flow in a double-throat nozzle at Re = 1600; (2) turbulent flow on an RAE2822 airfoil at freestream Mach number 0.75, alpha = 2.70, and Re = 6.2 x 10 to the 6th; and (3) turbulent flow in an LS59TG cascade at M(2is) = 1.31, alpha(1) = 30, and Re(1) = 600,000. Good agreement with published experimental data is demonstrated.

  11. 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.

  12. Upwind finite-volume method for natural and forced convection

    SciTech Connect

    Pan, D.; Chang, C.H. . Inst. of Aeronautics and Astronautics)

    1994-03-01

    A third-order upwind finite-volume method was applied to solve the incompressible Navier-Stokes equations via the use of artificial compressibility. The energy equation and the source terms representing thermal buoyancy are included in the system. The inviscid fluxes are evaluated by a MUSCL-type flux difference upwind scheme based on the inviscid eigensystem. An implicit approximate factorization (AF) scheme was used for time integration, and subiterations at each time step can be applied to obtain time accuracy. Various steady and unsteady tests are performed to validate the present method, including problems in natural convection and forced convection, and in particular the complex flow field over two circular cylinders displaced normally to free stream.

  13. Finite volume simulations of dynamos in ellipsoidal planets

    NASA Astrophysics Data System (ADS)

    Ernst-Hullermann, J.; Harder, H.; Hansen, U.

    2013-12-01

    So far, numerical simulations have mostly considered buoyancy as the driving mechanism of the dynamo process. However, also precession can drive a dynamo, as first suggested by Bullard in 1949. We investigate the properties of precession-driven dynamos in ellipsoidal planets by the use of a finite volume code. In planets, it is much more effective to drive a precessional flow by the pressure differences induced by the topography of the precessing body rather than by viscous coupling to the walls. Numerical simulations are the only method offering the possibility to investigate the influence of the topography since laboratory experiments normally are constrained by the predetermined geometry of the vessel. We discuss how ellipticity of the planets can be included in our simulations by the use of a non-orthogonal grid. Here, we will present some first results and conclude that laminar precession-driven flows can drive kinematic dynamos.

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

    2002-01-18

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

  15. 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.

  16. 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.

  17. 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.

  18. Modeling the convective and pressure terms in finite-volume LES with unresolved wall layers

    NASA Astrophysics Data System (ADS)

    Chang, Henry; Moser, Robert

    2010-11-01

    An incompressible turbulent channel flow is solved using a staggered grid finite volume LES. The grid is uniform with δy^+=50 and is therefore unresolved near the wall. Our primary focus is on accurately modeling the convective and pressure terms in the LES equations. We use the fractional-step method, along with a pressure model from Harlow and Welch (1965). We have found that the pressure model itself--a discrete divergence-free projection--is sufficiently accurate. It is actually the convective term and it's divergence-free projection that are inadequately modeled. In light of this, we are investigating methods for improving the convective model. For example, we are attempting to construct models which statistically represent both the convective and pressure terms from the Reynolds stress equation.

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

    NASA Astrophysics Data System (ADS)

    Nance, Douglas Vinson

    1997-11-01

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

  20. 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.

  1. 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.

  2. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2012-09-01

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

  4. 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.

  5. 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.

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

    DOE PAGES

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

    2015-12-15

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

  7. Nonlinear dynamic fluid-structure interaction calculations with coupled finite element and finite volume programs

    SciTech Connect

    Lewis, M.W.; Kashiwa, B.A.; Meier, R.W.; Bishop, S.

    1994-08-01

    Two- and three-dimensional fluid-structure interaction computer programs for the simulation of nonlinear dynamics were developed and applied to a number of problems. The programs were created by coupling Arbitrary Lagrangian-Eulerian finite volume fluid dynamics programs with strictly Lagrangian finite element structural dynamics programs. The resulting coupled programs can use either fully explicit or implicit time integration. The implicit time integration is accomplished by iterations of the fluid dynamics pressure solver and the structural dynamics system solver. The coupled programs have been used to solve problems involving incompressible fluids, membrane and shell elements, compressible multiphase flows, explosions in both air and water, and large displacements. In this paper, we present the approach used for the coupling and describe test problems that verify the two-dimensional programs against an experiment and an analytical linear problem. The experiment involves an explosion underwater near an instrumented thin steel plate. The analytical linear problem is the vibration of an infinite cylinder surrounded by an incompressible fluid to a given radius.

  8. Nonlinear dynamic fluid-structure interaction calculations with coupled finite element and finite volume programs

    NASA Astrophysics Data System (ADS)

    Lewis, M. W.; Kashiwa, B. A.; Meier, R. W.; Bishop, S.

    1994-07-01

    Two- and three-dimensional fluid-structure interaction computer programs for the simulation of nonlinear dynamics were developed and applied to a number of problems. The programs were created by coupling Arbitrary Lagrangian-Eulerian finite volume fluid dynamics programs with strictly Lagrangian finite element structural dynamics programs. The resulting coupled programs can use either fully explicit or implicit time integration. The implicit time integration is accomplished by iterations of the fluid dynamics pressure solver and the structural dynamics system solver. The coupled programs have been used to solve problems involving incompressible fluids, membrane and shell elements, compressible multiphase flows, explosions in both air and water, and large displacements. In this paper, we present the approach used for the coupling and describe test problems that verify the two-dimensional programs against an experiment and an analytical linear problem. The experiment involves an explosion underwater near an instrumented thin steel plate. The analytical linear problem is the vibration of an infinite cylinder surrounded by an incompressible fluid to a given radius.

  9. 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.

  10. Multiphase control volume finite element simulations of fractured reservoirs

    NASA Astrophysics Data System (ADS)

    Fu, Yao

    With rapid evolution of hardware and software techniques in energy sector, reservoir simulation has become a powerful tool for field development planning and reservoir management. Many of the widely used commercial simulators were originally designed for structured grids and implemented with finite difference method (FDM). In recent years, technical advances in griding, fluid modeling, linear solver, reservoir and geological modeling, etc. have created new opportunities. At the same time, new reservoir simulation technology is required for solving large-scale heterogeneous problems. A three-dimensional, three-phase black-oil reservoir simulator has been developed using the control volume finite element (CVFE) formulation. Flux-based upstream weighting is employed to ensure flux continuity. The CVFE method is embedded in a fully-implicit formulation. State-of-the-art parallel, linear solvers are used. The implementation takes the advantages of object-oriented programming capabilities of C++ to provide maximum reuse and extensibility for future students. The results from the simulator have excellent agreement with those from commercial simulators. The convergence properties of the new simulator are verified using the method of manufactured solutions. The pressure and saturation solutions are verified to be first-order convergent as expected. The efficiency of the simulators and their capability to handle real large-scale field models are improved by implementing the models in parallel. Another aspect of the work dealt with multiphase flow of fractured reservoirs was performed. The discrete-fracture model is implemented in the simulator. Fractures and faults are represented by lines and planes in two- and three-dimensional spaces, respectively. The difficult task of generating an unstructured mesh for complex domains with fractures and faults is accomplished in this study. Applications of this model for two-phase and three-phase simulations in a variety of fractured

  11. Parallel Higher-order Finite Element Method for Accurate Field Computations in Wakefield and PIC Simulations

    SciTech Connect

    Candel, A.; Kabel, A.; Lee, L.; Li, Z.; Limborg, C.; Ng, C.; Prudencio, E.; Schussman, G.; Uplenchwar, R.; Ko, K.; /SLAC

    2009-06-19

    Over the past years, SLAC's Advanced Computations Department (ACD), under SciDAC sponsorship, has developed a suite of 3D (2D) parallel higher-order finite element (FE) codes, T3P (T2P) and Pic3P (Pic2P), aimed at accurate, large-scale simulation of wakefields and particle-field interactions in radio-frequency (RF) cavities of complex shape. The codes are built on the FE infrastructure that supports SLAC's frequency domain codes, Omega3P and S3P, to utilize conformal tetrahedral (triangular)meshes, higher-order basis functions and quadratic geometry approximation. For time integration, they adopt an unconditionally stable implicit scheme. Pic3P (Pic2P) extends T3P (T2P) to treat charged-particle dynamics self-consistently using the PIC (particle-in-cell) approach, the first such implementation on a conformal, unstructured grid using Whitney basis functions. Examples from applications to the International Linear Collider (ILC), Positron Electron Project-II (PEP-II), Linac Coherent Light Source (LCLS) and other accelerators will be presented to compare the accuracy and computational efficiency of these codes versus their counterparts using structured grids.

  12. Finite Volume TVD Schemes for Magnetohydrodynamics on Unstructered Grids

    NASA Astrophysics Data System (ADS)

    Tanaka, T.

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

  13. 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.

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

    NASA Astrophysics Data System (ADS)

    Aslan, Erman; Taymaz, Imdat; Islamoglu, Yasar

    2016-03-01

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

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

    NASA Astrophysics Data System (ADS)

    Kim, Jihwan; Løvholt, Finn; Issler, Dieter

    2016-04-01

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

  16. Towards a Finite Volume Solution of Spherical Dynamo Problems

    NASA Astrophysics Data System (ADS)

    Harder, H.; Hansen, U.

    2001-12-01

    Presently, all existing numerical methods to simulate the geodynamo use a spectral approach. Although a spectral expansion in spherical harmonics avoids the well known pole problem, such an approach has certain drawbacks. An efficient calculation of non-linear terms requires a spectral transform method, which prevents an implicit implementation of these terms. In addition, spectral transformations require global communication, which makes these methods less suitable for massively parallel computation. To avoid these problems, we are currently developing a finite volume method to simulate the geodynamo. The governing equations are formulated in a cartesian frame of reference, but the discretisation is adapted to a spherical shell. The grid is generated by the projection of an inscribed cube to the spherical surface, followed by an orthogonalization of the grid. Topologically this method maps the spherical shell to six cubes. We use domain decomposition and standard message passing routines for a parallel implementation of the method. We will present and compare results for various convection problems: creeping flows, infinite Prandtl number flows, and flows in rapidly rotating spheres.

  17. Finite-volume component-wise TVD schemes for 2D shallow water equations

    NASA Astrophysics Data System (ADS)

    Lin, Gwo-Fong; Lai, Jihn-Sung; Guo, Wen-Dar

    Four finite-volume component-wise total variation diminishing (TVD) schemes are proposed for solving the two-dimensional shallow water equations. In the framework of the finite volume method, a proposed algorithm using the flux-splitting technique is established by modifying the MacCormack scheme to preserve second-order accuracy in both space and time. Based on this algorithm, four component-wise TVD schemes, including the Liou-Steffen splitting (LSS), van Leer splitting, Steger-Warming splitting and local Lax-Friedrichs splitting schemes, are developed. These schemes are verified through the simulations of the 1D dam-break, the oblique hydraulic jump, the partial dam-break and circular dam-break problems. It is demonstrated that the proposed schemes are accurate, efficient and robust to capture the discontinuous shock waves without any spurious oscillations in the complex flow domains with dry-bed situation, bottom slope or friction. The simulated results also show that the LSS scheme has the best numerical accuracy among the schemes tested.

  18. Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

    NASA Technical Reports Server (NTRS)

    Rizzi, Arthur W.; Bailey, Harry E.

    1976-01-01

    A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

  19. 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.

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

    NASA Technical Reports Server (NTRS)

    Molvik, Gregory A.

    1995-01-01

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

  1. Finite volume effects in B{sub K} with improved staggered fermions

    SciTech Connect

    Kim, Jangho; Kim, Hyung-Jin; Lee, Weonjong; Jung, Chulwoo; Sharpe, Stephen R.

    2011-06-01

    We extend our recent unquenched (N{sub f}=2+1 flavor) calculation of B{sub K} using improved staggered fermions by including in the fits the finite volume shift predicted by one-loop staggered chiral perturbation theory. The net result is to lower the result in the continuum limit by 0.6%. This shift is slightly smaller than our previous estimate of finite volume effects based on a direct comparison between different volumes.

  2. 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.

  3. The design of improved smoothing operators for finite volume flow solvers on unstructured meshes

    NASA Astrophysics Data System (ADS)

    de Foy, Benjamin; Dawes, William

    2001-08-01

    Spatial operators used in unstructured finite volume flow solvers are analysed for accuracy using Taylor series expansion and Fourier analysis. While approaching second-order accuracy on very regular grids, operators in common use are shown to have errors resulting in accuracy of only first-, zeroth- or even negative-order on three-dimensional tetrahedral meshes. A technique using least-squares optimization is developed to design improved operators on arbitrary meshes. This is applied to the fourth-order edge sum smoothing operator. The improved numerical dissipation leads to a much more accurate prediction of the Strouhal number for two-dimensional flow around a cylinder and a reduction of a factor of three in the loss coefficient for inviscid flow over a three-dimensional hump. Copyright

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  5. 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.

  6. A posteriori error analysis for a cut cell finite volume method

    SciTech Connect

    Haiying Wang; Michael Pernice; Simon Tavener; Don Estep

    2011-09-01

    We study the solution of a diffusive process in a domain where the diffusion coefficient changes discontinuously across a curved interface. We consider discretizations that use regularly-shaped meshes, so that the interface “cuts” through the cells (elements or volumes) without respecting the regular geometry of the mesh. Consequently, the discontinuity in the diffusion coefficients has a strong impact on the accuracy and convergence of the numerical method. This motivates the derivation of computational error estimates that yield accurate estimates for specified quantities of interest. For this purpose, we adapt the well-known adjoint based a posteriori error analysis technique used for finite element methods. In order to employ this method, we describe a systematic approach to discretizing a cut-cell problem that handles complex geometry in the interface in a natural fashion yet reduces to the well-known Ghost Fluid Method in simple cases. We test the accuracy of the estimates in a series of examples.

  7. 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.

  8. Practical do-it-yourself device for accurate volume measurement of breast.

    PubMed

    Tezel, E; Numanoğlu, A

    2000-03-01

    A simple and accurate method of measuring differences in breast volume based on Archimedes' principle is described. In this method, a plastic container is placed on the breast of the patient who is lying in supine position. While the breast occupies part of the container, the remaining part is filled with water and the volume is measured. This method allows the measurement of the volume differences of asymmetric breasts and also helps the surgeon to estimate the size of the prosthesis to be used in augmentation mammaplasty. PMID:10724264

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

    PubMed

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

    2008-01-28

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

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

    PubMed

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

    2008-01-28

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

  11. [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.

  12. 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

  13. 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.

  14. Computed-tomography-based finite-element models of long bones can accurately capture strain response to bending and torsion.

    PubMed

    Varghese, Bino; Short, David; Penmetsa, Ravi; Goswami, Tarun; Hangartner, Thomas

    2011-04-29

    Finite element (FE) models of long bones constructed from computed-tomography (CT) data are emerging as an invaluable tool in the field of bone biomechanics. However, the performance of such FE models is highly dependent on the accurate capture of geometry and appropriate assignment of material properties. In this study, a combined numerical-experimental study is performed comparing FE-predicted surface strains with strain-gauge measurements. Thirty-six major, cadaveric, long bones (humerus, radius, femur and tibia), which cover a wide range of bone sizes, were tested under three-point bending and torsion. The FE models were constructed from trans-axial volumetric CT scans, and the segmented bone images were corrected for partial-volume effects. The material properties (Young's modulus for cortex, density-modulus relationship for trabecular bone and Poisson's ratio) were calibrated by minimizing the error between experiments and simulations among all bones. The R(2) values of the measured strains versus load under three-point bending and torsion were 0.96-0.99 and 0.61-0.99, respectively, for all bones in our dataset. The errors of the calculated FE strains in comparison to those measured using strain gauges in the mechanical tests ranged from -6% to 7% under bending and from -37% to 19% under torsion. The observation of comparatively low errors and high correlations between the FE-predicted strains and the experimental strains, across the various types of bones and loading conditions (bending and torsion), validates our approach to bone segmentation and our choice of material properties.

  15. Finite element method for accurate 3D simulation of plasmonic waveguides

    NASA Astrophysics Data System (ADS)

    Burger, Sven; Zschiedrich, Lin; Pomplun, Jan; Schmidt, Frank

    2010-02-01

    Optical properties of hybrid plasmonic waveguides and of low-Q cavities, formed by waveguides of finite length are investigated numerically. These structures are of interest as building-blocks of plasmon lasers. We use a time-harmonic finite-element package including a propagation-mode solver, a resonance-mode solver and a scattering solver for studying various properties of the system. Numerical convergence of all used methods is demonstrated.

  16. 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.

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

    NASA Technical Reports Server (NTRS)

    Bui, Trong T.

    1999-01-01

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

  18. 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.

  19. Interface control volume finite element method for modelling multi-phase fluid flow in highly heterogeneous and fractured reservoirs

    NASA Astrophysics Data System (ADS)

    Abushaikha, Ahmad S.; Blunt, Martin J.; Gosselin, Olivier R.; Pain, Christopher C.; Jackson, Matthew D.

    2015-10-01

    We present a new control volume finite element method that improves the modelling of multi-phase fluid flow in highly heterogeneous and fractured reservoirs, called the Interface Control Volume Finite Element (ICVFE) method. The method drastically decreases the smearing effects in other CVFE methods, while being mass conservative and numerically consistent. The pressure is computed at the interfaces of elements, and the control volumes are constructed around them, instead of at the elements' vertices. This assures that a control volume straddles, at most, two elements, which decreases the fluid smearing between neighbouring elements when large variations in their material properties are present. Lowest order Raviart-Thomas vectorial basis functions are used for the pressure calculation and first-order Courant basis functions are used to compute fluxes. The method is a combination of Mixed Hybrid Finite Element (MHFE) and CVFE methods. Its accuracy and convergence are tested using three dimensional tetrahedron elements to represent heterogeneous reservoirs. Our new approach is shown to be more accurate than current CVFE methods.

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

    SciTech Connect

    Ait El Djoudi, A.; Ghenam, L.

    2012-06-27

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

  1. 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.

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

    DOE PAGES

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

    2015-06-24

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

  3. 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.

  4. Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

    NASA Astrophysics Data System (ADS)

    Patil, Dhiraj V.; Lakshmisha, K. N.

    2009-08-01

    A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

  5. Accuracy analysis of mimetic finite volume operators on geodesic grids and a consistent alternative

    NASA Astrophysics Data System (ADS)

    Peixoto, Pedro S.

    2016-04-01

    Many newly developed climate, weather and ocean global models are based on quasi-uniform spherical polygonal grids, aiming for high resolution and better scalability. Thuburn et al. (2009) and Ringler et al. (2010) developed a C staggered finite volume/difference method for arbitrary polygonal spherical grids suitable for these next generation dynamical cores. This method has many desirable mimetic properties and became popular, being adopted in some recent models, in spite of being known to possess low order of accuracy. In this work, we show that, for the nonlinear shallow water equations on non-uniform grids, the method has potentially 3 main sources of inconsistencies (local truncation errors not converging to zero as the grid is refined): (i) the divergence term of the continuity equation, (ii) the perpendicular velocity and (iii) the kinetic energy terms of the vector invariant form of the momentum equations. Although some of these inconsistencies have not impacted the convergence on some standard shallow water test cases up until now, they may constitute a potential problem for high resolution 3D models. Based on our analysis, we propose modifications for the method that will make it first order accurate in the maximum norm. It preserves many of the mimetic properties, albeit having non-steady geostrophic modes on the f-sphere. Experimental results show that the resulting model is a more accurate alternative to the existing formulations and should provide means of having a consistent, computationally cheap and scalable atmospheric or ocean model on C staggered Voronoi grids.

  6. 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.

  7. 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.

  8. 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.

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

    SciTech Connect

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

    2009-01-01

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

  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. 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; Colella, Phillip

    2015-09-04

    We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed-sphere. This approach combines a Runge--Kutta time discretization with a fourth-order accurate spatial discretization, and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy, but with many fewer operations.

  12. 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.

  13. Fast and accurate finite element analysis of large-scale three-dimensional photonic devices with a robust domain decomposition method.

    PubMed

    Xue, Ming-Feng; Kang, Young Mo; Arbabi, Amir; McKeown, Steven J; Goddard, Lynford L; Jin, Jian-Ming

    2014-02-24

    A fast and accurate full-wave technique based on the dual-primal finite element tearing and interconnecting method and the second-order transmission condition is presented for large-scale three-dimensional photonic device simulations. The technique decomposes a general three-dimensional electromagnetic problem into smaller subdomain problems so that parallel computing can be performed on distributed-memory computer clusters to reduce the simulation time significantly. With the electric fields computed everywhere, photonic device parameters such as transmission and reflection coefficients are extracted. Several photonic devices, with simulation volumes up to 1.9×10(4) (λ/n(avg))3 and modeled with over one hundred million unknowns, are simulated to demonstrate the application, efficiency, and capability of this technique. The simulations show good agreement with experimental results and in a special case with a simplified two-dimensional simulation.

  14. 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

  15. Accurate method to study static volume-pressure relationships in small fetal and neonatal animals.

    PubMed

    Suen, H C; Losty, P D; Donahoe, P K; Schnitzer, J J

    1994-08-01

    We designed an accurate method to study respiratory static volume-pressure relationships in small fetal and neonatal animals on the basis of Archimedes' principle. Our method eliminates the error caused by the compressibility of air (Boyle's law) and is sensitive to a volume change of as little as 1 microliters. Fetal and neonatal rats during the period of rapid lung development from day 19.5 of gestation (term = day 22) to day 3.5 postnatum were studied. The absolute lung volume at a transrespiratory pressure of 30-40 cmH2O increased 28-fold from 0.036 +/- 0.006 (SE) to 0.994 +/- 0.042 ml, the volume per gram of lung increased 14-fold from 0.39 +/- 0.07 to 5.59 +/- 0.66 ml/g, compliance increased 12-fold from 2.3 +/- 0.4 to 27.3 +/- 2.7 microliters/cmH2O, and specific compliance increased 6-fold from 24.9 +/- 4.5 to 152.3 +/- 22.8 microliters.cmH2O-1.g lung-1. This technique, which allowed us to compare changes during late gestation and the early neonatal period in small rodents, can be used to monitor and evaluate pulmonary functional changes after in utero pharmacological therapies in experimentally induced abnormalities such as pulmonary hypoplasia, surfactant deficiency, and congenital diaphragmatic hernia. PMID:8002489

  16. 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.

  17. 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.

  18. Optimization of tissue physical parameters for accurate temperature estimation from finite-element simulation of radiofrequency ablation

    NASA Astrophysics Data System (ADS)

    Subramanian, Swetha; Mast, T. Douglas

    2015-09-01

    Computational finite element models are commonly used for the simulation of radiofrequency ablation (RFA) treatments. However, the accuracy of these simulations is limited by the lack of precise knowledge of tissue parameters. In this technical note, an inverse solver based on the unscented Kalman filter (UKF) is proposed to optimize values for specific heat, thermal conductivity, and electrical conductivity resulting in accurately simulated temperature elevations. A total of 15 RFA treatments were performed on ex vivo bovine liver tissue. For each RFA treatment, 15 finite-element simulations were performed using a set of deterministically chosen tissue parameters to estimate the mean and variance of the resulting tissue ablation. The UKF was implemented as an inverse solver to recover the specific heat, thermal conductivity, and electrical conductivity corresponding to the measured area of the ablated tissue region, as determined from gross tissue histology. These tissue parameters were then employed in the finite element model to simulate the position- and time-dependent tissue temperature. Results show good agreement between simulated and measured temperature.

  19. Optimization of tissue physical parameters for accurate temperature estimation from finite-element simulation of radiofrequency ablation.

    PubMed

    Subramanian, Swetha; Mast, T Douglas

    2015-10-01

    Computational finite element models are commonly used for the simulation of radiofrequency ablation (RFA) treatments. However, the accuracy of these simulations is limited by the lack of precise knowledge of tissue parameters. In this technical note, an inverse solver based on the unscented Kalman filter (UKF) is proposed to optimize values for specific heat, thermal conductivity, and electrical conductivity resulting in accurately simulated temperature elevations. A total of 15 RFA treatments were performed on ex vivo bovine liver tissue. For each RFA treatment, 15 finite-element simulations were performed using a set of deterministically chosen tissue parameters to estimate the mean and variance of the resulting tissue ablation. The UKF was implemented as an inverse solver to recover the specific heat, thermal conductivity, and electrical conductivity corresponding to the measured area of the ablated tissue region, as determined from gross tissue histology. These tissue parameters were then employed in the finite element model to simulate the position- and time-dependent tissue temperature. Results show good agreement between simulated and measured temperature. PMID:26352462

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. Unstructured grid finite volume analysis for acoustic and pulsed wave propagation characteristics in exhaust silencer systems

    SciTech Connect

    Kim, J.T.; Kim, Y.M.; Maeng, J.S.; Lyu, M.S.; Ku, Y.G.

    1996-10-01

    The unstructured grid finite volume method has been applied to predict the linear and nonlinear attenuation characteristics of the expansion chamber type silencer system. In order to achieve grid flexibility and a solution adaptation for geometrically complex flow regions associated with the actual silencers, the unstructured mesh algorithm in context with the node-centered finite volume method has been employed. The validation cases for the linear and nonlinear wave propagation characteristics include the acoustic field of the concentric expansion chamber and the axisymmetric blast flow field with the open end. Effects of the chamber geometry on the nonlinear wave propagation characteristics are discussed in detail.

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

    NASA Technical Reports Server (NTRS)

    Nicholson, S.; Moore, J.

    1985-01-01

    Progress made in extending the finite volume explicit time marching method to laminar and turbulent flow during the time period from January to May 1985 is documented. Previously, extensions were made to the finite volume method to improve the accuracy of the calculation of total pressure in compressible inviscid flow. The current work extends these ideas and develops new ideas which allow the calculation of laminar and turbulent boundary layers in internal flows. The method is verified using four test cases with free-stream Mach numbers ranging from .075 to 1.20.

  6. Object strength--an accurate measure for small objects that is insensitive to partial volume effects.

    PubMed

    Tofts, P S; Silver, N C; Barker, G J; Gass, A

    2005-07-01

    There are currently four problems in characterising small nonuniform lesions or other objects in Magnetic Resonance images where partial volume effects are significant. Object size is over- or under-estimated; boundaries are often not reproducible; mean object value cannot be measured; and fuzzy borders cannot be accommodated. A new measure, Object Strength, is proposed. This is the sum of all abnormal intensities, above a uniform background value. For a uniform object, this is simply the product of the increase in intensity and the size of the object. Biologically, this could be at least as relevant as existing measures of size or mean intensity. We hypothesise that Object Strength will perform better than traditional area measurements in characterising small objects. In a pilot study, the reproducibility of object strength measurements was investigated using MR images of small multiple sclerosis (MS) lesions. In addition, accuracy was investigated using artificial lesions of known volume (0.3-6.2 ml) and realistic appearance. Reproducibility approached that of area measurements (in 33/90 lesion reports the difference between repeats was less than for area measurements). Total lesion volume was accurate to 0.2%. In conclusion, Object Strength has potential for improved characterisation of small lesions and objects in imaging and possibly spectroscopy.

  7. 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.

  8. 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.

  9. Finite-volume application of high-order ENO schemes to two-dimensional boundary-value problems

    NASA Technical Reports Server (NTRS)

    Casper, Jay

    1991-01-01

    Finite-volume applications of high-order accurate ENO schemes to two-dimensional boundary-value problems are studied. These schemes achieve high-order spatial accuracy, in smooth regions, by a piecewise polynomial approximation of the solution from cell averages. In addition, this spatial operation involves an adaptive stencil algorithm in order to avoid the oscillatory behavior that is associated with interpolation across steep gradients. High-order TVD Runge-Kutta methods are employed for time integration, thus making these schemes best suited for unsteady problems. Fifth- and sixth-order accurate applications are validated through a grid refinement study involving the solutions of scalar hyperbolic equations. A previously proposed extension for the Euler equations of gas dynamics is tested, including its application to solutions of boundary-value problems involving solid walls and curvilinear coordinates.

  10. Modeling of photon migration in the human lung using a finite volume solver

    NASA Astrophysics Data System (ADS)

    Sikorski, Zbigniew; Furmanczyk, Michal; Przekwas, Andrzej J.

    2006-02-01

    The application of the frequency domain and steady-state diffusive optical spectroscopy (DOS) and steady-state near infrared spectroscopy (NIRS) to diagnosis of the human lung injury challenges many elements of these techniques. These include the DOS/NIRS instrument performance and accurate models of light transport in heterogeneous thorax tissue. The thorax tissue not only consists of different media (e.g. chest wall with ribs, lungs) but its optical properties also vary with time due to respiration and changes in thorax geometry with contusion (e.g. pneumothorax or hemothorax). This paper presents a finite volume solver developed to model photon migration in the diffusion approximation in heterogeneous complex 3D tissues. The code applies boundary conditions that account for Fresnel reflections. We propose an effective diffusion coefficient for the void volumes (pneumothorax) based on the assumption of the Lambertian diffusion of photons entering the pleural cavity and accounting for the local pleural cavity thickness. The code has been validated using the MCML Monte Carlo code as a benchmark. The code environment enables a semi-automatic preparation of 3D computational geometry from medical images and its rapid automatic meshing. We present the application of the code to analysis/optimization of the hybrid DOS/NIRS/ultrasound technique in which ultrasound provides data on the localization of thorax tissue boundaries. The code effectiveness (3D complex case computation takes 1 second) enables its use to quantitatively relate detected light signal to absorption and reduced scattering coefficients that are indicators of the pulmonary physiologic state (hemoglobin concentration and oxygenation).

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

    PubMed

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

    2002-02-01

    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.

  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. Lateral impact validation of a geometrically accurate full body finite element model for blunt injury prediction.

    PubMed

    Vavalle, Nicholas A; Moreno, Daniel P; Rhyne, Ashley C; Stitzel, Joel D; Gayzik, F Scott

    2013-03-01

    This study presents four validation cases of a mid-sized male (M50) full human body finite element model-two lateral sled tests at 6.7 m/s, one sled test at 8.9 m/s, and a lateral drop test. Model results were compared to transient force curves, peak force, chest compression, and number of fractures from the studies. For one of the 6.7 m/s impacts (flat wall impact), the peak thoracic, abdominal and pelvic loads were 8.7, 3.1 and 14.9 kN for the model and 5.2 ± 1.1 kN, 3.1 ± 1.1 kN, and 6.3 ± 2.3 kN for the tests. For the same test setup in the 8.9 m/s case, they were 12.6, 6, and 21.9 kN for the model and 9.1 ± 1.5 kN, 4.9 ± 1.1 kN, and 17.4 ± 6.8 kN for the experiments. The combined torso load and the pelvis load simulated in a second rigid wall impact at 6.7 m/s were 11.4 and 15.6 kN, respectively, compared to 8.5 ± 0.2 kN and 8.3 ± 1.8 kN experimentally. The peak thorax load in the drop test was 6.7 kN for the model, within the range in the cadavers, 5.8-7.4 kN. When analyzing rib fractures, the model predicted Abbreviated Injury Scale scores within the reported range in three of four cases. Objective comparison methods were used to quantitatively compare the model results to the literature studies. The results show a good match in the thorax and abdomen regions while the pelvis results over predicted the reaction loads from the literature studies. These results are an important milestone in the development and validation of this globally developed average male FEA model in lateral impact.

  14. Is internal target volume accurate for dose evaluation in lung cancer stereotactic body radiotherapy?

    PubMed Central

    Peng, Jiayuan; Zhang, Zhen; Wang, Jiazhou; Xie, Jiang; Hu, Weigang

    2016-01-01

    Purpose 4DCT delineated internal target volume (ITV) was applied to determine the tumor motion and used as planning target in treatment planning in lung cancer stereotactic body radiotherapy (SBRT). This work is to study the accuracy of using ITV to predict the real target dose in lung cancer SBRT. Materials and methods Both for phantom and patient cases, the ITV and gross tumor volumes (GTVs) were contoured on the maximum intensity projection (MIP) CT and ten CT phases, respectively. A SBRT plan was designed using ITV as the planning target on average projection (AVG) CT. This plan was copied to each CT phase and the dose distribution was recalculated. The GTV_4D dose was acquired through accumulating the GTV doses over all ten phases and regarded as the real target dose. To analyze the ITV dose error, the ITV dose was compared to the real target dose by endpoints of D99, D95, D1 (doses received by the 99%, 95% and 1% of the target volume), and dose coverage endpoint of V100(relative volume receiving at least the prescription dose). Results The phantom study shows that the ITV underestimates the real target dose by 9.47%∼19.8% in D99, 4.43%∼15.99% in D95, and underestimates the dose coverage by 5% in V100. The patient cases show that the ITV underestimates the real target dose and dose coverage by 3.8%∼10.7% in D99, 4.7%∼7.2% in D95, and 3.96%∼6.59% in V100 in motion target cases. Conclusions Cautions should be taken that ITV is not accurate enough to predict the real target dose in lung cancer SBRT with large tumor motions. Restricting the target motion or reducing the target dose heterogeneity could reduce the ITV dose underestimation effect in lung SBRT. PMID:26968812

  15. 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

  16. 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.

  17. 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

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

    SciTech Connect

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

    1995-05-01

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

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

    SciTech Connect

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

    2009-02-01

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

  20. 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.

  1. 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.

  2. Voronoi-cell finite difference method for accurate electronic structure calculation of polyatomic molecules on unstructured grids

    SciTech Connect

    Son, Sang-Kil

    2011-03-01

    We introduce a new numerical grid-based method on unstructured grids in the three-dimensional real-space to investigate the electronic structure of polyatomic molecules. The Voronoi-cell finite difference (VFD) method realizes a discrete Laplacian operator based on Voronoi cells and their natural neighbors, featuring high adaptivity and simplicity. To resolve multicenter Coulomb singularity in all-electron calculations of polyatomic molecules, this method utilizes highly adaptive molecular grids which consist of spherical atomic grids. It provides accurate and efficient solutions for the Schroedinger equation and the Poisson equation with the all-electron Coulomb potentials regardless of the coordinate system and the molecular symmetry. For numerical examples, we assess accuracy of the VFD method for electronic structures of one-electron polyatomic systems, and apply the method to the density-functional theory for many-electron polyatomic molecules.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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...

  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. Suppression of nonlinear optical signals in finite interaction volumes of bulk materials.

    PubMed

    Cattaneo, Stefano; Siltanen, Mikael; Xiang Wang, Fu; Kauranen, Martti

    2005-11-28

    We show that nonlinear optical signals generated by non-phase-matched interactions are strongly suppressed when the interaction volume is finite and localized deep inside the bulk of a homogeneous material, as opposed to the case where the interaction volume extends across a boundary of the material. The suppression in the bulk originates from destructive interference between the signals generated in the two regions where the interaction is gradually turned on and off and depends on the ratio of the coherence length to the characteristic length of the interaction volume.

  10. 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

  11. Pseudoscalar mesons in a finite cubic volume with twisted boundary conditions

    NASA Astrophysics Data System (ADS)

    Colangelo, Gilberto; Vaghi, Alessio

    2016-07-01

    We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We first apply chiral perturbation theory in the p-regime and calculate the corrections for masses, decay constants, pseudoscalar coupling constants and form factors at next-to-leading order. We show that the Feynman-Hellmann theorem and the relevant Ward-Takahashi identity are satisfied. We then derive asymptotic formulae à la Lüscher for twisted boundary conditions. We show that chiral Ward identities for masses and decay constants are satisfied by the asymptotic formulae in finite volume as a consequence of infinite-volume Ward identities. Applying asymptotic formulae in combination with chiral perturbation theory we estimate corrections beyond next-to-leading order for twisted boundary conditions.

  12. 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...

  13. The Treatment of Reacting Surfaces for Finite-Volume Schemes on Unstructured Meshes

    NASA Astrophysics Data System (ADS)

    Mazumder, Sandip; Lowry, Samuel A.

    2001-11-01

    A rigorous and robust numerical procedure to treat surface reaction boundary conditions for finite-volume schemes in unstructured meshes is presented. The procedure is applicable to arbitrary cell topologies and multistep finite-rate surface reactions of arbitrary complexity. The accuracy of the numerical procedure has been verified by systematically comparing solutions obtained using unstructured meshes with perfectly orthogonal meshes for both two-dimensional and three-dimensional geometries. Validation results presented for gallium arsenide growth in a full-scale commercial metal organic-chemical vapor-deposition reactor, exhibit excellent match with experimental data.

  14. 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.

  15. Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes

    NASA Astrophysics Data System (ADS)

    Anastasiou, K.; Chan, C. T.

    1997-06-01

    A 2D, depth-integrated, free surface flow solver for the shallow water equations is developed and tested. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov-type second-order upwind finite volume formulation, whereby the inviscid fluxes of the system of equations are obtained using Roes flux function. The eigensystem of the 2D shallow water equations is derived and is used for the construction of Roes matrix on an unstructured mesh. The viscous terms of the shallow water equations are computed using a finite volume formulation which is second-order-accurate. Verification of the solution technique for the inviscid form of the governing equations as well as for the full system of equations is carried out by comparing the model output with documented published results and very good agreement is obtained. A numerical experiment is also conducted in order to evaluate the performance of the solution technique as applied to linear convection problems. The presented results show that the solution technique is robust.

  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. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Investigation of mouse conductance catheter position deviation effects on volume measurements by finite element models.

    PubMed

    Wei, Chia-Ling; Wu, Po-Yi

    2008-01-01

    The conductance catheter system is used to measure the instantaneous ventricular conductance, and real-time ventricular volumes is then determined by converting the measured conductance to volume. In fact, two different conductance-to-volume conversion equations for conductance catheters have been proposed, the Baan's classic equation and Wei's nonlinear equation. The accuracy of this volume estimation method is limited by several factors, such as the deviation of the catheter position inside the ventricle. The effects of the mouse catheter radial and longitudinal position deviations on the measured conductance are investigated with finite element models. Moreover, the capacities of the two conversion equations to calibrate the error induced by the catheter position variation are evaluated and compared. According to the simulation results, the error-calibrated capacity of the nonlinear conversion equation is better.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. Dirac Variables and Zero Modes of Gauss Constraint in Finite-Volume Two-Dimensional QED

    NASA Astrophysics Data System (ADS)

    Gogilidze, S.; Ilieva, Nevena; Pervushin, V. N.

    The finite-volume QED1+1 is formulated in terms of Dirac variables by an explicit solution of the Gauss constraint with possible nontrivial boundary conditions taken into account. The intrinsic nontrivial topology of the gauge group is thus revealed together with its zero-mode residual dynamics. Topologically nontrivial gauge transformations generate collective excitations of the gauge field above Coleman's ground state, that are completely decoupled from local dynamics, the latter being equivalent to a free massive scalar field theory.

  8. Logically rectangular finite volume methods with adaptive refinement on the sphere.

    PubMed

    Berger, Marsha J; Calhoun, Donna A; Helzel, Christiane; LeVeque, Randall J

    2009-11-28

    The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the GeoClaw software and demonstrate well-balanced methods that exactly maintain equilibrium solutions, such as shallow water equations for an ocean at rest over arbitrary bathymetry.

  9. 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.

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

    SciTech Connect

    Ju, Lili; Tian, Li; Wang, Desheng

    2009-01-01

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

  11. 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.

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

    NASA Technical Reports Server (NTRS)

    Baysal, Oktay; Lessard, Victor R.

    1990-01-01

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

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

    PubMed

    Johnston, Peter R

    2010-01-01

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

  14. An accurate analytic approximation to the non-linear change in volume of solids with applied pressure

    NASA Technical Reports Server (NTRS)

    Schlosser, Herbert; Ferrante, John

    1989-01-01

    An accurate analytic expression for the nonlinear change of the volume of a solid as a function of applied pressure is of great interest in high-pressure experimentation. It is found that a two-parameter analytic expression, fits the experimental volume-change data to within a few percent over the entire experimentally attainable pressure range. Results are presented for 24 different materials including metals, ceramic semiconductors, polymers, and ionic and rare-gas solids.

  15. A study of finite volume effect on the multiple-frequencies coherence of VHF radar

    NASA Astrophysics Data System (ADS)

    Chen, Tsai-Yuan; Chu, Yen-Hsyang

    1993-08-01

    In the past few years, the technique of frequency domain interferometry (FDI) has been developed on VHF radar. By using this technique, the characteristics of a very thin atmospheric lay structure, which is embedded in the radar volume and cannot be solved by conventional VHF radar with only one operational frequency, can be determined through the calculation of the coherence and the phase from the two echo signals with different operational frequencies. According to FDI theory, assuming that the range and antenna beam weighting effect can be ignored, the coherence will approach zero if the layer thickness is fairly greater than the radar volume. However, in this study, it will be shown that if a rectangular pulse is transmitted and the atmospheric refractivity irregularities are distributed uniformly in the radar volume, that is, there is no narrow layer structure existing in the scattering volume, the coherence of two signals with different operational frequencies is still high and its behavior can be described by the equation C is approximately equal to Sinc((Delta)k L)/(l + N/S), where C is the coherence, Delta K is the wavenumber difference between two carrier frequencies, L is the effective scale of scattering volume, and N/S is the noise-to-signal power ratio. This feature can be interpreted physically by the finite volume filtering effect on the turbulent wavenumber spectrum. This theoretical prediction has been compared with the FDI experiments carried out by the Chung-Li VHF radar, and the results are quite reasonable. Thus, it is suggested that when the FDI technique is applied to estimate the thickness and the position of a thin layer, the finite volume filtering effect should be taken into account.

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

    NASA Astrophysics Data System (ADS)

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

    2012-09-01

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

  17. 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

  18. 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.

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

    PubMed Central

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

    2014-01-01

    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. PMID:23860257

  20. Two-dimensional free surface flow in branch channels by a finite-volume TVD scheme

    NASA Astrophysics Data System (ADS)

    Wang, Jiasong; He, Yousheng; Ni, Hangen

    Free surface flow, in particular caused by dam-breaks in branch channels or other arbitrary geometrical rivers is an attention getting subject to the engineering practice, however the studies are few to be reported. In this paper a finite-volume total variation diminishing (TVD) scheme is presented for modeling unsteady free surface flows caused by dam-breaks in branch channels. In order to extend the finite-difference TVD scheme to finite-volume form, a mesh topology is defined relating a node and an element. The solver is implemented for the 2D shallow water equations on arbitrary quadrilateral meshes, and based upon a second-order hybrid TVD scheme with an optimum-selected limiter in the space discretization and a two-step Runge-Kutta approach in the time discretization. Verification for two typical dam-break problems is carried out by comparing the present results with others and very good agreement is obtained. The present algorithm is then used to predict the characteristics of free surface flows due to dam breaking in branch channels, for example, in a symmetrical trifurcated channel and a natural bifurcated channel, on coarse meshes and fine meshes, respectively. The characteristics of complex unsteady free surface flows in these examples are clearly shown.

  1. 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.

  2. Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1992-01-01

    A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

  3. A parallel finite volume algorithm for large-eddy simulation of turbulent flows

    NASA Astrophysics Data System (ADS)

    Bui, Trong Tri

    1998-11-01

    A parallel unstructured finite volume algorithm is developed for large-eddy simulation of compressible turbulent flows. Major components of the algorithm include piecewise linear least-square reconstruction of the unknown variables, trilinear finite element interpolation for the spatial coordinates, Roe flux difference splitting, and second-order MacCormack explicit time marching. The computer code is designed from the start to take full advantage of the additional computational capability provided by the current parallel computer systems. Parallel implementation is done using the message passing programming model and message passing libraries such as the Parallel Virtual Machine (PVM) and Message Passing Interface (MPI). The development of the numerical algorithm is presented in detail. The parallel strategy and issues regarding the implementation of a flow simulation code on the current generation of parallel machines are discussed. The results from parallel performance studies show that the algorithm is well suited for parallel computer systems that use the message passing programming model. Nearly perfect parallel speedup is obtained on MPP systems such as the Cray T3D and IBM SP2. Performance comparison with the older supercomputer systems such as the Cray YMP show that the simulations done on the parallel systems are approximately 10 to 30 times faster. The results of the accuracy and performance studies for the current algorithm are reported. To validate the flow simulation code, a number of Euler and Navier-Stokes simulations are done for internal duct flows. Inviscid Euler simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle shows that the algorithm is capable of simultaneously tracking the very small disturbances of the acoustic wave and capturing the shock wave. Navier-Stokes simulations are made for fully developed laminar flow in a square duct, developing laminar flow in a

  4. Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion

    NASA Astrophysics Data System (ADS)

    Lin, Zhigui; Ruiz-Baier, Ricardo; Tian, Canrong

    2014-01-01

    This paper is concerned with the study of pattern formation for an inhomogeneous Brusselator model with cross-diffusion, modeling an autocatalytic chemical reaction taking place in a three-dimensional domain. For the spatial discretization of the problem we develop a novel finite volume element (FVE) method associated to a piecewise linear finite element approximation of the cross-diffusion system. We study the main properties of the unique equilibrium of the related dynamical system. A rigorous linear stability analysis around the spatially homogeneous steady state is provided and we address in detail the formation of Turing patterns driven by the cross-diffusion effect. In addition we focus on the spatial accuracy of the FVE method, and a series of numerical simulations confirm the expected behavior of the solutions. In particular we show that, depending on the spatial dimension, the magnitude of the cross-diffusion influences the selection of spatial patterns.

  5. 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…

  6. 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.

  7. 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. PMID:18488965

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

    NASA Technical Reports Server (NTRS)

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

    2004-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

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

    SciTech Connect

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

    2015-06-24

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

  11. 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

  12. 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.

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

    SciTech Connect

    Ismagilov, Timur Z.

    2015-02-01

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

  14. Flow control simulations around a circular cylinder by a finite-volume scheme

    NASA Astrophysics Data System (ADS)

    Lin, San-Yih; Wu, Tsuen-Muh

    1993-07-01

    A numerical study is made of the flow past a circular cylinder with/without flow control devices. The Reynolds number ranges from 20 to 200. The numerical method for the solutions of the incompressible Navier-Stokes equations is based on an artificial compressibility approach and an upwind finite-volume method. Two kinds of the flow control devices are investigated: (1) placing an attached or a detached splitter plate in the wake behind the circular cylinder, and (2) placing a second small cylinder (control cylinder) behind the circular cylinder. The numerical investigations show that both of two are effective on the suppression of vortex shedding and the reduction of drag.

  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. 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.

  17. Two-dimensional Euler computations on a triangular mesh using an upwind, finite-volume scheme

    NASA Technical Reports Server (NTRS)

    Whitaker, D. L.; Grossman, B.; Lohner, R.

    1989-01-01

    A numerical procedure was developed for the finite-volume solution of the Euler equations on unstructured triangular meshes based on a flux-difference split upwind method. Techniques for implementing Roe's (1985) approximate Reimann solver together with the preprocessing MUSCL differencing on unstructured grids are presented. Applications and comparisons with structured grid problems are carried out for a supersonic shock reflection problem, the supersonic flow over a blunt body, the transonic flow over NACA 0012 and RAE 2822 airfoils, and the flow about a double element Karman-Trefftz airfoil.

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

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

  19. Measurement of testicular volume in smaller testes: how accurate is the conventional orchidometer?

    PubMed

    Lin, Chih-Chieh; Huang, William J S; Chen, Kuang-Kuo

    2009-01-01

    The aim of this study was to evaluate the accuracy of different methods, including the Seager orchidometer (SO) and ultrasonography (US), for assessing testicular volume of smaller testes (testes volume less than 18 mL). Moreover, the equations used for the calculations--the Hansen formula (length [L] x width [W](2) x 0.52, equation A), the prolate ellipsoid formula (L x W x height [H] x 0.52, equation B), and the Lambert equation (L x W x H x 0.71, equation C)--were also examined and compared with the gold standard testicular volume obtained by water displacement (Archimedes principle). In this study, 30 testes from 15 men, mean age 75.3 (+/-8.3) years, were included. They all had advanced prostate cancer and were admitted for orchiectomy. Before the procedure, all the testes were assessed using SO and US. The dimensions were then input into each equation to obtain the volume estimates. The testicular volume by water displacement was 8.1 +/- 3.5 mL. Correlation coefficients (R(2)) of the 2 different methods (SO, US) to the gold standard were 0.70 and 0.85, respectively. The calculated testicular volumes were 9.2 +/- 3.9 mL (measured by SO, equation A), 11.9 +/- 5.2 mL (measured by SO, equation C), 7.3 +/- 4.2 mL (measured by US, equation A), 6.5 +/- 3.3 mL (measured by US, equation B) and 8.9 +/- 4.5 mL (measured by US, equation C). Only the mean size measured by US and volume calculated with the Hansen equation (equation A) and the mean size measured by US and volume calculated with the Lambert equation (equation C) showed no significant differences when compared with the volumes estimated by water displacement (mean difference 0.81 mL, P = .053, and 0.81 mL, P = .056, respectively). Based on our measurements, we categorized testicular volume by different cutoff values (7.0 mL, 7.5 mL, 8.0 mL, and 8.5 mL) to calculate a new constant for use in the Hansen equation. The new constant was 0.59. We then reexamined the equations using the new 0.59 constant, and found

  20. Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids.

    PubMed

    Anissimov, Y G; Roberts, M S

    2001-04-01

    The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and

  1. 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.

  2. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

  4. 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.

  5. An explicit finite-volume time-marching procedure for turbulent flow calculations

    NASA Technical Reports Server (NTRS)

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

    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. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is not required. Different time steps are used in the different governing equations. 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 (length/height - 1000). The method is compared with two test cases. Essentially incompressible turbulent boundary layer flow in an adverse pressure gradient is calculated and the computed distributions of mean velocity and shear are in good agreement with the measurements. Transonic viscous flow in a converging diverging nozzle is calculated; 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.

  6. 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

  7. Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers

    NASA Astrophysics Data System (ADS)

    Balsara, Dinshaw S.; Dumbser, Michael

    2015-10-01

    Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on

  8. 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.

  9. 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.

  10. 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

  11. 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.

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

    NASA Astrophysics Data System (ADS)

    Kim, Jihwan; Issler, Dieter

    2015-04-01

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

  13. 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.

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

    NASA Technical Reports Server (NTRS)

    Diskin, Boris; Thomas, James L.

    2011-01-01

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

  15. Study on fluid-structure interaction in liquid oxygen feeding pipe systems using finite volume method

    NASA Astrophysics Data System (ADS)

    Wei, Xin; Sun, Bing

    2011-10-01

    The fluid-structure interaction may occur in space launch vehicles, which would lead to bad performance of vehicles, damage equipments on vehicles, or even affect astronauts' health. In this paper, analysis on dynamic behavior of liquid oxygen (LOX) feeding pipe system in a large scale launch vehicle is performed, with the effect of fluid-structure interaction (FSI) taken into consideration. The pipe system is simplified as a planar FSI model with Poisson coupling and junction coupling. Numerical tests on pipes between the tank and the pump are solved by the finite volume method. Results show that restrictions weaken the interaction between axial and lateral vibrations. The reasonable results regarding frequencies and modes indicate that the FSI affects substantially the dynamic analysis, and thus highlight the usefulness of the proposed model. This study would provide a reference to the pipe test, as well as facilitate further studies on oscillation suppression.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

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

    SciTech Connect

    Mirin, A A; Sawyer, W B

    2004-09-24

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

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

    SciTech Connect

    Sawyer, W B; Mirin, A A

    2004-11-30

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

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

    SciTech Connect

    Sawyer, W; Mirin, A

    2004-06-25

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

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

    SciTech Connect

    Sawyer, W B; Mirin, A A

    2005-07-26

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

  4. 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.

  5. The Development of A Finite Volume Approach For Spherical Dynamo Problems

    NASA Astrophysics Data System (ADS)

    Harder, H.; Breuer, M.; Hansen, U.

    We will present the development towards a Finite Volume solution of spherical dy- namo problems. The governing equations are formulated in a cartesian frame of ref- erence, the discretisation is then adapted to a spherical shell. We use an implicit time- stepping method, namely the Crank-Nicolson scheme. The discretised equations are solved iteratively by point relaxation methods, except for the pressure correction equa- tion. For the latter we will give a comparison of conjugate gradient and bi-conjugate gradient methods and we will discuss their efficiency with various preconditioners. For the parallel implementation of the method we use domain decomposition and standard message passing routines. The advantages of this approach as compared to the presently existing spectral codes will be discussed and results for various convec- tion ploblems like creeping flows, infinite Prandtl number flows, and flows in rapidly rotating spheres will be presented.

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

    NASA Astrophysics Data System (ADS)

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

    2015-10-01

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

  7. A domain decomposition approach to finite volume solutions of the Euler equations on unstructured triangular meshes

    NASA Astrophysics Data System (ADS)

    Dolean, Victoria; Lanteri, Stéphane

    2001-11-01

    We report on our recent efforts on the formulation and the evaluation of a domain decomposition algorithm for the parallel solution of two-dimensional compressible inviscid flows. The starting point is a flow solver for the Euler equations, which is based on a mixed finite element/finite volume formulation on unstructured triangular meshes. Time integration of the resulting semi-discrete equations is obtained using a linearized backward Euler implicit scheme. As a result, each pseudo-time step requires the solution of a sparse linear system for the flow variables. In this study, a non-overlapping domain decomposition algorithm is used for advancing the solution at each implicit time step. First, we formulate an additive Schwarz algorithm using appropriate matching conditions at the subdomain interfaces. In accordance with the hyperbolic nature of the Euler equations, these transmission conditions are Dirichlet conditions for the characteristic variables corresponding to incoming waves. Then, we introduce interface operators that allow us to express the domain decomposition algorithm as a Richardson-type iteration on the interface unknowns. Algebraically speaking, the Schwarz algorithm is equivalent to a Jacobi iteration applied to a linear system whose matrix has a block structure. A substructuring technique can be applied to this matrix in order to obtain a fully implicit scheme in terms of interface unknowns. In our approach, the interface unknowns are numerical (normal) fluxes. Copyright

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

    PubMed

    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.

  9. 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

  10. 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.

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

    SciTech Connect

    Ghenam, L.; Djoudi, A. Ait El

    2012-06-27

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

  12. Accurate automatic estimation of total intracranial volume: a nuisance variable with less nuisance.

    PubMed

    Malone, Ian B; Leung, Kelvin K; Clegg, Shona; Barnes, Josephine; Whitwell, Jennifer L; Ashburner, John; Fox, Nick C; Ridgway, Gerard R

    2015-01-01

    Total intracranial volume (TIV/ICV) is an important covariate for volumetric analyses of the brain and brain regions, especially in the study of neurodegenerative diseases, where it can provide a proxy of maximum pre-morbid brain volume. The gold-standard method is manual delineation of brain scans, but this requires careful work by trained operators. We evaluated Statistical Parametric Mapping 12 (SPM12) automated segmentation for TIV measurement in place of manual segmentation and also compared it with SPM8 and FreeSurfer 5.3.0. For T1-weighted MRI acquired from 288 participants in a multi-centre clinical trial in Alzheimer's disease we find a high correlation between SPM12 TIV and manual TIV (R(2)=0.940, 95% Confidence Interval (0.924, 0.953)), with a small mean difference (SPM12 40.4±35.4ml lower than manual, amounting to 2.8% of the overall mean TIV in the study). The correlation with manual measurements (the key aspect when using TIV as a covariate) for SPM12 was significantly higher (p<0.001) than for either SPM8 (R(2)=0.577 CI (0.500, 0.644)) or FreeSurfer (R(2)=0.801 CI (0.744, 0.843)). These results suggest that SPM12 TIV estimates are an acceptable substitute for labour-intensive manual estimates even in the challenging context of multiple centres and the presence of neurodegenerative pathology. We also briefly discuss some aspects of the statistical modelling approaches to adjust for TIV. PMID:25255942

  13. STEALTH: a Lagrange explicit finite-difference code for solid, structural, and thermohydraulic analysis. Volume 8B. STEALTH/WHAMSE: a 3-D fluid-structure interaction code

    SciTech Connect

    Not Available

    1984-10-01

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

  14. 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.

  15. 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.

  16. 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.

  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. 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.

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

    NASA Astrophysics Data System (ADS)

    Degawa, Masashi

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

  20. 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

    2016-01-01

    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

  1. 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

  2. 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.

  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. 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

  5. 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.

  6. Accurate kinematic measurement at interfaces between dissimilar materials using conforming finite-element-based digital image correlation

    NASA Astrophysics Data System (ADS)

    Tao, Ran; Moussawi, Ali; Lubineau, Gilles; Pan, Bing

    2016-06-01

    Digital image correlation (DIC) is now an extensively applied full-field measurement technique with subpixel accuracy. A systematic drawback of this technique, however, is the smoothening of the kinematic field (e.g., displacement and strains) across interfaces between dissimilar materials, where the deformation gradient is known to be large. This can become an issue when a high level of accuracy is needed, for example, in the interfacial region of composites or joints. In this work, we described the application of global conforming finite-element-based DIC technique to obtain precise kinematic fields at interfaces between dissimilar materials. Speckle images from both numerical and actual experiments processed by the described global DIC technique better captured sharp strain gradient at the interface than local subset-based DIC.

  7. 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.

  8. 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.

  9. 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

  10. A non-empirical, parameter-free, hybrid functional for accurate calculations of optoelectronic properties of finite systems

    NASA Astrophysics Data System (ADS)

    Brawand, Nicholas; Vörös, Márton; Govoni, Marco; Galli, Giulia

    The accurate prediction of optoelectronic properties of molecules and solids is a persisting challenge for current density functional theory (DFT) based methods. We propose a hybrid functional where the mixing fraction of exact and local exchange is determined by a non-empirical, system dependent function. This functional yields ionization potentials, fundamental and optical gaps of many, diverse systems in excellent agreement with experiments, including organic and inorganic molecules and nanocrystals. We further demonstrate that the newly defined hybrid functional gives the correct alignment between the energy level of the exemplary TTF-TCNQ donor-acceptor system. DOE-BES: DE-FG02-06ER46262.

  11. 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.

  12. Tetrahedral finite-volume solutions to the Navier-Stokes equations on complex configurations

    NASA Astrophysics Data System (ADS)

    Frink, N. T.; Pirzadeh, S. Z.

    1999-09-01

    A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the USA for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

  13. 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.

  14. 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

  15. 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.

  16. A finite volume Fokker-Planck collision operator in constants-of-motion coordinates

    NASA Astrophysics Data System (ADS)

    Xiong, Z.; Xu, X. Q.; Cohen, B. I.; Cohen, R.; Dorr, M. R.; Hittinger, J. A.; Kerbel, G.; Nevins, W. M.; Rognlien, T.

    2006-04-01

    TEMPEST is a 5D gyrokinetic continuum code for edge plasmas. Constants of motion, namely, the total energy E and the magnetic moment μ, are chosen as coordinate s because of their advantage in minimizing numerical diffusion in advection operato rs. Most existing collision operators are written in other coordinates; using them by interpolating is shown to be less satisfactory in maintaining overall numerical accuracy and conservation. Here we develop a Fokker-Planck collision operator directly in (E,μ) space usin g a finite volume approach. The (E, μ) grid is Cartesian, and the turning point boundary represents a straight line cutting through the grid that separates the ph ysical and non-physical zones. The resulting cut-cells are treated by a cell-mergin g technique to ensure a complete particle conservation. A two dimensional fourth or der reconstruction scheme is devised to achieve good numerical accuracy with modest number of grid points. The new collision operator will be benchmarked by numerical examples.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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. PMID:26944687

  2. An unstructured-grid finite-volume surface wave model (FVCOM-SWAVE): Implementation, validations and applications

    NASA Astrophysics Data System (ADS)

    Qi, Jianhua; Chen, Changsheng; Beardsley, Robert C.; Perrie, Will; Cowles, Geoffrey W.; Lai, Zhigang

    The structured-grid surface wave model SWAN (Simulating Waves Nearshore) has been converted into an unstructured-grid finite-volume version (hereafter referred to as FVCOM-SWAVE) for use in coastal ocean regions with complex irregular geometry. The implementation is made using the Flux-Corrected Transport (FCT) algorithm in frequency space, the implicit Crank-Nicolson method in directional space and options of explicit or implicit second-order upwind finite-volume schemes in geographic space. FVCOM-SWAVE is validated using four idealized benchmark test problems with emphasis on numerical dispersion, wave-current interactions, wave propagation over a varying-bathymetry shallow water region, and the basic wave grow curves. Results demonstrate that in the rectangular geometric domain, the second-order finite-volume method used in FVCOM-SWAVE has the same accuracy as the third-order finite-difference method used in SWAN. FVCOM-SWAVE was then applied to simulate wind-induced surface waves on the US northeast shelf with a central focus in the Gulf of Maine and New England Shelf. Through improved geometric fitting of the complex irregular coastline, FVCOM-SWAVE was able to robustly capture the spatial and temporal variation of surface waves in both deep and shallow regions along the US northeast coast.

  3. 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.; Waltz, Jacob; Wohlbier, John G.

    2015-03-11

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

  4. 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.

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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.

  10. A 3-D implicit finite-volume model of shallow water flows

    NASA Astrophysics Data System (ADS)

    Wu, Weiming; Lin, Qianru

    2015-09-01

    A three-dimensional (3-D) model has been developed to simulate shallow water flows in large water bodies, such as coastal and estuarine waters. The eddy viscosity is determined using a newly modified mixing length model that uses different mixing length functions for the horizontal and vertical shear strain rates. The 3-D shallow water flow equations with the hydrostatic pressure assumption are solved using an implicit finite-volume method based on a quadtree (telescoping) rectangular mesh on the horizontal plane and the sigma coordinate in the vertical direction. The quadtree technique can locally refine the mesh around structures or in high-gradient regions by splitting a coarse cell into four child cells. The grid nodes are numbered with a one-dimensional index system that has unstructured grid feature for better grid flexibility. All the primary variables are arranged in a non-staggered grid system. Fluxes at cell faces are determined using a Rhie and Chow-type momentum interpolation, to avoid the possible spurious checkerboard oscillations caused by linear interpolation. Each of the discretized governing equations is solved iteratively using the flexible GMRES method with ILUT preconditioning, and coupling of water level and velocity among these equations is achieved by using the SIMPLEC algorithm with under-relaxation. The model has been tested in four cases, including steady flow near a spur-dyke, tidal flows in San Francisco Bay and Gironde Estuary, and wind-induced current in a flume. The calculated water levels and velocities are in good agreement with the measured values.

  11. Moduli thermalization and finite temperature effects in "big" divisor large volume D3/ D7 Swiss-cheese compactification

    NASA Astrophysics Data System (ADS)

    Shukla, Pramod

    2011-01-01

    In the context of Type IIB compactified on a large volume Swiss-Cheese orientifold in the presence of a mobile space-time filling D3-brane and stacks of fluxed D7-branes wrapping the "big" divisor Σ B of a Swiss-Cheese Calabi Yau in WCP 4[1, 1, 1, 6, 9], we explore various implications of moduli dynamics and discuss their couplings and decay into MSSM (-like) matter fields early in the history of universe to reach thermal equilibrium. Like finite temperature effects in O'KKLT, we observe that the local minimum of zero-temperature effective scalar potential is stable against any finite temperature corrections (up to two-loops) in large volume scenarios as well. Also we find that moduli are heavy enough to avoid any cosmological moduli problem.

  12. 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.

  13. A cut-cell finite volume - finite element coupling approach for fluid-structure interaction in compressible flow

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

    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.

  14. 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.

  15. 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.

  16. 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.

  17. Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1998-01-01

    We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.

  18. 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.

  19. A fourth order accurate adaptive mesh refinement method forpoisson's equation

    SciTech Connect

    Barad, Michael; Colella, Phillip

    2004-08-20

    We present a block-structured adaptive mesh refinement (AMR) method for computing solutions to Poisson's equation in two and three dimensions. It is based on a conservative, finite-volume formulation of the classical Mehrstellen methods. This is combined with finite volume AMR discretizations to obtain a method that is fourth-order accurate in solution error, and with easily verifiable solvability conditions for Neumann and periodic boundary conditions.

  20. 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.

  1. A numerically efficient finite element hydroelastic analysis. Volume 1: Theory and results

    NASA Technical Reports Server (NTRS)

    Coppolino, R. N.

    1976-01-01

    Symmetric finite element matrix formulations for compressible and incompressible hydroelasticity are developed on the basis of Toupin's complementary formulation of classical mechanics. Results of implementation of the new technique in the NASTRAN structural analysis program are presented which demonstrate accuracy and efficiency.

  2. 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.)

  3. Stable, high-order SBP-SAT finite difference operators to enable accurate simulation of compressible turbulent flows on curvilinear grids, with application to predicting turbulent jet noise

    NASA Astrophysics Data System (ADS)

    Byun, Jaeseung; Bodony, Daniel; Pantano, Carlos

    2014-11-01

    Improved order-of-accuracy discretizations often require careful consideration of their numerical stability. We report on new high-order finite difference schemes using Summation-By-Parts (SBP) operators along with the Simultaneous-Approximation-Terms (SAT) boundary condition treatment for first and second-order spatial derivatives with variable coefficients. In particular, we present a highly accurate operator for SBP-SAT-based approximations of second-order derivatives with variable coefficients for Dirichlet and Neumann boundary conditions. These terms are responsible for approximating the physical dissipation of kinetic and thermal energy in a simulation, and contain grid metrics when the grid is curvilinear. Analysis using the Laplace transform method shows that strong stability is ensured with Dirichlet boundary conditions while weaker stability is obtained for Neumann boundary conditions. Furthermore, the benefits of the scheme is shown in the direct numerical simulation (DNS) of a Mach 1.5 compressible turbulent supersonic jet using curvilinear grids and skew-symmetric discretization. Particularly, we show that the improved methods allow minimization of the numerical filter often employed in these simulations and we discuss the qualities of the simulation.

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

    NASA Astrophysics Data System (ADS)

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

    2014-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2013-12-01

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

  6. 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.

  7. 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.

  8. Modelling capillary trapping using finite-volume simulation of two-phase flow directly on micro-CT images

    NASA Astrophysics Data System (ADS)

    Raeini, Ali Q.; Bijeljic, Branko; Blunt, Martin J.

    2015-09-01

    We study capillary trapping in porous media using direct pore-scale simulation of two-phase flow on micro-CT images of a Berea sandstone and a sandpack. The trapped non-wetting phase saturations are predicted by solving the full Navier-Stokes equations using a volume-of-fluid based finite-volume framework to simulate primary drainage followed by water injection. Using these simulations, we analyse the effects of initial non-wetting-phase saturation, capillary number and flow direction on the residual saturation. The predictions from our numerical method are in agreement with published experimental measurements of capillary trapping curves. This shows that our direct simulation method can be used to elucidate the effect of pore structure and flow pattern of capillary trapping and provides a platform to study the physics of multiphase flow at the pore scale.

  9. 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.

  10. 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

    2016-10-01

    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.

  11. 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

  12. 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.

  13. Simulation of vapor-liquid coexistence in finite volumes: a method to compute the surface free energy of droplets.

    PubMed

    Schrader, Manuel; Virnau, Peter; Binder, Kurt

    2009-06-01

    When a fluid at a constant density rho in between the densities of coexisting vapor (rhov) and liquid (rhol) at temperatures below criticality is studied in a (cubic) box of finite linear dimension L , phase separation occurs in this finite volume, provided L is large enough. For a range of densities, one can observe a liquid droplet (at density rhol' slightly exceeding rhol) coexisting in stable thermal equilibrium with surrounding vapor (with density rhov'>rhov, so in the thermodynamic limit such a vapor would be supersaturated). We show, via Monte Carlo simulations of a Lennard-Jones model of a fluid and based on a phenomenological thermodynamic analysis, that via recording the chemical potential micro as function of rho, one can obtain precise estimates of the droplet surface free energy for a wide range of droplet radii. We also show that the deviations of this surface free energy from the prediction based on the "capillarity approximation" of classical nucleation theory (i.e., using the interfacial free energy of a flat liquid-vapor interface for the surface free energy of a droplet irrespective of its radius) are rather small. We also study carefully the limitation of the present method due to the "droplet evaporation/condensation transition" occurring for small volumes and demonstrate that very good equilibrium is achieved in our study, by showing that the radial profile of the local chemical potential from the droplet center to the outside is perfectly flat.

  14. Coupled numerical approach combining finite volume and lattice Boltzmann methods for multi-scale multi-physicochemical processes

    SciTech Connect

    Chen, Li; He, Ya-Ling; Kang, Qinjun; Tao, Wen-Quan

    2013-12-15

    A coupled (hybrid) simulation strategy spatially combining the finite volume method (FVM) and the lattice Boltzmann method (LBM), called CFVLBM, is developed to simulate coupled multi-scale multi-physicochemical processes. In the CFVLBM, computational domain of multi-scale problems is divided into two sub-domains, i.e., an open, free fluid region and a region filled with porous materials. The FVM and LBM are used for these two regions, respectively, with information exchanged at the interface between the two sub-domains. A general reconstruction operator (RO) is proposed to derive the distribution functions in the LBM from the corresponding macro scalar, the governing equation of which obeys the convection–diffusion equation. The CFVLBM and the RO are validated in several typical physicochemical problems and then are applied to simulate complex multi-scale coupled fluid flow, heat transfer, mass transport, and chemical reaction in a wall-coated micro reactor. The maximum ratio of the grid size between the FVM and LBM regions is explored and discussed. -- Highlights: •A coupled simulation strategy for simulating multi-scale phenomena is developed. •Finite volume method and lattice Boltzmann method are coupled. •A reconstruction operator is derived to transfer information at the sub-domains interface. •Coupled multi-scale multiple physicochemical processes in micro reactor are simulated. •Techniques to save computational resources and improve the efficiency are discussed.

  15. 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.

  16. Computation of full-field displacements in a scaffold implant using digital volume correlation and finite element analysis.

    PubMed

    Madi, K; Tozzi, G; Zhang, Q H; Tong, J; Cossey, A; Au, A; Hollis, D; Hild, F

    2013-09-01

    Measurements of three-dimensional displacements in a scaffold implant under uniaxial compression have been obtained by two digital volume correlation (DVC) methods, and compared with those obtained from micro-finite element models. The DVC methods were based on two approaches, a local approach which registers independent small volumes and yields discontinuous displacement fields; and a global approach where the registration is performed on the whole volume of interest, leading to continuous displacement fields. A customised mini-compression device was used to perform in situ step-wise compression of the scaffold within a micro-computed tomography (μCT) chamber, and the data were collected at steps of interest. Displacement uncertainties, ranging from 0.006 to 0.02 voxel (i.e. 0.12-0.4 μm), with a strain uncertainty between 60 and 600 με, were obtained with a spatial resolution of 32 voxels using both approaches, although the global approach has lower systematic errors. Reduced displacement and strain uncertainties may be obtained using the global approach by increasing the element size; and using the local approach by increasing the number of intermediary sub-volumes. Good agreements between the results from the DVC measurements and the FE simulations were obtained in the primary loading direction as well as in the lateral directions. This study demonstrates that volumetric strain measurements can be obtained successfully using DVC, which may be a useful tool to investigate mechanical behaviour of porous implants.

  17. 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.

  18. ABAQUS-EPGEN: a general-purpose finite-element code. Volume 4. Systems manual

    SciTech Connect

    Hibbitt, H.D.; Karlsson, B.I.; Sorensen, E.P.

    1985-06-01

    This document is the Systems Manual for ABAQUS/EPGEN, a general purpose finite element computer program designed specifically to serve advanced structural analysis needs. ABAQUS/EPGEN is a large, modular, software system, made up of libraries of finite elements, constitutive models, arithmetic routines, and executive level routines that control the flow through the program to provide various analysis procedures. ABAQUS has extensive data files which are managed independently from the engineering/modeling code. The program is written in FORTRAN 77, with additional conventions within the language to ensure that the code is readily portable across different computers and operating systems. This includes support of fully single and fully double precision versions. This manual documents the system design of the code, including detailed descriptions of data file contents, and dictionaries of subroutines and common blocks. This outline can help programmers and development engineers understand the structure of the code and its use on different computers and operating systems. The highly sophisticated, nonlinear computer code supports advanced structural analyses for nuclear and fossil fuel power plant designs. The ABAQUS-EPGEN code analyzes such general nonlinear phenomena as fluid-structure interactions, reinforced concrete behavior, thermal stress, fracture mechanics, and high-temperature structural behavior. 18 refs.

  19. Finite volume analysis of temperature effects induced by active MRI implants with cylindrical symmetry: 1. Properly working devices

    PubMed Central

    Busch, Martin HJ; Vollmann, Wolfgang; Schnorr, Jörg; Grönemeyer, Dietrich HW

    2005-01-01

    Background Active Magnetic Resonance Imaging implants are constructed as resonators tuned to the Larmor frequency of a magnetic resonance system with a specific field strength. The resonating circuit may be embedded into or added to the normal metallic implant structure. The resonators build inductively coupled wireless transmit and receive coils and can amplify the signal, normally decreased by eddy currents, inside metallic structures without affecting the rest of the spin ensemble. During magnetic resonance imaging the resonators generate heat, which is additional to the usual one described by the specific absorption rate. This induces temperature increases of the tissue around the circuit paths and inside the lumen of an active implant and may negatively influence patient safety. Methods This investigation provides an overview of the supplementary power absorbed by active implants with a cylindrical geometry, corresponding to vessel implants such as stents, stent grafts or vena cava filters. The knowledge of the overall absorbed power is used in a finite volume analysis to estimate temperature maps around different implant structures inside homogeneous tissue under worst-case assumptions. The "worst-case scenario" assumes thermal heat conduction without blood perfusion inside the tissue around the implant and mostly without any cooling due to blood flow inside vessels. Results The additional power loss of a resonator is proportional to the volume and the quality factor, as well as the field strength of the MRI system and the specific absorption rate of the applied sequence. For properly working devices the finite volume analysis showed only tolerable heating during MRI investigations in most cases. Only resonators transforming a few hundred mW into heat may reach temperature increases over 5 K. This requires resonators with volumes of several ten cubic centimeters, short inductor circuit paths with only a few 10 cm and a quality factor above ten. Using MR

  20. 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.

  1. 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.

  2. 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.

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

    NASA Astrophysics Data System (ADS)

    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.

  5. 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.

  6. Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium

    NASA Astrophysics Data System (ADS)

    Mishra, S.; Schwab, Ch.; Šukys, J.

    2016-05-01

    We consider the very challenging problem of efficient uncertainty quantification for acoustic wave propagation in a highly heterogeneous, possibly layered, random medium, characterized by possibly anisotropic, piecewise log-exponentially distributed Gaussian random fields. A multi-level Monte Carlo finite volume method is proposed, along with a novel, bias-free upscaling technique that allows to represent the input random fields, generated using spectral FFT methods, efficiently. Combined together with a recently developed dynamic load balancing algorithm that scales to massively parallel computing architectures, the proposed method is able to robustly compute uncertainty for highly realistic random subsurface formations that can contain a very high number (millions) of sources of uncertainty. Numerical experiments, in both two and three space dimensions, illustrating the efficiency of the method are presented.

  7. 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.

  8. 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.

  9. Contribution of the finite volume point dilution method for measurement of groundwater fluxes in a fractured aquifer.

    PubMed

    Jamin, P; Goderniaux, P; Bour, O; Le Borgne, T; Englert, A; Longuevergne, L; Brouyère, S

    2015-11-01

    Measurement of groundwater fluxes is the basis of all hydrogeological study, from hydraulic characterization to the most advanced reactive transport modeling. Usual groundwater flux estimation with Darcy's law may lead to cumulated errors on spatial variability, especially in fractured aquifers where local direct measurement of groundwater fluxes becomes necessary. In the present study, both classical point dilution method (PDM) and finite volume point dilution method (FVPDM) are compared on the fractured crystalline aquifer of Ploemeur, France. The manipulation includes the first use of the FVPDM in a fractured aquifer using a double packer. This configuration limits the vertical extent of the tested zone to target a precise fracture zone of the aquifer. The result of this experiment is a continuous monitoring of groundwater fluxes that lasted for more than 4 days. Measurements of groundwater flow rate in the fracture (Q(t)) by PDM provide good estimates only if the mixing volume (V(w)) (volume of water in which the tracer is mixed) is precisely known. Conversely, the FVPDM allows for an independent estimation of V(w) and Q(t), leading to better precision in case of complex experimental setup such as the one used. The precision of a PDM does not rely on the duration of the experiment while a FVPDM may require long experimental duration to guarantees a good precision. Classical PDM should then be used for rapid estimation of groundwater flux using simple experimental setup. On the other hand, the FVPDM is a more precise method that has a great potential for development but may require longer duration experiment to achieve a good precision if the groundwater fluxes investigated are low and/or the mixing volume is large. PMID:26519822

  10. 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.

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

    SciTech Connect

    Burton, D.E.

    1994-10-17

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

  12. Modeling of Flow and Water Quality Processes with Finite Volume Method due to Spreading and Dispersion of Petrochemical Pollution in the Hydro-Environments

    NASA Astrophysics Data System (ADS)

    Sarhadi Zadeh, Ehsan; Hejazi, Kourosh

    2009-11-01

    Having two water frontiers, namely (everlasting) Persian Gulf and Oman Sea in the south and Caspian Sea in the north, intense dependence on extracting and exporting oil, especially via marine fleets and ever-increasing development of petrochemical industry, Iran is exposed to severe environmental damages caused by oil and petrochemical industries. This essay investigates how oil spill is diffused and its environmental pollution is spread. The movement of oil spill, and its diffusion in water and its effects on water and the environment has been simulated by developing a Depth-Averaged numerical model and using the Finite Volume method. The existing models are not efficient enough to fulfill current modeling needs. The developed model uses the parameters useful in the advection and diffusion of oil pollutions in a model appropriate for predicting the transport of oil spill. Since the Navier-Stokes Equations play an important role in the advection and diffusion of oil pollutions, it is highly important to choose an appropriate numerical method in the advection and diffusion section. In this essay, choosing the methods used in the advection and diffusion have been emphasized and highly-accurate algorithms has been used in the advection terms. These algorithms are not present in similar models. The resulting equations have been solved using the ADI method. This method solves the unknown parameters with solving a Penta-Diagonal matrix in each time step. It does so without sacrificing the desired precision.

  13. 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.

  14. 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.

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

    SciTech Connect

    Gross, M.B.

    1984-10-01

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

  16. 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.

  17. 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.

  18. Compact high order finite volume method on unstructured grids II: Extension to two-dimensional Euler equations

    NASA Astrophysics Data System (ADS)

    Wang, Qian; Ren, Yu-Xin; Li, Wanai

    2016-06-01

    In this paper, the compact least-squares finite volume method on unstructured grids proposed in our previous paper is extended to multi-dimensional systems, namely the two-dimensional Euler equations. The key element of this scheme is the compact least-squares reconstruction in which a set of constitutive relations are constructed by requiring the reconstruction polynomial and its spatial derivatives on the control volume of interest to conserve their averages on the face-neighboring cells. These relations result in an over-determined linear equation system. A large sparse system of linear equations is resulted by using the least-squares technique. An efficient solution strategy is of crucial importance for the application of the proposed scheme in multi-dimensional problems since both direct and iterative solvers for this system are computationally very expensive. In the present paper, it is found that in the cases of steady flow simulation and unsteady flow simulation using dual time stepping technique, the present reconstruction method can be coupled with temporal discretization scheme to achieve high computational efficiency. The WBAP limiter and a problem-independent shock detector are used in the simulation of flow with discontinuities. Numerical results demonstrate the high order accuracy, high computational efficiency and capability of handling both complex physics and geometries of the proposed schemes.

  19. Three-dimensional digital holographic aperture synthesis for rapid and highly-accurate large-volume metrology

    NASA Astrophysics Data System (ADS)

    Crouch, Stephen; Kaylor, Brant M.; Barber, Zeb W.; Reibel, Randy R.

    2015-09-01

    Currently large volume, high accuracy three-dimensional (3D) metrology is dominated by laser trackers, which typically utilize a laser scanner and cooperative reflector to estimate points on a given surface. The dependency upon the placement of cooperative targets dramatically inhibits the speed at which metrology can be conducted. To increase speed, laser scanners or structured illumination systems can be used directly on the surface of interest. Both approaches are restricted in their axial and lateral resolution at longer stand-off distances due to the diffraction limit of the optics used. Holographic aperture ladar (HAL) and synthetic aperture ladar (SAL) can enhance the lateral resolution of an imaging system by synthesizing much larger apertures by digitally combining measurements from multiple smaller apertures. Both of these approaches only produce two-dimensional imagery and are therefore not suitable for large volume 3D metrology. We combined the SAL and HAL approaches to create a swept frequency digital holographic 3D imaging system that provides rapid measurement speed for surface coverage with unprecedented axial and lateral resolution at longer standoff ranges. The technique yields a "data cube" of Fourier domain data, which can be processed with a 3D Fourier transform to reveal a 3D estimate of the surface. In this paper, we provide the theoretical background for the technique and show experimental results based on an ultra-wideband frequency modulated continuous wave (FMCW) chirped heterodyne ranging system showing ~100 micron lateral and axial precisions at >2 m standoff distances.

  20. STEALTH: a Lagrange explicit finite difference code for solids, structural, and thermohydraulic analysis. Volume 7: implicit hydrodynamics. Computer code manual. [PWR; BWR

    SciTech Connect

    McKay, M.W.

    1982-06-01

    STEALTH is a family of computer codes that solve the equations of motion for a general continuum. These codes can be used to calculate a variety of physical processes in which the dynamic behavior of a continuum is involved. The versions of STEALTH described in this volume were designed for the calculation of problems involving low-speed fluid flow. They employ an implicit finite difference technique to solve the one- and two-dimensional equations of motion, written for an arbitrary coordinate system, for both incompressible and compressible fluids. The solution technique involves an iterative solution of the implicit, Lagrangian finite difference equations. Convection terms that result from the use of an arbitrarily-moving coordinate system are calculated separately. This volume provides the theoretical background, the finite difference equations, and the input instructions for the one- and two-dimensional codes; a discussion of several sample problems; and a listing of the input decks required to run those problems.

  1. 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.

  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. An adaptive finite volume solver for steady Euler equations with non-oscillatory k-exact reconstruction

    NASA Astrophysics Data System (ADS)

    Hu, Guanghui; Yi, Nianyu

    2016-05-01

    In this paper, we present an adaptive finite volume method for steady Euler equations with a non-oscillatory k-exact reconstruction on unstructured mesh. The numerical framework includes a Newton method as an outer iteration to linearize the Euler equations, and a geometrical multigrid method as an inner iteration to solve the derived linear system. A non-oscillatory k-exact reconstruction of the conservative solution in each element is proposed for the high order and non-oscillatory behavior of the numerical solutions. The importance on handling the curved boundary in an appropriate way is also studied with the numerical experiments. The h-adaptive method is introduced to enhance the efficiency of the algorithm. The numerical tests show successfully that the quality solutions can be obtained smoothly with the proposed algorithm, i.e., the expected convergence order of the numerical solution with the mesh refinement can be reached, while the non-oscillation shock structure can be obtained. Furthermore, the mesh adaptive method with the appropriate error indicators can effectively enhance the implementation efficiency of numerical method, while the steady state convergence and numerical accuracy are kept in the meantime.

  4. A two-dimensional coupled flow-mass transport model based on an improved unstructured finite volume algorithm.

    PubMed

    Zhou, Jianzhong; Song, Lixiang; Kursan, Suncana; Liu, Yi

    2015-05-01

    A two-dimensional coupled water quality model is developed for modeling the flow-mass transport in shallow water. To simulate shallow flows on complex topography with wetting and drying, an unstructured grid, well-balanced, finite volume algorithm is proposed for numerical resolution of a modified formulation of two-dimensional shallow water equations. The slope-limited linear reconstruction method is used to achieve second-order accuracy in space. The algorithm adopts a HLLC-based integrated solver to compute the flow and mass transport fluxes simultaneously, and uses Hancock's predictor-corrector scheme for efficient time stepping as well as second-order temporal accuracy. The continuity and momentum equations are updated in both wet and dry cells. A new hybrid method, which can preserve the well-balanced property of the algorithm for simulations involving flooding and recession, is proposed for bed slope terms approximation. The effectiveness and robustness of the proposed algorithm are validated by the reasonable good agreement between numerical and reference results of several benchmark test cases. Results show that the proposed coupled flow-mass transport model can simulate complex flows and mass transport in shallow water. PMID:25686488

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

    NASA Astrophysics Data System (ADS)

    Liu, Hongxu; Jiao, Xiangmin

    2016-06-01

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

  6. 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.

  7. XTROEM-FV: a new code for computational astrophysics based on very high order finite-volume methods - I. Magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

    The present work describes the building blocks of a new code for computational magnetohydrodynamics based on very high order finite volume methods on Cartesian meshes. Spatial high-order accuracy is obtained with a weighted essentially non-oscillatory (WENO) reconstruction operator up to seventh order, while the time discretization is performed with a fourth-order strong-stability preserving Runge-Kutta method. Based on a shock-detection approach, the reconstruction operator employs a very high order WENO scheme in smooth flow regions and a third-order WENO scheme in those parts of the flow with discontinuities or shocks. The generalized Lagrange multiplier method is employed to enforce the solenoidal constraint on the magnetic field. Extensive numerical computations in one and two space dimensions are reported. Convergence rates for smooth flows verify the high-order accuracy of the scheme, and tests with strong shocks, including the Orszag-Tang vortex, the cylindrical blast wave problem, the rotor problem, and the Kelvin-Helmholtz instability, confirm the robustness and stability of the approach.

  8. 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.

  9. A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries

    NASA Astrophysics Data System (ADS)

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

    2013-03-01

    A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach.

  10. Shorter sampling periods and accurate estimates of milk volume and components are possible for pasture based dairy herds milked with automated milking systems.

    PubMed

    Kamphuis, Claudia; Burke, Jennie K; Taukiri, Sarah; Petch, Susan-Fay; Turner, Sally-Anne

    2016-08-01

    Dairy cows grazing pasture and milked using automated milking systems (AMS) have lower milking frequencies than indoor fed cows milked using AMS. Therefore, milk recording intervals used for herd testing indoor fed cows may not be suitable for cows on pasture based farms. We hypothesised that accurate standardised 24 h estimates could be determined for AMS herds with milk recording intervals of less than the Gold Standard (48 hs), but that the optimum milk recording interval would depend on the herd average for milking frequency. The Gold Standard protocol was applied on five commercial dairy farms with AMS, between December 2011 and February 2013. From 12 milk recording test periods, involving 2211 cow-test days and 8049 cow milkings, standardised 24 h estimates for milk volume and milk composition were calculated for the Gold Standard protocol and compared with those collected during nine alternative sampling scenarios, including six shorter sampling periods and three in which a fixed number of milk samples per cow were collected. Results infer a 48 h milk recording protocol is unnecessarily long for collecting accurate estimates during milk recording on pasture based AMS farms. Collection of two milk samples only per cow was optimal in terms of high concordance correlation coefficients for milk volume and components and a low proportion of missed cow-test days. Further research is required to determine the effects of diurnal variations in milk composition on standardised 24 h estimates for milk volume and components, before a protocol based on a fixed number of samples could be considered. Based on the results of this study New Zealand have adopted a split protocol for herd testing based on the average milking frequency for the herd (NZ Herd Test Standard 8100:2015). PMID:27600967

  11. 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.

  12. An implicit finite element method for simulating inhomogeneous deformation and shear bands of amorphous alloys based on the free-volume model

    SciTech Connect

    Gao, Yanfei

    2006-01-01

    Inhomogeneous deformation of amorphous alloys is caused by the initiation, multiplication and interaction of shear bands (i.e., narrow bands with large plastic deformation). Based on the free volume model under the generalized multiaxial stress state, this work develops a finite element scheme to model the individual processes of shear bands that contribute to the macroscopic plasticity behavior. In this model, the stress-driven increase of the free volume reduces the viscosity and thus leads to the strain localization in the shear band. Using the small-strain and rate-dependent plasticity framework, the plastic strain is assumed to be proportional to the deviatoric stress, and the flow stress is a function of the free volume, while the temporal change of the free volume is also coupled with the stress state. Nonlinear equations from the incremental finite element formulation are solved by the Newton-Raphson method, in which the corresponding material tangent is obtained by simultaneously and implicitly integrating the plastic flow equation and the evolution equation of the free volume field. This micromechanical model allows us to study the interaction between individual shear bands and between the shear bands and the background stress fields. To illustrate its capabilities, the method is used to solve representative boundary value problems.

  13. 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.

  14. 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.

  15. 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).

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

    SciTech Connect

    Hofmann, R.

    1981-11-01

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

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

    SciTech Connect

    Hofmann, R.

    1981-11-01

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

  18. STEALTH: a Lagrange explicit finite difference code for solids, structural, and thermohydraulic analysis. Volume 3: programmer's manual. Computer code manual. [PWR; BWR

    SciTech Connect

    Hofmann, R.

    1981-11-01

    This volume contains a description of a programming and documentation structure for the STEALTH finite difference computer programs based on general principles applicable to most large scientific computer programs. Program modularization (as well as documentation format) is based entirely on the theoretical elements of analysis of a physical system that were presented in Volume 1. FORTRAN programming and naming conventions are also described. Among the programming formats presented is a FORTRAN manual (Appendix FTN) which can be used as the basis for developing portable codes. STEALTH was developed on a CDC 7600. However, it has been designed so that it can be installed on most large scientific computers. Installation documentation exists for some facilities and can be generated easily for others.

  19. Finite Element Heat & Mass Transfer Code

    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; andmore » double porosity and double porosity/double permeability capabilities.« less

  20. Finite-volume corrections to the CP-odd nucleon matrix elements of the electromagnetic current from the QCD vacuum angle

    NASA Astrophysics Data System (ADS)

    Akan, Tarik; Guo, Feng-Kun; Meißner, Ulf-G.

    2014-09-01

    Nucleon electric dipole moments originating from strong CP-violation are being calculated by several groups using lattice QCD. We revisit the finite volume corrections to the CP-odd nucleon matrix elements of the electromagnetic current, which can be related to the electric dipole moments in the continuum, in the framework of chiral perturbation theory up to next-to-leading order taking into account the breaking of Lorentz symmetry. A chiral extrapolation of the recent lattice results of both the neutron and proton electric dipole moments is performed, which results in dn=(-2.7±1.2)×10-16eθ0 cm and dp=(2.1±1.2)×10-16eθ0 cm.

  1. Large-eddy simulations of 3D Taylor-Green vortex: comparison of Smoothed Particle Hydrodynamics, Lattice Boltzmann and Finite Volume methods

    NASA Astrophysics Data System (ADS)

    Kajzer, A.; Pozorski, J.; Szewc, K.

    2014-08-01

    In the paper we present Large-eddy simulation (LES) results of 3D Taylor- Green vortex obtained by the three different computational approaches: Smoothed Particle Hydrodynamics (SPH), Lattice Boltzmann Method (LBM) and Finite Volume Method (FVM). The Smagorinsky model was chosen as a subgrid-scale closure in LES for all considered methods and a selection of spatial resolutions have been investigated. The SPH and LBM computations have been carried out with the use of the in-house codes executed on GPU and compared, for validation purposes, with the FVM results obtained using the open-source CFD software OpenFOAM. A comparative study in terms of one-point statistics and turbulent energy spectra shows a good agreement of LES results for all methods. An analysis of the GPU code efficiency and implementation difficulties has been made. It is shown that both SPH and LBM may offer a significant advantage over mesh-based CFD methods.

  2. 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.)

  3. Finite-volume energy spectrum, fractionalized strings, and low-energy effective field theory for the quantum dimer model on the square lattice

    NASA Astrophysics Data System (ADS)

    Banerjee, D.; Bögli, M.; Hofmann, C. P.; Jiang, F.-J.; Widmer, P.; Wiese, U.-J.

    2016-09-01

    We present detailed analytic calculations of finite-volume energy spectra, mean-field theory, as well as a systematic low-energy effective field theory for the square lattice quantum dimer model. An emergent approximate spontaneously broken SO(2 ) symmetry gives rise to a pseudo-Goldstone boson. Remarkably, this soft phononlike excitation, which is massless at the Rokhsar-Kivelson (RK) point, exists far beyond this point. The Goldstone physics is captured by a systematic low-energy effective field theory. We determine its low-energy parameters by matching the analytic effective field theory with exact diagonalization results. This confirms that the model exists in the columnar (and not in a plaquette or mixed) phase all the way to the RK point.

  4. Parallel computation of unsteady, three-dimensional, chemically reacting, nonequilibrium flow using a time-split finite-volume method on the Illiac IV

    NASA Technical Reports Server (NTRS)

    Reinhardt, W. A.

    1977-01-01

    A description is presented of the split finite-volume method which is a viable numerical procedure for performing with the aid of a modern special purpose vector computer numerical simulation studies of complicated flow fields, including chemical reactions, about geometrically complex bodies. Such numerical studies are needed for the development of atmospheric entry vehicles such as the space shuttle. The equations which are approximated are quite general and can be used in studies of combustion, pollution, and other chemically reacting flow phenomena, where convective transport effects dominate the influence of radiative, viscous, and other transport mechanisms. The shock perturbed flow about a shuttle orbiter flying at a large angle of attack during atmospheric entry is illustrated. The method uses a time splitting of the convection differencing operator to achieve efficient data management.

  5. Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

    NASA Technical Reports Server (NTRS)

    Bui, Trong T.; Mankbadi, Reda R.

    1995-01-01

    Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

  6. Finite-volume versus streaming-based lattice Boltzmann algorithm for fluid-dynamics simulations: A one-to-one accuracy and performance study.

    PubMed

    Shrestha, Kalyan; Mompean, Gilmar; Calzavarini, Enrico

    2016-02-01

    A finite-volume (FV) discretization method for the lattice Boltzmann (LB) equation, which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard streaming lattice Boltzmann equation algorithm. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken as the method of choice in fluid-dynamics LB simulations. For this reason the comparative analysis is further extended to the case of realistic flows, in particular thermally driven flows in turbulent conditions. We report the successful simulation of high-Rayleigh number convective flow performed by a lattice Boltzmann FV-based algorithm with wall grid refinement.

  7. 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.

  8. 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

  9. 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.

  10. 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

  11. 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.

  12. Implicit and explicit schemes for mass consistency preservation in hybrid particle/finite-volume algorithms for turbulent reactive flows

    SciTech Connect

    Popov, Pavel P. Pope, Stephen B.

    2014-01-15

    This work addresses the issue of particle mass consistency in Large Eddy Simulation/Probability Density Function (LES/PDF) methods for turbulent reactive flows. Numerical schemes for the implicit and explicit enforcement of particle mass consistency (PMC) are introduced, and their performance is examined in a representative LES/PDF application, namely the Sandia–Sydney Bluff-Body flame HM1. A new combination of interpolation schemes for velocity and scalar fields is found to better satisfy PMC than multilinear and fourth-order Lagrangian interpolation. A second-order accurate time-stepping scheme for stochastic differential equations (SDE) is found to improve PMC relative to Euler time stepping, which is the first time that a second-order scheme is found to be beneficial, when compared to a first-order scheme, in an LES/PDF application. An explicit corrective velocity scheme for PMC enforcement is introduced, and its parameters optimized to enforce a specified PMC criterion with minimal corrective velocity magnitudes.

  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

  14. A Controls-CFD Approach for Estimation of Concentration from a Moving Aerial Source: Advantages of a Finite Volume-TVD implementation with Guidance-Based Grid Adaptation

    NASA Astrophysics Data System (ADS)

    Egorova, Tatiana; Gatsonis, Nikolaos A.; Demetriou, Michael A.

    2013-11-01

    In this work the process of gas release into the atmosphere by a moving aerial source is simulated and estimated using a sensing aerial vehicle (SAV). The process is modeled with atmospheric advection diffusion equation, which is solved by the finite volume method (FVM). Advective fluxes are constrained using total variation diminishing (TVD) approach. The estimator provides on-line estimates of concentration field and proximity of the source. The guidance of the SAV is dictated by the performance of the estimator. To further improve the estimation algorithm from the computational prospective, the grid is adapted dynamically through local refinement and coarsening. The adaptation algorithm uses the current sensor position as a center of refinement, with the areas further away from the SAV being covered by a coarse grid. This leads to the time varying state matrix of the estimator and the variation depends on the SAV motion. Advantages of the adaptive FVM-TVD implementation are illustrated on the examples of estimator performance for different source trajectories.

  15. 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.

  16. 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.

  17. 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.

  18. An investigation of Newton-Krylov algorithms for solving incompressible and low Mach number compressible fluid flow and heat transfer problems using finite volume discretization

    SciTech Connect

    McHugh, P.R.

    1995-10-01

    Fully coupled, Newton-Krylov algorithms are investigated for solving strongly coupled, nonlinear systems of partial differential equations arising in the field of computational fluid dynamics. Primitive variable forms of the steady incompressible and compressible Navier-Stokes and energy equations that describe the flow of a laminar Newtonian fluid in two-dimensions are specifically considered. Numerical solutions are obtained by first integrating over discrete finite volumes that compose the computational mesh. The resulting system of nonlinear algebraic equations are linearized using Newton`s method. Preconditioned Krylov subspace based iterative algorithms then solve these linear systems on each Newton iteration. Selected Krylov algorithms include the Arnoldi-based Generalized Minimal RESidual (GMRES) algorithm, and the Lanczos-based Conjugate Gradients Squared (CGS), Bi-CGSTAB, and Transpose-Free Quasi-Minimal Residual (TFQMR) algorithms. Both Incomplete Lower-Upper (ILU) factorization and domain-based additive and multiplicative Schwarz preconditioning strategies are studied. Numerical techniques such as mesh sequencing, adaptive damping, pseudo-transient relaxation, and parameter continuation are used to improve the solution efficiency, while algorithm implementation is simplified using a numerical Jacobian evaluation. The capabilities of standard Newton-Krylov algorithms are demonstrated via solutions to both incompressible and compressible flow problems. Incompressible flow problems include natural convection in an enclosed cavity, and mixed/forced convection past a backward facing step.

  19. 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.

  20. Shallow-water sloshing in a moving vessel with variable cross-section and wetting-drying using an extension of George's well-balanced finite volume solver

    NASA Astrophysics Data System (ADS)

    Alemi Ardakani, Hamid; Bridges, Thomas J.; Turner, Matthew R.

    2016-06-01

    A class of augmented approximate Riemann solvers due to George (2008) [12] is extended to solve the shallow-water equations in a moving vessel with variable bottom topography and variable cross-section with wetting and drying. A class of Roe-type upwind solvers for the system of balance laws is derived which respects the steady-state solutions. The numerical solutions of the new adapted augmented f-wave solvers are validated against the Roe-type solvers. The theory is extended to solve the shallow-water flows in moving vessels with arbitrary cross-section with influx-efflux boundary conditions motivated by the shallow-water sloshing in the ocean wave energy converter (WEC) proposed by Offshore Wave Energy Ltd. (OWEL) [1]. A fractional step approach is used to handle the time-dependent forcing functions. The numerical solutions are compared to an extended new Roe-type solver for the system of balance laws with a time-dependent source function. The shallow-water sloshing finite volume solver can be coupled to a Runge-Kutta integrator for the vessel motion.

  1. 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.

  2. 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.

  3. Finite volume TVD scheme on an unstructured grid system for three-dimensional MHD simulation of inhomogeneous systems including strong background potential fields

    NASA Astrophysics Data System (ADS)

    Tanaka, T.

    1994-04-01

    A three-dimensional (3D) high-resolution magnetohydrodynamic (MHD) simulation scheme on an unstructured grid system is developed for inhomogeneous systems, including strong background potential fields. The scheme is based on the finite volume method (FVM) with an upwinding numerical flux by the linearized Riemann solver. Upwindings on an unstructured grid system are realized from the fact that the MHD equations are symmetric with the rotation of the space. The equation system is modified to avoid direct inclusions of the background potential field as a dependent variable, through the use of changed dependent variables. Despite such a change of the equation system, the eigenvectors in the mode-synthesis matrix that are necessary for the evaluation of the upwinding numerical flux vectors can still be written analytically. The eigenvalues of the MHD flux Jacobian matrix that are also necessary for the upwinding calculations are derived from the well-known Alfven, fast and slow, velocities. The calculations of the eigenvectors is done with special care when the wave propagations become parallel or perpendicular to the ambient magnetic field, because degeneration of the eigenvalues occurs in these cases. To obtain a higher order of accuracy, the upwinding flux is extended to the second-order TVD numerical flux in the calculation of FVM, through the MUSCL approach and Van Leer's differentiable limiter. In order to show the efficiency of the above scheme, a numerical example is given for the interaction process of high-beta supersonic plasma flow with the region of a strong dipole field, including magnetized low-beta plasma.

  4. 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.

  5. 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

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. 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

    NASA Astrophysics Data System (ADS)

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

    2013-11-01

    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

  11. 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

  12. Numerical solution of the potential due to dipole sources in volume conductors with arbitrary geometry and conductivity.

    PubMed

    Rosenfeld, M; Tanami, R; Abboud, S

    1996-07-01

    The integral conservation equation for biological volume conductors with general geometry and arbitrary distribution of electrical conductivity is solved using a finite volume method. An effective conductivity was defined for the boundaries between regions with abrupt change of the conductivity to allow the simultaneous solution of the entire domain although the derivatives are not continuous. The geometrical singularities arising from the spherical topology of the coordinate system are removed using the conservation law. The resulting finite volume solution method is efficient both in central processing unit (CPU) time and memory requirements, allowing the solution of the volume conductor equation using a large number of mesh points (of the order of 10(5)) even on small workstations (like SGI Indigo). It results in very accurate solutions, as several comparisons with analytical solutions of head models reveal. The proposed finite volume method is an attractive alternative to the finite element and boundary element methods that are more common in bioelectric applications.

  13. LaRC design analysis report for National Transonic Facility for 9% nickel tunnel shell. Volume 1: 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.

  14. 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.

  15. Component mode synthesis and large deflection vibration of complex structures. Volume 2: Single-mode large deflection vibrations of beams and plates using finite element method

    NASA Technical Reports Server (NTRS)

    Mei, Chuh

    1987-01-01

    A finite element method is presented for the large amplitude vibrations of complex structures that can be modelled with beam and rectangular plate elements subjected to harmonic excitation. Both inplane deformation and inertia are considered in the formulation. Derivation of the harmonic force and nonlinear stiffness matrices for a beam and a rectangular plate element are presented. Solution procedures and convergence characteristics of the finite element method are described. Nonlinear response to uniform and concentrated harmonic loadings and improved nonlinear free vibration results are presented for beams and rectangular plates of various boundary conditions.

  16. STEALTH: a Lagrange explicit finite difference code for solids, structural, and thermohydraulic analysis. Volume 6: piping systems manual. Computer code manual

    SciTech Connect

    Cohen, L.M.

    1982-03-01

    This volume documents the STEALTH piping numerical code, which can simulate the time-dependent flow phenomena that occur in piping systems. This volume also contains the input instructions for the STEALTH piping code, and a sample problem of a pipe flow simulation.

  17. 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.

  18. HipMatch: an object-oriented cross-platform program for accurate determination of cup orientation using 2D-3D registration of single standard X-ray radiograph and a CT volume.

    PubMed

    Zheng, Guoyan; Zhang, Xuan; Steppacher, Simon D; Murphy, Stephen B; Siebenrock, Klaus A; Tannast, Moritz

    2009-09-01

    The widely used procedure of evaluation of cup orientation following total hip arthroplasty using single standard anteroposterior (AP) radiograph is known inaccurate, largely due to the wide variability in individual pelvic orientation relative to X-ray plate. 2D-3D image registration methods have been introduced for an accurate determination of the post-operative cup alignment with respect to an anatomical reference extracted from the CT data. Although encouraging results have been reported, their extensive usage in clinical routine is still limited. This may be explained by their requirement of a CAD model of the prosthesis, which is often difficult to be organized from the manufacturer due to the proprietary issue, and by their requirement of either multiple radiographs or a radiograph-specific calibration, both of which are not available for most retrospective studies. To address these issues, we developed and validated an object-oriented cross-platform program called "HipMatch" where a hybrid 2D-3D registration scheme combining an iterative landmark-to-ray registration with a 2D-3D intensity-based registration was implemented to estimate a rigid transformation between a pre-operative CT volume and the post-operative X-ray radiograph for a precise estimation of cup alignment. No CAD model of the prosthesis is required. Quantitative and qualitative results evaluated on cadaveric and clinical datasets are given, which indicate the robustness and the accuracy of the program. HipMatch is written in object-oriented programming language C++ using cross-platform software Qt (TrollTech, Oslo, Norway), VTK, and Coin3D and is transportable to any platform. PMID:19328585

  19. Lattice gluon and ghost propagators and the strong coupling in pure SU(3) Yang-Mills theory: Finite lattice spacing and volume effects

    NASA Astrophysics Data System (ADS)

    Duarte, Anthony G.; Oliveira, Orlando; Silva, Paulo J.

    2016-07-01

    The dependence of the Landau gauge two-point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to 1284 and for two lattice spacings 0.10 fm and 0.06 fm corresponding to volumes of ˜(13 fm )4 and ˜(8 fm )4 , respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators change with the lattice spacing a in the infrared region, with the gluon propagator having a stronger dependence on a compared to the ghost propagator. In what concerns the strong coupling constant αs(p2), as defined from gluon and ghost two-point functions, the simulations show a sizeable dependence on the lattice spacing for the infrared region and for momenta up to ˜1 GeV .

  20. 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.

  1. 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.

  2. 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

    2012-04-01

    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.

  3. An analysis of supersonic flows with low-Reynolds number compressible two-equation turbulence models using LU finite volume implicit numerical techniques

    NASA Technical Reports Server (NTRS)

    Lee, J.

    1994-01-01

    A generalized flow solver using an implicit Lower-upper (LU) diagonal decomposition based numerical technique has been coupled with three low-Reynolds number kappa-epsilon models for analysis of problems with engineering applications. The feasibility of using the LU technique to obtain efficient solutions to supersonic problems using the kappa-epsilon model has been demonstrated. The flow solver is then used to explore limitations and convergence characteristics of several popular two equation turbulence models. Several changes to the LU solver have been made to improve the efficiency of turbulent flow predictions. In general, the low-Reynolds number kappa-epsilon models are easier to implement than the models with wall-functions, but require much finer near-wall grid to accurately resolve the physics. The three kappa-epsilon models use different approaches to characterize the near wall regions of the flow. Therefore, the limitations imposed by the near wall characteristics have been carefully resolved. The convergence characteristics of a particular model using a given numerical technique are also an important, but most often overlooked, aspect of turbulence model predictions. It is found that some convergence characteristics could be sacrificed for more accurate near-wall prediction. However, even this gain in accuracy is not sufficient to model the effects of an external pressure gradient imposed by a shock-wave/ boundary-layer interaction. Additional work on turbulence models, especially for compressibility, is required since the solutions obtained with base line turbulence are in only reasonable agreement with the experimental data for the viscous interaction problems.

  4. A well-balanced finite volume scheme for the Euler equations with gravitation. The exact preservation of hydrostatic equilibrium with arbitrary entropy stratification

    NASA Astrophysics Data System (ADS)

    Käppeli, R.; Mishra, S.

    2016-03-01

    Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure gradient is nearly balanced by gravitational forces. Aims: We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. It therefore can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately. Methods: A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the well-balanced property is achieved. Results: The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code that solves time explicitly or implicitly the compressible hydrodynamics equations. We demonstrate the performance of the well-balanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for core-collapse supernovae, convection in carbon shell burning, and a realistic proto-neutron star.

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. Automatic, accurate, and reproducible segmentation of the brain and cerebro-spinal fluid in T1-weighted volume MRI scans and its application to serial cerebral and intracranial volumetry

    NASA Astrophysics Data System (ADS)

    Lemieux, Louis

    2001-07-01

    A new fully automatic algorithm for the segmentation of the brain and cerebro-spinal fluid (CSF) from T1-weighted volume MRI scans of the head was specifically developed in the context of serial intra-cranial volumetry. The method is an extension of a previously published brain extraction algorithm. The brain mask is used as a basis for CSF segmentation based on morphological operations, automatic histogram analysis and thresholding. Brain segmentation is then obtained by iterative tracking of the brain-CSF interface. Grey matter (GM), white matter (WM) and CSF volumes are calculated based on a model of intensity probability distribution that includes partial volume effects. Accuracy was assessed using a digital phantom scan. Reproducibility was assessed by segmenting pairs of scans from 20 normal subjects scanned 8 months apart and 11 patients with epilepsy scanned 3.5 years apart. Segmentation accuracy as measured by overlap was 98% for the brain and 96% for the intra-cranial tissues. The volume errors were: total brain (TBV): -1.0%, intra-cranial (ICV):0.1%, CSF: +4.8%. For repeated scans, matching resulted in improved reproducibility. In the controls, the coefficient of reliability (CR) was 1.5% for the TVB and 1.0% for the ICV. In the patients, the Cr for the ICV was 1.2%.

  10. 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.

  11. 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.

  12. Achieving Finite Element Mesh Quality via Optimization of the Jacobian Matrix Norm and Associated Quantities, Part II - A Framework for Volume Mesh Optimization and the Condition Number of the Jacobian Matrix

    SciTech Connect

    Knupp, P.M.

    1999-03-26

    Three-dimensional unstructured tetrahedral and hexahedral finite element mesh optimization is studied from a theoretical perspective and by computer experiments to determine what objective functions are most effective in attaining valid, high quality meshes. The approach uses matrices and matrix norms to extend the work in Part I to build suitable 3D objective functions. Because certain matrix norm identities which hold for 2 x 2 matrices do not hold for 3 x 3 matrices. significant differences arise between surface and volume mesh optimization objective functions. It is shown, for example, that the equivalence in two-dimensions of the Smoothness and Condition Number of the Jacobian matrix objective functions does not extend to three dimensions and further. that the equivalence of the Oddy and Condition Number of the Metric Tensor objective functions in two-dimensions also fails to extend to three-dimensions. Matrix norm identities are used to systematically construct dimensionally homogeneous groups of objective functions. The concept of an ideal minimizing matrix is introduced for both hexahedral and tetrahedral elements. Non-dimensional objective functions having barriers are emphasized as the most logical choice for mesh optimization. The performance of a number of objective functions in improving mesh quality was assessed on a suite of realistic test problems, focusing particularly on all-hexahedral ''whisker-weaved'' meshes. Performance is investigated on both structured and unstructured meshes and on both hexahedral and tetrahedral meshes. Although several objective functions are competitive, the condition number objective function is particularly attractive. The objective functions are closely related to mesh quality measures. To illustrate, it is shown that the condition number metric can be viewed as a new tetrahedral element quality measure.

  13. 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.

  14. iPhone 4s Photoplethysmography: Which Light Color Yields the Most Accurate Heart Rate and Normalized Pulse Volume Using the iPhysioMeter Application in the Presence of Motion Artifact?

    PubMed Central

    Matsumura, Kenta; Rolfe, Peter; Lee, Jihyoung; Yamakoshi, Takehiro

    2014-01-01

    Recent progress in information and communication technologies has made it possible to measure heart rate (HR) and normalized pulse volume (NPV), which are important physiological indices, using only a smartphone. This has been achieved with reflection mode photoplethysmography (PPG), by using a smartphone’s embedded flash as a light source and the camera as a light sensor. Despite its widespread use, the method of PPG is susceptible to motion artifacts as physical displacements influence photon propagation phenomena and, thereby, the effective optical path length. Further, it is known that the wavelength of light used for PPG influences the photon penetration depth and we therefore hypothesized that influences of motion artifact could be wavelength-dependant. To test this hypothesis, we made measurements in 12 healthy volunteers of HR and NPV derived from reflection mode plethysmograms recorded simultaneously at three different spectral regions (red, green and blue) at the same physical location with a smartphone. We then assessed the accuracy of the HR and NPV measurements under the influence of motion artifacts. The analyses revealed that the accuracy of HR was acceptably high with all three wavelengths (all rs > 0.996, fixed biases: −0.12 to 0.10 beats per minute, proportional biases: r = −0.29 to 0.03), but that of NPV was the best with green light (r = 0.791, fixed biases: −0.01 arbitrary units, proportional bias: r = 0.11). Moreover, the signal-to-noise ratio obtained with green and blue light PPG was higher than that of red light PPG. These findings suggest that green is the most suitable color for measuring HR and NPV from the reflection mode photoplethysmogram under motion artifact conditions. We conclude that the use of green light PPG could be of particular benefit in ambulatory monitoring where motion artifacts are a significant issue. PMID:24618594

  15. iPhone 4s photoplethysmography: which light color yields the most accurate heart rate and normalized pulse volume using the iPhysioMeter Application in the presence of motion artifact?

    PubMed

    Matsumura, Kenta; Rolfe, Peter; Lee, Jihyoung; Yamakoshi, Takehiro

    2014-01-01

    Recent progress in information and communication technologies has made it possible to measure heart rate (HR) and normalized pulse volume (NPV), which are important physiological indices, using only a smartphone. This has been achieved with reflection mode photoplethysmography (PPG), by using a smartphone's embedded flash as a light source and the camera as a light sensor. Despite its widespread use, the method of PPG is susceptible to motion artifacts as physical displacements influence photon propagation phenomena and, thereby, the effective optical path length. Further, it is known that the wavelength of light used for PPG influences the photon penetration depth and we therefore hypothesized that influences of motion artifact could be wavelength-dependant. To test this hypothesis, we made measurements in 12 healthy volunteers of HR and NPV derived from reflection mode plethysmograms recorded simultaneously at three different spectral regions (red, green and blue) at the same physical location with a smartphone. We then assessed the accuracy of the HR and NPV measurements under the influence of motion artifacts. The analyses revealed that the accuracy of HR was acceptably high with all three wavelengths (all rs > 0.996, fixed biases: -0.12 to 0.10 beats per minute, proportional biases: r =  -0.29 to 0.03), but that of NPV was the best with green light (r = 0.791, fixed biases: -0.01 arbitrary units, proportional bias: r = 0.11). Moreover, the signal-to-noise ratio obtained with green and blue light PPG was higher than that of red light PPG. These findings suggest that green is the most suitable color for measuring HR and NPV from the reflection mode photoplethysmogram under motion artifact conditions. We conclude that the use of green light PPG could be of particular benefit in ambulatory monitoring where motion artifacts are a significant issue.

  16. iPhone 4s photoplethysmography: which light color yields the most accurate heart rate and normalized pulse volume using the iPhysioMeter Application in the presence of motion artifact?

    PubMed

    Matsumura, Kenta; Rolfe, Peter; Lee, Jihyoung; Yamakoshi, Takehiro

    2014-01-01

    Recent progress in information and communication technologies has made it possible to measure heart rate (HR) and normalized pulse volume (NPV), which are important physiological indices, using only a smartphone. This has been achieved with reflection mode photoplethysmography (PPG), by using a smartphone's embedded flash as a light source and the camera as a light sensor. Despite its widespread use, the method of PPG is susceptible to motion artifacts as physical displacements influence photon propagation phenomena and, thereby, the effective optical path length. Further, it is known that the wavelength of light used for PPG influences the photon penetration depth and we therefore hypothesized that influences of motion artifact could be wavelength-dependant. To test this hypothesis, we made measurements in 12 healthy volunteers of HR and NPV derived from reflection mode plethysmograms recorded simultaneously at three different spectral regions (red, green and blue) at the same physical location with a smartphone. We then assessed the accuracy of the HR and NPV measurements under the influence of motion artifacts. The analyses revealed that the accuracy of HR was acceptably high with all three wavelengths (all rs > 0.996, fixed biases: -0.12 to 0.10 beats per minute, proportional biases: r =  -0.29 to 0.03), but that of NPV was the best with green light (r = 0.791, fixed biases: -0.01 arbitrary units, proportional bias: r = 0.11). Moreover, the signal-to-noise ratio obtained with green and blue light PPG was higher than that of red light PPG. These findings suggest that green is the most suitable color for measuring HR and NPV from the reflection mode photoplethysmogram under motion artifact conditions. We conclude that the use of green light PPG could be of particular benefit in ambulatory monitoring where motion artifacts are a significant issue. PMID:24618594

  17. 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.

  18. 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.

  19. Knots in finite memory walks

    NASA Astrophysics Data System (ADS)

    Horwath, Eric; Clisby, Nathan; Virnau, Peter

    2016-09-01

    We investigate the occurrence and size of knots in a continuum polymer model with finite memory via Monte Carlo simulations. Excluded volume interactions are local and extend only to a fixed number of successive beads along the chain, ensuring that at short length scales the excluded volume effect dominates, while at longer length scales the polymer behaves like a random walk. As such, this model may be useful for understanding the behavior of polymers in a melt or semi-dilute solution, where exactly the same crossover is believed to occur. In particular, finite memory walks allow us to investigate the role of local interactions in the transition from highly knotted ideal polymers to almost unknotted self-avoiding polymers. Even though knotting decreases substantially when a few next-nearest neighbor interactions are considered, we find that the knotting probability of a polymer chain of modest length of 500 steps only decays slowly as a function of the range of the excluded volume interaction. In this context, we also find evidence that for length scales up to the interaction length the knotting behavior of the finite memory walk resembles that of a self-avoiding walk (effectively suppressing small knots), while for larger length scales it resembles that of a random walk.

  20. 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.

  1. 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

  2. Accurate Optical Reference Catalogs

    NASA Astrophysics Data System (ADS)

    Zacharias, N.

    2006-08-01

    Current and near future all-sky astrometric catalogs on the ICRF are reviewed with the emphasis on reference star data at optical wavelengths for user applications. The standard error of a Hipparcos Catalogue star position is now about 15 mas per coordinate. For the Tycho-2 data it is typically 20 to 100 mas, depending on magnitude. The USNO CCD Astrograph Catalog (UCAC) observing program was completed in 2004 and reductions toward the final UCAC3 release are in progress. This all-sky reference catalogue will have positional errors of 15 to 70 mas for stars in the 10 to 16 mag range, with a high degree of completeness. Proper motions for the about 60 million UCAC stars will be derived by combining UCAC astrometry with available early epoch data, including yet unpublished scans of the complete set of AGK2, Hamburg Zone astrograph and USNO Black Birch programs. Accurate positional and proper motion data are combined in the Naval Observatory Merged Astrometric Dataset (NOMAD) which includes Hipparcos, Tycho-2, UCAC2, USNO-B1, NPM+SPM plate scan data for astrometry, and is supplemented by multi-band optical photometry as well as 2MASS near infrared photometry. The Milli-Arcsecond Pathfinder Survey (MAPS) mission is currently being planned at USNO. This is a micro-satellite to obtain 1 mas positions, parallaxes, and 1 mas/yr proper motions for all bright stars down to about 15th magnitude. This program will be supplemented by a ground-based program to reach 18th magnitude on the 5 mas level.

  3. 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.

  4. 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.

  5. 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.

  6. Three-Dimensional Simulation of Scalp Soft Tissue Expansion Using Finite Element Method

    PubMed Central

    Guan, Qiu; Du, Xiaochen; Shao, Yan; Lin, Lili; Chen, Shengyong

    2014-01-01

    Scalp soft tissue expansion is one of the key medical techniques to generate new skin tissue for correcting various abnormalities and defects of skin in plastic surgery. Therefore, it is very important to work out the appropriate approach to evaluate the increase of expanded scalp area and to predict the shape, size, number, and placement of the expander. A novel method using finite element model is proposed to solve large deformation of scalp expansion in this paper. And the procedure to implement the scalp tissue expansion with finite element method is also described in detail. The three-dimensional simulation results show that the proposed method is effective, and the analysis of simulation experiment shows that the volume and area of the expansion scalp can be accurately calculated and the quantity, location, and size of the expander can also be predicted successfully with the proposed model. PMID:25110514

  7. 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.

  8. 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…

  9. Nilpotent -local finite groups

    NASA Astrophysics Data System (ADS)

    Cantarero, José; Scherer, Jérôme; Viruel, Antonio

    2014-10-01

    We provide characterizations of -nilpotency for fusion systems and -local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.

  10. Accurate Molecular Polarizabilities Based on Continuum Electrostatics

    PubMed Central

    Truchon, Jean-François; Nicholls, Anthony; Iftimie, Radu I.; Roux, Benoît; Bayly, Christopher I.

    2013-01-01

    A novel approach for representing the intramolecular polarizability as a continuum dielectric is introduced to account for molecular electronic polarization. It is shown, using a finite-difference solution to the Poisson equation, that the Electronic Polarization from Internal Continuum (EPIC) model yields accurate gas-phase molecular polarizability tensors for a test set of 98 challenging molecules composed of heteroaromatics, alkanes and diatomics. The electronic polarization originates from a high intramolecular dielectric that produces polarizabilities consistent with B3LYP/aug-cc-pVTZ and experimental values when surrounded by vacuum dielectric. In contrast to other approaches to model electronic polarization, this simple model avoids the polarizability catastrophe and accurately calculates molecular anisotropy with the use of very few fitted parameters and without resorting to auxiliary sites or anisotropic atomic centers. On average, the unsigned error in the average polarizability and anisotropy compared to B3LYP are 2% and 5%, respectively. The correlation between the polarizability components from B3LYP and this approach lead to a R2 of 0.990 and a slope of 0.999. Even the F2 anisotropy, shown to be a difficult case for existing polarizability models, can be reproduced within 2% error. In addition to providing new parameters for a rapid method directly applicable to the calculation of polarizabilities, this work extends the widely used Poisson equation to areas where accurate molecular polarizabilities matter. PMID:23646034

  11. Conservative properties of finite difference schemes for incompressible flow

    NASA Technical Reports Server (NTRS)

    Morinishi, Youhei

    1995-01-01

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

  12. 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.

  13. Geological applications of automatic grid generation tools for finite elements applied to porous flow modeling

    SciTech Connect

    Gable, C.W.; Trease, H.E.; Cherry, T.A.

    1996-04-01

    The construction of grids that accurately reflect geologic structure and stratigraphy for computational flow and transport models poses a formidable task. Even with a complete understanding of stratigraphy, material properties, boundary and initial conditions, the task of incorporating data into a numerical model can be difficult and time consuming. Furthermore, most tools available for representing complex geologic surfaces and volumes are not designed for producing optimal grids for flow and transport computation. We have developed a modeling tool, GEOMESH, for automating finite element grid generation that maintains the geometric integrity of geologic structure and stratigraphy. The method produces an optimal (Delaunay) tetrahedral grid that can be used for flow and transport computations. The process of developing a flow and transport model can be divided into three parts: (1) Developing accurate conceptual models inclusive of geologic interpretation, material characterization and construction of a stratigraphic and hydrostratigraphic framework model, (2) Building and initializing computational frameworks; grid generation, boundary and initial conditions, (3) Computational physics models of flow and transport. Process (1) and (3) have received considerable attention whereas (2) has not. This work concentrates on grid generation and its connections to geologic characterization and process modeling. Applications of GEOMESH illustrate grid generation for two dimensional cross sections, three dimensional regional models, and adaptive grid refinement in three dimensions. Examples of grid representation of wells and tunnels with GEOMESH can be found in Cherry et al. The resulting grid can be utilized by unstructured finite element or integrated finite difference models.

  14. 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.

  15. Preparation and accurate measurement of pure ozone.

    PubMed

    Janssen, Christof; Simone, Daniela; Guinet, Mickaël

    2011-03-01

    Preparation of high purity ozone as well as precise and accurate measurement of its pressure are metrological requirements that are difficult to meet due to ozone decomposition occurring in pressure sensors. The most stable and precise transducer heads are heated and, therefore, prone to accelerated ozone decomposition, limiting measurement accuracy and compromising purity. Here, we describe a vacuum system and a method for ozone production, suitable to accurately determine the pressure of pure ozone by avoiding the problem of decomposition. We use an inert gas in a particularly designed buffer volume and can thus achieve high measurement accuracy and negligible degradation of ozone with purities of 99.8% or better. The high degree of purity is ensured by comprehensive compositional analyses of ozone samples. The method may also be applied to other reactive gases. PMID:21456766

  16. Line gas sampling system ensures accurate analysis

    SciTech Connect

    Not Available

    1992-06-01

    Tremendous changes in the natural gas business have resulted in new approaches to the way natural gas is measured. Electronic flow measurement has altered the business forever, with developments in instrumentation and a new sensitivity to the importance of proper natural gas sampling techniques. This paper reports that YZ Industries Inc., Snyder, Texas, combined its 40 years of sampling experience with the latest in microprocessor-based technology to develop the KynaPak 2000 series, the first on-line natural gas sampling system that is both compact and extremely accurate. This means the composition of the sampled gas must be representative of the whole and related to flow. If so, relative measurement and sampling techniques are married, gas volumes are accurately accounted for and adjustments to composition can be made.

  17. 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.

  18. 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.

  19. Stretching and folding in finite time.

    PubMed

    Ma, Tian; Ouellette, Nicholas T; Bollt, Erik M

    2016-02-01

    Complex flows mix efficiently, and this process can be understood by considering the stretching and folding of material volumes. Although many metrics have been devised to characterize stretching, fewer are able to capture folding in a quantitative way in spatiotemporally variable flows. Here, we extend our previous methods based on the finite-time curving of fluid-element trajectories to nonzero scales and show that this finite-scale finite-time curvature contains information about both stretching and folding. We compare this metric to the more commonly used finite-time Lyapunov exponent and illustrate our methods using experimental flow-field data from a quasi-two-dimensional laboratory flow. Our new analysis tools add to the growing set of Lagrangian methods for characterizing mixing in complex, aperiodic fluid flows.

  20. Accurate source location from P waves scattered by surface topography

    NASA Astrophysics Data System (ADS)

    Wang, N.; Shen, Y.

    2015-12-01

    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. The grid search method is combined with the 3D strain Green's tensor database type method to improve the search efficiency as well as the quality of hypocenter solution. The strain Green's tensor is calculated by the 3D collocated-grid finite difference method on curvilinear grids. Solutions in the search volume are then obtained based on the least-square misfit between the 'observed' and predicted P and P-coda waves. A 95% confidence interval of the solution is also provided as a posterior error estimation. We find that the scattered waves are mainly due to topography in comparison with random velocity heterogeneity characterized by the von Kάrmάn-type power spectral density function. When only P wave data is used, the 'best' solution is offset from the real source location mostly in the vertical direction. The incorporation of P coda significantly improves solution accuracy and reduces its uncertainty. The solution remains robust with a range of random noises in data, un-modeled random velocity heterogeneities, and uncertainties in moment tensors that we tested.

  1. 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.

  2. NNLOPS accurate associated HW production

    NASA Astrophysics Data System (ADS)

    Astill, William; Bizon, Wojciech; Re, Emanuele; Zanderighi, Giulia

    2016-06-01

    We present a next-to-next-to-leading order accurate description of associated HW production consistently matched to a parton shower. The method is based on reweighting events obtained with the HW plus one jet NLO accurate calculation implemented in POWHEG, extended with the MiNLO procedure, to reproduce NNLO accurate Born distributions. Since the Born kinematics is more complex than the cases treated before, we use a parametrization of the Collins-Soper angles to reduce the number of variables required for the reweighting. We present phenomenological results at 13 TeV, with cuts suggested by the Higgs Cross section Working Group.

  3. 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

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

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

    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 Tc = 1.3128 ± 0.0016, ρc = 0.316 ± 0.004, and pc = 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 ≤ ρt ≤ 0.336) agree to within the statistical uncertainties. For simulations with tail corrections, data obtained using rcut = 3.5σ yield Tc and pc that are higher by 0.2% and 1.4% than simulations with rcut = 5 and 8σ but still with overlapping 95% confidence intervals. In contrast, GEMC simulations with a truncated and shifted potential show that rcut = 8σ is insufficient to obtain accurate results. Additional GEMC simulations for hard-core square-well particles with various ranges of the

  5. Finite element radiation transport in one dimension

    SciTech Connect

    Painter, J.F.

    1997-05-09

    A new physics package solves radiation transport equations in one space dimension, multiple energy groups and directions. A discontinuous finite element method discretizes radiation intensity with respect to space and angle, and a continuous finite element method discretizes electron temperature `in space. A splitting method solves the resulting linear equations. This is a one-dimensional analog of Kershaw and Harte`s two-dimensional package. This package has been installed in a two-dimensional inertial confinement fusion code, and has given excellent results for both thermal waves and highly directional radiation. In contrast, the traditional discrete ordinate and spherical harmonic methods show less accurate results in both cases.

  6. An Accurately Stable Thermo-Hydro-Mechanical Model for Geo-Environmental Simulations

    NASA Astrophysics Data System (ADS)

    Gambolati, G.; Castelletto, N.; Ferronato, M.

    2011-12-01

    In real-world applications involving complex 3D heterogeneous domains the use of advanced numerical algorithms is of paramount importance to stabily, accurately and efficiently solve the coupled system of partial differential equations governing the mass and the energy balance in deformable porous media. The present communication discusses a novel coupled 3-D numerical model based on a suitable combination of Finite Elements (FEs), Mixed FEs (MFEs), and Finite Volumes (FVs) developed with the aim at stabilizing the numerical solution. Elemental pressures and temperatures, nodal displacements and face normal Darcy and Fourier fluxes are the selected primary variables. Such an approach provides an element-wise conservative velocity field, with both pore pressure and stress having the same order of approximation, and allows for the accurate prediction of sharp temperature convective fronts. In particular, the flow-deformation problem is addressed jointly by FEs and MFEs and is coupled to the heat transfer equation using an ad hoc time splitting technique that separates the time temperature evolution into two partial differential equations, accounting for the convective and the diffusive contribution, respectively. The convective part is addressed by a FV scheme which proves effective in treating sharp convective fronts, while the diffusive part is solved by a MFE formulation. A staggered technique is then implemented for the global solution of the coupled thermo-hydro-mechanical problem, solving iteratively the flow-deformation and the heat transport at each time step. Finally, the model is successfully experimented with in realistic applications dealing with geothermal energy extraction and injection.

  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

    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

  9. 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.

  10. 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.

  11. 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…

  12. Finite difference computation of blast diffraction

    NASA Astrophysics Data System (ADS)

    Hillier, R.; Graham, J. M. R.

    1985-07-01

    This paper discusses the use of numerical finite difference methods for predicting flow fields in which a shock or blast wave is diffracted at a sharp edge. Three different types of method are studied: Donor Cell differencing with and without Flux Corrected Transport, a Finite Volume method with an explicit artificial viscosity and Runge-Kutta time stepping, and a second order upwind method based on the solution of a Riemann wave problem at cell interfaces. In the case of weak shock waves a comparison is made with the flow field predicted by acoustic theory including flow separation. Results for stronger shocks are also presented.

  13. Accurate Thermal Conductivities from First Principles

    NASA Astrophysics Data System (ADS)

    Carbogno, Christian

    2015-03-01

    In spite of significant research efforts, a first-principles determination of the thermal conductivity at high temperatures has remained elusive. On the one hand, Boltzmann transport techniques that include anharmonic effects in the nuclear dynamics only perturbatively become inaccurate or inapplicable under such conditions. On the other hand, non-equilibrium molecular dynamics (MD) methods suffer from enormous finite-size artifacts in the computationally feasible supercells, which prevent an accurate extrapolation to the bulk limit of the thermal conductivity. In this work, we overcome this limitation by performing ab initio MD simulations in thermodynamic equilibrium that account for all orders of anharmonicity. The thermal conductivity is then assessed from the auto-correlation function of the heat flux using the Green-Kubo formalism. Foremost, we discuss the fundamental theory underlying a first-principles definition of the heat flux using the virial theorem. We validate our approach and in particular the techniques developed to overcome finite time and size effects, e.g., by inspecting silicon, the thermal conductivity of which is particularly challenging to converge. Furthermore, we use this framework to investigate the thermal conductivity of ZrO2, which is known for its high degree of anharmonicity. Our calculations shed light on the heat resistance mechanism active in this material, which eventually allows us to discuss how the thermal conductivity can be controlled by doping and co-doping. This work has been performed in collaboration with R. Ramprasad (University of Connecticut), C. G. Levi and C. G. Van de Walle (University of California Santa Barbara).

  14. Effects of the inlet conditions and blood models on accurate prediction of hemodynamics in the stented coronary arteries

    NASA Astrophysics Data System (ADS)

    Jiang, Yongfei; Zhang, Jun; Zhao, Wanhua

    2015-05-01

    Hemodynamics altered by stent implantation is well-known to be closely related to in-stent restenosis. Computational fluid dynamics (CFD) method has been used to investigate the hemodynamics in stented arteries in detail and help to analyze the performances of stents. In this study, blood models with Newtonian or non-Newtonian properties were numerically investigated for the hemodynamics at steady or pulsatile inlet conditions respectively employing CFD based on the finite volume method. The results showed that the blood model with non-Newtonian property decreased the area of low wall shear stress (WSS) compared with the blood model with Newtonian property and the magnitude of WSS varied with the magnitude and waveform of the inlet velocity. The study indicates that the inlet conditions and blood models are all important for accurately predicting the hemodynamics. This will be beneficial to estimate the performances of stents and also help clinicians to select the proper stents for the patients.

  15. New finite difference formulas for numerical differentiation

    NASA Astrophysics Data System (ADS)

    Khan, Ishtiaq Rasool; Ohba, Ryoji

    2000-12-01

    Conventional numerical differentiation formulas based on interpolating polynomials, operators and lozenge diagrams can be simplified to one of the finite difference approximations based on Taylor series, and closed-form expressions of these finite difference formulas have already been presented. In this paper, we present new finite difference formulas, which are more accurate than the available ones, especially for the oscillating functions having frequency components near the Nyquist frequency. Closed-form expressions of the new formulas are given for arbitrary order. A comparison of the previously available three types of approximations is given with the presented formulas. A computer program written in MATHEMATICA, based on new formulas is given in the appendix for numerical differentiation of a function at a specified mesh point.

  16. Finite representations of continuum environments

    NASA Astrophysics Data System (ADS)

    Zwolak, Michael

    2008-09-01

    Understanding dissipative and decohering processes is fundamental to the study of quantum systems. An accurate and generic method for investigating these processes is to simulate both the system and environment, which, however, is computationally very demanding. We develop a novel approach to constructing finite representations of the environment based on the influence of different frequency scales on the system's dynamics. As an illustration, we analyze a solvable model of an optical mode decaying into a reservoir. The influence of the environment modes is constant for small frequencies, but drops off rapidly for large frequencies, allowing for a very sparse representation at high frequencies that gives a significant computational speedup in simulating the environment. This approach provides a general framework for simulating open quantum systems.

  17. Convexity at finite temperature and non-extensive thermodynamics

    NASA Astrophysics Data System (ADS)

    Alexandre, J.

    2016-09-01

    Assuming that tunnel effect between two degenerate bare minima occurs, in a scalar field theory at finite volume, this article studies the consequences for the effective potential, to all loop orders. Convexity is achieved only if the two bare minima are taken into account in the path integral, and a new derivation of the effective potential is given, in the large volume limit. The effective potential then has a universal form, it is suppressed by the space time volume, and does not feature spontaneous symmetry breaking as long as the volume is finite. The finite temperature analysis leads to surprising thermal properties, following from the non-extensive expression for the free energy. Although the physical relevance of these results is not clear, the potential application to ultra-light scalar particles is discussed.

  18. A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws

    NASA Astrophysics Data System (ADS)

    Dumbser, Michael; Zanotti, Olindo; Loubère, Raphaël; Diot, Steven

    2014-12-01

    The purpose of this work is to propose a novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hyperbolic conservation laws in multiple space dimensions that works well for arbitrary high order of accuracy in space and time and that does not destroy the natural subcell resolution properties of the DG method. High order time discretization is achieved via a one-step ADER approach that uses a local space-time discontinuous Galerkin predictor method to evolve the data locally in time within each cell. Our new limiting strategy is based on the so-called MOOD paradigm, which a posteriori verifies the validity of a discrete candidate solution against physical and numerical detection criteria after each time step. Here, we employ a relaxed discrete maximum principle in the sense of piecewise polynomials and the positivity of the numerical solution as detection criteria. Within the DG scheme on the main grid, the discrete solution is represented by piecewise polynomials of degree N. For those troubled cells that need limiting, our new limiter approach recomputes the discrete solution by scattering the DG polynomials at the previous time step onto a set of Ns=2N+1 finite volume subcells per space dimension. A robust but accurate ADER-WENO finite volume scheme then updates the subcell averages of the conservative variables within the detected troubled cells. The recomputed subcell averages are subsequently gathered back into high order cell-centered DG polynomials on the main grid via a subgrid reconstruction operator. The choice of Ns=2N+1 subcells is optimal since it allows to match the maximum admissible time step of the finite volume scheme on the subgrid with the maximum admissible time step of the DG scheme on the main grid, minimizing at the same time also the local truncation error of the subcell finite volume scheme. It furthermore provides an excellent subcell resolution of

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

    SciTech Connect

    Dexun Fu; Yanwen Ma

    1997-06-01

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

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. Profitable capitation requires accurate costing.

    PubMed

    West, D A; Hicks, L L; Balas, E A; West, T D

    1996-01-01

    In the name of costing accuracy, nurses are asked to track inventory use on per treatment basis when more significant costs, such as general overhead and nursing salaries, are usually allocated to patients or treatments on an average cost basis. Accurate treatment costing and financial viability require analysis of all resources actually consumed in treatment delivery, including nursing services and inventory. More precise costing information enables more profitable decisions as is demonstrated by comparing the ratio-of-cost-to-treatment method (aggregate costing) with alternative activity-based costing methods (ABC). Nurses must participate in this costing process to assure that capitation bids are based upon accurate costs rather than simple averages. PMID:8788799

  5. Simulation of two-dimensional waterflooding using mixed finite elements

    SciTech Connect

    Chavent, G.; Jaffre, J.; Cohen, G.; Dupuy, M.; Dieste, I.

    1982-01-01

    A new method for the simulation of incompressible diphasic flows in two dimensions is presented, the distinctive features of which are: (1) reformation of the basic equation and specific choices of the finite element approximation of the same; (11) use of a mixed finite elements method, approximating both scalar and vector functions. Several test examples are shown, including gravity and capillary effects. The use of discontinuous basis functions proved successful for an accurate representation of sharp fronts. 16 refs.

  6. Accurate documentation and wound measurement.

    PubMed

    Hampton, Sylvie

    This article, part 4 in a series on wound management, addresses the sometimes routine yet crucial task of documentation. Clear and accurate records of a wound enable its progress to be determined so the appropriate treatment can be applied. Thorough records mean any practitioner picking up a patient's notes will know when the wound was last checked, how it looked and what dressing and/or treatment was applied, ensuring continuity of care. Documenting every assessment also has legal implications, demonstrating due consideration and care of the patient and the rationale for any treatment carried out. Part 5 in the series discusses wound dressing characteristics and selection.

  7. 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

  8. Converging finite-strength shocks

    NASA Astrophysics Data System (ADS)

    Axford, R. A.; Holm, D. D.

    1981-01-01

    The converging shock problem was first solved by Guderley and later by Landau and Stanyukovich for infinitely strong shocks in an ideal gas with spherical and cylindrical symmetry. This problem is solved herein for finite-strength shocks and a non-ideal-gas equation of state with an adiabatic bulk modulus of the type Bs= {- v∂ p}/{∂ v| s} = ( p +B) f( v) , where B is a constant with the dimensions of pressure, and f(v) is an arbitrary function of the specific volume. Self-similar profiles of the particle velocity and thermodynamic variables are studied explicitly for two cases with constant specific heat at constant volume; the Tait-Kirkwood-Murnaghan equation, f(v) = constant, and the Walsh equation, f(v) = v/A, where A = constant. The first case reduces to the ideal gas when B = 0. In both cases the flow behind the shock front exhibits an unbalanced buoyant force instability at a critical Mach number which depends upon equation-of-state parameters.

  9. An efficient finite element solution for gear dynamics

    NASA Astrophysics Data System (ADS)

    Cooley, C. G.; Parker, R. G.; Vijayakar, S. M.

    2010-06-01

    A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.

  10. 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.

  11. 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.

  12. 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.

  13. Optical breast shape capture and finite-element mesh generation for electrical impedance tomography.

    PubMed

    Forsyth, J; Borsic, A; Halter, R J; Hartov, A; Paulsen, K D

    2011-07-01

    X-ray mammography is the standard for breast cancer screening. The development of alternative imaging modalities is desirable because mammograms expose patients to ionizing radiation. Electrical impedance tomography (EIT) may be used to determine tissue conductivity, a property which is an indicator of cancer presence. EIT is also a low-cost imaging solution and does not involve ionizing radiation. In breast EIT, impedance measurements are made using electrodes placed on the surface of the patient's breast. The complex conductivity of the volume of the breast is estimated by a reconstruction algorithm. EIT reconstruction is a severely ill-posed inverse problem. As a result, noisy instrumentation and incorrect modelling of the electrodes and domain shape produce significant image artefacts. In this paper, we propose a method that has the potential to reduce these errors by accurately modelling the patient breast shape. A 3D hand-held optical scanner is used to acquire the breast geometry and electrode positions. We develop methods for processing the data from the scanner and producing volume meshes accurately matching the breast surface and electrode locations, which can be used for image reconstruction. We demonstrate this method for a plaster breast phantom and a human subject. Using this approach will allow patient-specific finite-element meshes to be generated which has the potential to improve the clinical value of EIT for breast cancer diagnosis.

  14. Calculation of compressible boundary layer flow about airfoils by a finite element/finite difference method

    NASA Technical Reports Server (NTRS)

    Strong, Stuart L.; Meade, Andrew J., Jr.

    1992-01-01

    Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.

  15. SPLASH: Accurate OH maser positions

    NASA Astrophysics Data System (ADS)

    Walsh, Andrew; Gomez, Jose F.; Jones, Paul; Cunningham, Maria; Green, James; Dawson, Joanne; Ellingsen, Simon; Breen, Shari; Imai, Hiroshi; Lowe, Vicki; Jones, Courtney

    2013-10-01

    The hydroxyl (OH) 18 cm lines are powerful and versatile probes of diffuse molecular gas, that may trace a largely unstudied component of the Galactic ISM. SPLASH (the Southern Parkes Large Area Survey in Hydroxyl) is a large, unbiased and fully-sampled survey of OH emission, absorption and masers in the Galactic Plane that will achieve sensitivities an order of magnitude better than previous work. In this proposal, we request ATCA time to follow up OH maser candidates. This will give us accurate (~10") positions of the masers, which can be compared to other maser positions from HOPS, MMB and MALT-45 and will provide full polarisation measurements towards a sample of OH masers that have not been observed in MAGMO.

  16. 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.

  17. Accurate thickness measurement of graphene

    NASA Astrophysics Data System (ADS)

    Shearer, Cameron J.; Slattery, Ashley D.; Stapleton, Andrew J.; Shapter, Joseph G.; Gibson, Christopher T.

    2016-03-01

    Graphene has emerged as a material with a vast variety of applications. The electronic, optical and mechanical properties of graphene are strongly influenced by the number of layers present in a sample. As a result, the dimensional characterization of graphene films is crucial, especially with the continued development of new synthesis methods and applications. A number of techniques exist to determine the thickness of graphene films including optical contrast, Raman scattering and scanning probe microscopy techniques. Atomic force microscopy (AFM), in particular, is used extensively since it provides three-dimensional images that enable the measurement of the lateral dimensions of graphene films as well as the thickness, and by extension the number of layers present. However, in the literature AFM has proven to be inaccurate with a wide range of measured values for single layer graphene thickness reported (between 0.4 and 1.7 nm). This discrepancy has been attributed to tip-surface interactions, image feedback settings and surface chemistry. In this work, we use standard and carbon nanotube modified AFM probes and a relatively new AFM imaging mode known as PeakForce tapping mode to establish a protocol that will allow users to accurately determine the thickness of graphene films. In particular, the error in measuring the first layer is reduced from 0.1-1.3 nm to 0.1-0.3 nm. Furthermore, in the process we establish that the graphene-substrate adsorbate layer and imaging force, in particular the pressure the tip exerts on the surface, are crucial components in the accurate measurement of graphene using AFM. These findings can be applied to other 2D materials.

  18. Accurate thickness measurement of graphene.

    PubMed

    Shearer, Cameron J; Slattery, Ashley D; Stapleton, Andrew J; Shapter, Joseph G; Gibson, Christopher T

    2016-03-29

    Graphene has emerged as a material with a vast variety of applications. The electronic, optical and mechanical properties of graphene are strongly influenced by the number of layers present in a sample. As a result, the dimensional characterization of graphene films is crucial, especially with the continued development of new synthesis methods and applications. A number of techniques exist to determine the thickness of graphene films including optical contrast, Raman scattering and scanning probe microscopy techniques. Atomic force microscopy (AFM), in particular, is used extensively since it provides three-dimensional images that enable the measurement of the lateral dimensions of graphene films as well as the thickness, and by extension the number of layers present. However, in the literature AFM has proven to be inaccurate with a wide range of measured values for single layer graphene thickness reported (between 0.4 and 1.7 nm). This discrepancy has been attributed to tip-surface interactions, image feedback settings and surface chemistry. In this work, we use standard and carbon nanotube modified AFM probes and a relatively new AFM imaging mode known as PeakForce tapping mode to establish a protocol that will allow users to accurately determine the thickness of graphene films. In particular, the error in measuring the first layer is reduced from 0.1-1.3 nm to 0.1-0.3 nm. Furthermore, in the process we establish that the graphene-substrate adsorbate layer and imaging force, in particular the pressure the tip exerts on the surface, are crucial components in the accurate measurement of graphene using AFM. These findings can be applied to other 2D materials.

  19. 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.

  20. An accurate method for two-point boundary value problems

    NASA Technical Reports Server (NTRS)

    Walker, J. D. A.; Weigand, G. G.

    1979-01-01

    A second-order method for solving two-point boundary value problems on a uniform mesh is presented where the local truncation error is obtained for use with the deferred correction process. In this simple finite difference method the tridiagonal nature of the classical method is preserved but the magnitude of each term in the truncation error is reduced by a factor of two. The method is applied to a number of linear and nonlinear problems and it is shown to produce more accurate results than either the classical method or the technique proposed by Keller (1969).

  1. Finite q-oscillator

    NASA Astrophysics Data System (ADS)

    Atakishiyev, Natig M.; Klimyk, Anatoliy U.; Wolf, Kurt Bernardo

    2004-05-01

    The finite q-oscillator is a model that obeys the dynamics of the harmonic oscillator, with the operators of position, momentum and Hamiltonian being functions of elements of the q-algebra suq(2). The spectrum of position in this discrete system, in a fixed representation j, consists of 2j + 1 'sensor'-points x_s={\\case12}[2s]_q, s\\in\\{-j,-j+1,\\ldots,j\\} , and similarly for the momentum observable. The spectrum of energies is finite and equally spaced, so the system supports coherent states. The wavefunctions involve dual q-Kravchuk polynomials, which are solutions to a finite-difference Schrödinger equation. Time evolution (times a phase) defines the fractional Fourier-q-Kravchuk transform. In the classical limit as q rarr 1 we recover the finite oscillator Lie algebra, the N = 2j rarr infin limit returns the Macfarlane-Biedenharn q-oscillator and both limits contract the generators to the standard quantum-mechanical harmonic oscillator.

  2. Automatic finite element generators

    NASA Technical Reports Server (NTRS)

    Wang, P. S.

    1984-01-01

    The design and implementation of a software system for generating finite elements and related computations are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and element stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions are discussed. Automatic FORTRAN code generation is described with emphasis on improving the efficiency of the resultant code.

  3. 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. PMID:26099201

  4. Chaotic cross-waves in tanks of finite sizes

    NASA Astrophysics Data System (ADS)

    Krasnopolskaya, Tatyana; Pechuk, Evgeniy; Spektor, Viacheslav

    2014-11-01

    The phenomenon of chaotic cross-waves generation in fluid free surface in two finite size containers is studied. The waves may be excited by harmonic axisymmetric deformations of the inner shell in the volume between two cylinders and in a rectangular tank when one wall is a flap wavemaker. The existence of chaotic attractors was established for the dynamical system presenting cross-waves and forced waves interaction at fluid free-surface in a volume between two cylinders of finite length. In the case of one cross-wave in a rectangular tank no chaotic regimes were found.

  5. 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

  6. 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.

  7. Accurate adjoint design sensitivities for nano metal optics.

    PubMed

    Hansen, Paul; Hesselink, Lambertus

    2015-09-01

    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. PMID:26368483

  8. 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

  9. 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.

  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. Finite Element Interface to Linear Solvers

    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 themore » 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.« less

  12. Volume MLS ray casting.

    PubMed

    Ledergerber, Christian; Guennebaud, Gaël; Meyer, Miriah; Bächer, Moritz; Pfister, Hanspeter

    2008-01-01

    The method of Moving Least Squares (MLS) is a popular framework for reconstructing continuous functions from scattered data due to its rich mathematical properties and well-understood theoretical foundations. This paper applies MLS to volume rendering, providing a unified mathematical framework for ray casting of scalar data stored over regular as well as irregular grids. We use the MLS reconstruction to render smooth isosurfaces and to compute accurate derivatives for high-quality shading effects. We also present a novel, adaptive preintegration scheme to improve the efficiency of the ray casting algorithm by reducing the overall number of function evaluations, and an efficient implementation of our framework exploiting modern graphics hardware. The resulting system enables high-quality volume integration and shaded isosurface rendering for regular and irregular volume data.

  13. Monte Carlo Simulations for Dosimetry in Prostate Radiotherapy with Different Intravesical Volumes and Planning Target Volume Margins

    PubMed Central

    Lv, Wei; Yu, Dong; He, Hengda; Liu, Qian

    2016-01-01

    In prostate radiotherapy, the influence of bladder volume variation on the dose absorbed by the target volume and organs at risk is significant and difficult to predict. In addition, the resolution of a typical medical image is insufficient for visualizing the bladder wall, which makes it more difficult to precisely evaluate the dose to the bladder wall. This simulation study aimed to quantitatively investigate the relationship between the dose received by organs at risk and the intravesical volume in prostate radiotherapy. The high-resolution Visible Chinese Human phantom and the finite element method were used to construct 10 pelvic models with specific intravesical volumes ranging from 100 ml to 700 ml to represent bladders of patients with different bladder filling capacities during radiotherapy. This series of models was utilized in six-field coplanar 3D conformal radiotherapy simulations with different planning target volume (PTV) margins. Each organ’s absorbed dose was calculated using the Monte Carlo method. The obtained bladder wall displacements during bladder filling were consistent with reported clinical measurements. The radiotherapy simulation revealed a linear relationship between the dose to non-targeted organs and the intravesical volume and indicated that a 10-mm PTV margin for a large bladder and a 5-mm PTV margin for a small bladder reduce the effective dose to the bladder wall to similar degrees. However, larger bladders were associated with evident protection of the intestines. Detailed dosimetry results can be used by radiation oncologists to create more accurate, individual water preload protocols according to the patient’s anatomy and bladder capacity. PMID:27441944

  14. Monte Carlo Simulations for Dosimetry in Prostate Radiotherapy with Different Intravesical Volumes and Planning Target Volume Margins.

    PubMed

    Lv, Wei; Yu, Dong; He, Hengda; Liu, Qian

    2016-01-01

    In prostate radiotherapy, the influence of bladder volume variation on the dose absorbed by the target volume and organs at risk is significant and difficult to predict. In addition, the resolution of a typical medical image is insufficient for visualizing the bladder wall, which makes it more difficult to precisely evaluate the dose to the bladder wall. This simulation study aimed to quantitatively investigate the relationship between the dose received by organs at risk and the intravesical volume in prostate radiotherapy. The high-resolution Visible Chinese Human phantom and the finite element method were used to construct 10 pelvic models with specific intravesical volumes ranging from 100 ml to 700 ml to represent bladders of patients with different bladder filling capacities during radiotherapy. This series of models was utilized in six-field coplanar 3D conformal radiotherapy simulations with different planning target volume (PTV) margins. Each organ's absorbed dose was calculated using the Monte Carlo method. The obtained bladder wall displacements during bladder filling were consistent with reported clinical measurements. The radiotherapy simulation revealed a linear relationship between the dose to non-targeted organs and the intravesical volume and indicated that a 10-mm PTV margin for a large bladder and a 5-mm PTV margin for a small bladder reduce the effective dose to the bladder wall to similar degrees. However, larger bladders were associated with evident protection of the intestines. Detailed dosimetry results can be used by radiation oncologists to create more accurate, individual water preload protocols according to the patient's anatomy and bladder capacity.

  15. Leading slow roll corrections to the volume of the universe and the entropy bound

    NASA Astrophysics Data System (ADS)

    Lewandowski, Matthew; Perko, Ashley

    2014-12-01

    We make an extension to recent calculations of the probability density ρ( V ) for the volume of the universe after inflation. Previous results have been accurate to leading order in the slow roll parameters and , and 1 /N c , where H is the Hubble parameter and N c is the classical number of e-foldings. Here, we present a modification which captures effects of order ɛN c , which amounts to letting the parameters of inflation H and depend on the value of the inflaton ϕ. The phase of slow roll eternal inflation can be defined as when the probability to have an infinite volume is greater than zero. Using this definition, we study the Laplace transform of ρ( V ) numerically to determine the condition that triggers the transition to eternal inflation. We also study the average volume < V > analytically and show that it satisfies the universal volume bound. This bound states that, in any realization of inflation which ends with a finite volume, an initial volume must grow by less than a factor of , where S dS is the de Sitter (dS) entropy.

  16. Finite Element Analysis Code

    2006-03-08

    MAPVAR-KD is designed to transfer solution results from one finite element mesh to another. MAPVAR-KD draws heavily from the structure and coding of MERLIN II, but it employs a new finite element data base, EXODUS II, and offers enhanced speed and new capabilities not available in MERLIN II. In keeping with the MERLIN II documentation, the computational algorithms used in MAPVAR-KD are described. User instructions are presented. Example problems are included to demonstrate the operationmore » of the code and the effects of various input options. MAPVAR-KD is a modification of MAPVAR in which the search algorithm was replaced by a kd-tree-based search for better performance on large problems.« less

  17. Finite Element Analysis Code

    SciTech Connect

    Sjaardema, G.; Wellman, G.; Gartling, D.

    2006-03-08

    MAPVAR-KD is designed to transfer solution results from one finite element mesh to another. MAPVAR-KD draws heavily from the structure and coding of MERLIN II, but it employs a new finite element data base, EXODUS II, and offers enhanced speed and new capabilities not available in MERLIN II. In keeping with the MERLIN II documentation, the computational algorithms used in MAPVAR-KD are described. User instructions are presented. Example problems are included to demonstrate the operation of the code and the effects of various input options. MAPVAR-KD is a modification of MAPVAR in which the search algorithm was replaced by a kd-tree-based search for better performance on large problems.

  18. 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.

  19. Finite Element Analysis Code

    SciTech Connect

    Forsythe, C.; Smith, M.; Sjaardema, G.

    2005-06-26

    Exotxt is an analysis code that reads finite element results data stored in an exodusII file and generates a file in a structured text format. The text file can be edited or modified via a number of text formatting tools. Exotxt is used by analysis to translate data from the binary exodusII format into a structured text format which can then be edited or modified and then either translated back to exodusII format or to another format.

  20. 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