Science.gov

Sample records for adaptive finite volume

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2012-12-01

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

  7. 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.

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

    SciTech Connect

    Delanaye, M.; Essers, J.A.

    1997-04-01

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

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

    SciTech Connect

    Ware, J.; Berzins, M.

    1995-12-31

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

  10. 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.

  11. 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.

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

    SciTech Connect

    McCorquodale, Peter; Ullrich, Paul; Johansen, Hans; Colella, Phillip

    2015-09-04

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

  13. 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.

  14. Twisted mass finite volume effects

    SciTech Connect

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

    2010-08-01

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

  15. GeoClawSed: A Model with Finite Volume and Adaptive Refinement Method for Tsunami Sediment Transport

    NASA Astrophysics Data System (ADS)

    Tang, H.; Weiss, R.

    2015-12-01

    The shallow-water and advection-diffusion equations are commonly used for tsunami sediment-transport modeling. GeoClawSed is based on GeoClaw and adds a bed updating and avalanching scheme to the two-dimensional coupled system combining the shallow- water and advection-diffusion equations, which is a set of hyperbolic integral conservation laws. The modeling system consists of three coupled model components: (1) the shallow-water equations for hydrodynamics; (2) advection-diffusion equation for sediment transport; and (3) an equation for morphodynamics. For the hydrodynamic part, the finite-volume wave propagation methods (high resolution Godunov-type methods) are applied to the shallow-water equations. The well-known Riemann solver in GeoClaw is capable of dealing with diverse flow regimes present during tsunami flows. For the sediment-transport part, the advection-diffusion equation is employed to calculate the distribution of sediment in the water column. In the fully-coupled version, the advection-diffusion equation is also included in the Riemann solver. The Van Leer method is applied for calculating sediment flux in each direction. The bed updating and avalanching scheme (morphodynamics) is used for updating topography during tsunami wave propagation. Adaptive refinement method is extended to hydrodynamic part, sediment transport model and topography. GeoClawSed can evolve different resolution and accurately capture discontinuities in both flow dynamic and sediment transport. Together, GeoClawSed is designed for modeling tsunami propagation, inundation, sediment transport as well as topography change. Finally, GeoClawSed is applied for studying marine and terrestrial deposit distribution after tsunami wave. Keywords: Tsunami; Sediment Transport; Shallow Water Equations; Advection-Diffusion Equation; Adaptive Refinement Method

  16. Finite-volume scheme for anisotropic diffusion

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. Critical behavior and finite volume

    SciTech Connect

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

    1986-10-01

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

  2. Diagonal multisoliton matrix elements in finite volume

    NASA Astrophysics Data System (ADS)

    Pálmai, T.; Takács, G.

    2013-02-01

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

  3. 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.

  4. Image space adaptive volume rendering

    NASA Astrophysics Data System (ADS)

    Corcoran, Andrew; Dingliana, John

    2012-01-01

    We present a technique for interactive direct volume rendering which provides adaptive sampling at a reduced memory requirement compared to traditional methods. Our technique exploits frame to frame coherence to quickly generate a two-dimensional importance map of the volume which guides sampling rate optimisation and allows us to provide interactive frame rates for user navigation and transfer function changes. In addition our ray casting shader detects any inconsistencies in our two-dimensional map and corrects them on the fly to ensure correct classification of important areas of the volume.

  5. Adaptive Finite Element Methods in Geodynamics

    NASA Astrophysics Data System (ADS)

    Davies, R.; Davies, H.; Hassan, O.; Morgan, K.; Nithiarasu, P.

    2006-12-01

    Adaptive finite element methods are presented for improving the quality of solutions to two-dimensional (2D) and three-dimensional (3D) convection dominated problems in geodynamics. The methods demonstrate the application of existing technology in the engineering community to problems within the `solid' Earth sciences. Two-Dimensional `Adaptive Remeshing': The `remeshing' strategy introduced in 2D adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code `ConMan'. An unstructured quadrilateral mesh generator is utilised, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermo-chemical problems with known benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy whilst increasing computational efficiency. For thermo-chemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies. Three-Dimensional Adaptive Multigrid: We extend the ideas from our 2D work into the 3D realm in the context of a pre-existing 3D-spherical mantle dynamics code, `TERRA'. In its original format, `TERRA' is computationally highly efficient since it employs a multigrid solver that depends upon a grid utilizing a clever

  6. 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.

  7. Shape optimization including finite element grid adaptation

    NASA Technical Reports Server (NTRS)

    Kikuchi, N.; Taylor, J. E.

    1984-01-01

    The prediction of optimal shape design for structures depends on having a sufficient level of precision in the computation of structural response. These requirements become critical in situations where the region to be designed includes stress concentrations or unilateral contact surfaces, for example. In the approach to shape optimization discussed here, a means to obtain grid adaptation is incorporated into the finite element procedures. This facility makes it possible to maintain a level of quality in the computational estimate of response that is surely adequate for the shape design problem.

  8. Massless sunset diagrams in finite asymmetric volumes

    NASA Astrophysics Data System (ADS)

    Niedermayer, F.; Weisz, P.

    2016-06-01

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

  9. LARGE volume string compactifications at finite temperature

    NASA Astrophysics Data System (ADS)

    Anguelova, Lilia; Calò, Vincenzo; Cicoli, Michele

    2009-10-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-09-01

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

  11. Solution-adaptive finite element method in computational fracture mechanics

    NASA Technical Reports Server (NTRS)

    Min, J. B.; Bass, J. M.; Spradley, L. W.

    1993-01-01

    Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.

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

    NASA Astrophysics Data System (ADS)

    Lee, Jong-Wan; Tiburzi, Brian C.

    2016-02-01

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

  13. Adaptive Finite-Element Computation In Fracture Mechanics

    NASA Technical Reports Server (NTRS)

    Min, J. B.; Bass, J. M.; Spradley, L. W.

    1995-01-01

    Report discusses recent progress in use of solution-adaptive finite-element computational methods to solve two-dimensional problems in linear elastic fracture mechanics. Method also shown extensible to three-dimensional problems.

  14. 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.

  15. A finite volume method for numerical grid generation

    NASA Astrophysics Data System (ADS)

    Beale, S. B.

    1999-07-01

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

  16. Adaptive finite difference for seismic wavefield modelling in acoustic media.

    PubMed

    Yao, Gang; Wu, Di; Debens, Henry Alexander

    2016-01-01

    Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang's optimised finite difference scheme. PMID:27491333

  17. Adaptive finite difference for seismic wavefield modelling in acoustic media

    NASA Astrophysics Data System (ADS)

    Yao, Gang; Wu, Di; Debens, Henry Alexander

    2016-08-01

    Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang’s optimised finite difference scheme.

  18. Adaptive finite difference for seismic wavefield modelling in acoustic media

    PubMed Central

    Yao, Gang; Wu, Di; Debens, Henry Alexander

    2016-01-01

    Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang’s optimised finite difference scheme. PMID:27491333

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

    SciTech Connect

    Mishev, I.D.

    1996-12-31

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

  20. 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...

  1. Adaptive finite-element method for diffraction gratings

    NASA Astrophysics Data System (ADS)

    Bao, Gang; Chen, Zhiming; Wu, Haijun

    2005-06-01

    A second-order finite-element adaptive strategy with error control for one-dimensional grating problems is developed. The unbounded computational domain is truncated to a bounded one by a perfectly-matched-layer (PML) technique. The PML parameters, such as the thickness of the layer and the medium properties, are determined through sharp a posteriori error estimates. The adaptive finite-element method is expected to increase significantly the accuracy and efficiency of the discretization as well as reduce the computation cost. Numerical experiments are included to illustrate the competitiveness of the proposed adaptive method.

  2. Auto-adaptive finite element meshes

    NASA Technical Reports Server (NTRS)

    Richter, Roland; Leyland, Penelope

    1995-01-01

    Accurate capturing of discontinuities within compressible flow computations is achieved by coupling a suitable solver with an automatic adaptive mesh algorithm for unstructured triangular meshes. The mesh adaptation procedures developed rely on non-hierarchical dynamical local refinement/derefinement techniques, which hence enable structural optimization as well as geometrical optimization. The methods described are applied for a number of the ICASE test cases are particularly interesting for unsteady flow simulations.

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

    NASA Astrophysics Data System (ADS)

    Vinokur, Marcel

    1989-03-01

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

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

    NASA Astrophysics Data System (ADS)

    Vinokur, Marcel

    1986-06-01

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

  5. 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.

  6. 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.

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

    NASA Technical Reports Server (NTRS)

    Leonard, B. P.

    1992-01-01

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

  8. 3-D dynamic rupture simulations by a finite volume method

    NASA Astrophysics Data System (ADS)

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

    2009-07-01

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

  9. 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.

  10. 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.

  11. 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.

  12. Finite element error estimation and adaptivity based on projected stresses

    SciTech Connect

    Jung, J.

    1990-08-01

    This report investigates the behavior of a family of finite element error estimators based on projected stresses, i.e., continuous stresses that are a least squared error fit to the conventional Gauss point stresses. An error estimate based on element force equilibrium appears to be quite effective. Examples of adaptive mesh refinement for a one-dimensional problem are presented. Plans for two-dimensional adaptivity are discussed. 12 refs., 82 figs.

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

    SciTech Connect

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

    2011-11-01

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

  14. Adaptive Finite Element Methods for Continuum Damage Modeling

    NASA Technical Reports Server (NTRS)

    Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.

    1995-01-01

    The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.

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

    PubMed

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

    2012-01-01

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

  16. a Finite Nucleon Extended Volume Model for Nuclear Matter

    NASA Astrophysics Data System (ADS)

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

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

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

    PubMed

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

    2014-01-01

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

  18. Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

    NASA Astrophysics Data System (ADS)

    Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.

    2016-09-01

    In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.

  19. 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.

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

    NASA Astrophysics Data System (ADS)

    Narasimhan, T. N.

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

  1. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

  3. Parallel, adaptive finite element methods for conservation laws

    NASA Technical Reports Server (NTRS)

    Biswas, Rupak; Devine, Karen D.; Flaherty, Joseph E.

    1994-01-01

    We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.

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

    NASA Technical Reports Server (NTRS)

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

    2001-01-01

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

  5. Stimulating rupture surfaces in a finite rock volume

    NASA Astrophysics Data System (ADS)

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

    2012-12-01

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

  6. Model of adaptive temporal development of structured finite systems

    NASA Astrophysics Data System (ADS)

    Patera, Jiri; Shaw, Gordon L.; Slansky, Richard; Leng, Xiaodan

    1989-07-01

    The weight systems of level-zero representations of affine Kac-Moody algebras provide an appropriate kinematical framework for studying structured finite systems with adaptive temporal development. Much of the structure is determined by Lie algebra theory, so it is possible to restrict greatly the connection space and analytic results are possible. The time development of these systems often evolves to cyclic temporal-spatial patterns, depending on the definition of the dynamics. The purpose of this paper is to set up the mathematical formalism for this ``memory in Lie algebras'' class of models. An illustration is used to show the kinds of complex behavior that occur in simple cases.

  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. Ablation problems using a finite control volume technique

    SciTech Connect

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

    1993-03-01

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

  9. Ablation problems using a finite control volume technique

    SciTech Connect

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

    1993-01-01

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

  10. Compact finite volume methods for the diffusion equation

    NASA Technical Reports Server (NTRS)

    Rose, Milton E.

    1989-01-01

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

  11. Compact finite volume methods for the diffusion equation

    NASA Technical Reports Server (NTRS)

    Rose, Milton E.

    1989-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Gallo, Claudio; Manzini, Gianmarco

    1998-03-01

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

  13. 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.

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

    NASA Astrophysics Data System (ADS)

    Narayanan, Kiran; Samtaney, Ravi; Moran, Brian

    2015-11-01

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

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

    NASA Technical Reports Server (NTRS)

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

    2001-01-01

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

  16. Language Model Combination and Adaptation Using Weighted Finite State Transducers

    NASA Technical Reports Server (NTRS)

    Liu, X.; Gales, M. J. F.; Hieronymus, J. L.; Woodland, P. C.

    2010-01-01

    In speech recognition systems language model (LMs) are often constructed by training and combining multiple n-gram models. They can be either used to represent different genres or tasks found in diverse text sources, or capture stochastic properties of different linguistic symbol sequences, for example, syllables and words. Unsupervised LM adaption may also be used to further improve robustness to varying styles or tasks. When using these techniques, extensive software changes are often required. In this paper an alternative and more general approach based on weighted finite state transducers (WFSTs) is investigated for LM combination and adaptation. As it is entirely based on well-defined WFST operations, minimum change to decoding tools is needed. A wide range of LM combination configurations can be flexibly supported. An efficient on-the-fly WFST decoding algorithm is also proposed. Significant error rate gains of 7.3% relative were obtained on a state-of-the-art broadcast audio recognition task using a history dependently adapted multi-level LM modelling both syllable and word sequences

  17. 3D Finite Element Trajectory Code with Adaptive Meshing

    NASA Astrophysics Data System (ADS)

    Ives, Lawrence; Bui, Thuc; Vogler, William; Bauer, Andy; Shephard, Mark; Beal, Mark; Tran, Hien

    2004-11-01

    Beam Optics Analysis, a new, 3D charged particle program is available and in use for the design of complex, 3D electron guns and charged particle devices. The code reads files directly from most CAD and solid modeling programs, includes an intuitive Graphical User Interface (GUI), and a robust mesh generator that is fully automatic. Complex problems can be set up, and analysis initiated in minutes. The program includes a user-friendly post processor for displaying field and trajectory data using 3D plots and images. The electrostatic solver is based on the standard nodal finite element method. The magnetostatic field solver is based on the vector finite element method and is also called during the trajectory simulation process to solve for self magnetic fields. The user imports the geometry from essentially any commercial CAD program and uses the GUI to assign parameters (voltages, currents, dielectric constant) and designate emitters (including work function, emitter temperature, and number of trajectories). The the mesh is generated automatically and analysis is performed, including mesh adaptation to improve accuracy and optimize computational resources. This presentation will provide information on the basic structure of the code, its operation, and it's capabilities.

  18. 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.

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

    NASA Astrophysics Data System (ADS)

    Rizzi, A.

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

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

    2002-01-18

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

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

    NASA Technical Reports Server (NTRS)

    Gnoffo, Peter A.

    2006-01-01

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

  3. 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.

  4. 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.

  5. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

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

    SciTech Connect

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

    1999-01-01

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

  8. 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.

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

    DOE PAGESBeta

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

    2015-12-15

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

  10. 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.

  11. Adaptive finite element methods for two-dimensional problems in computational fracture mechanics

    NASA Technical Reports Server (NTRS)

    Min, J. B.; Bass, J. M.; Spradley, L. W.

    1994-01-01

    Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

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

    PubMed

    Bolborici, V; Dawson, F P

    2016-03-01

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

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

    PubMed

    Coralic, Vedran; Colonius, Tim

    2014-10-01

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

  14. 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).

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. Blood Volume: Its Adaptation to Endurance Training

    NASA Technical Reports Server (NTRS)

    Convertino, Victor A.

    1991-01-01

    Expansion of blood volume (hypervolemia) has been well documented in both cross-sectional and longitudinal studies as a consequence of endurance exercise training. Plasma volume expansion can account for nearly all of the exercise-induced hypervolemia up to 2-4 wk; after this time expansion may be distributed equally between plasma and red cell volumes. The exercise stimulus for hypervolemia has both thermal and nonthermal components that increase total circulating plasma levels of electrolytes and proteins. Although protein and fluid shifts from the extravascular to intravascular space may provide a mechanism for rapid hypervolemia immediately after exercise, evidence supports the notion that chronic hypervolemia associated with exercise training represents a net expansion of total body water and solutes. This net increase of body fluids with exercise training is associated with increased water intake and decreased urine volume output. The mechanism of reduced urine output appears to be increased renal tubular reabsorption of sodium through a more sensitive aldosterone action in man. Exercise training-induced hypervolemia appears to be universal among most animal species, although the mechanisms may be quite different. The hypervolemia may provide advantages of greater body fluid for heat dissipation and thermoregulatory stability as well as larger vascular volume and filling pressure for greater cardiac stroke volume and lower heart rates during exercise.

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

    NASA Astrophysics Data System (ADS)

    Lai, Wencong; Ogden, Fred L.

    2015-04-01

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

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

    NASA Technical Reports Server (NTRS)

    Hung, C. M.; Kordulla, W.

    1983-01-01

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

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

    SciTech Connect

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

    2005-12-01

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

  3. 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.

  4. Methods and evaluations of MRI content-adaptive finite element mesh generation for bioelectromagnetic problems

    NASA Astrophysics Data System (ADS)

    Lee, W. H.; Kim, T.-S.; Cho, M. H.; Ahn, Y. B.; Lee, S. Y.

    2006-12-01

    In studying bioelectromagnetic problems, finite element analysis (FEA) offers several advantages over conventional methods such as the boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropic conductivity. For FEA, mesh generation is the first critical requirement and there exist many different approaches. However, conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes (cMeshes), resulting in numerous nodes and elements in modelling the conducting domain, and thereby increasing computational load and demand. In this work, we present efficient content-adaptive mesh generation schemes for complex biological volumes of MR images. The presented methodology is fully automatic and generates FE meshes that are adaptive to the geometrical contents of MR images, allowing optimal representation of conducting domain for FEA. We have also evaluated the effect of cMeshes on FEA in three dimensions by comparing the forward solutions from various cMesh head models to the solutions from the reference FE head model in which fine and equidistant FEs constitute the model. The results show that there is a significant gain in computation time with minor loss in numerical accuracy. We believe that cMeshes should be useful in the FEA of bioelectromagnetic problems.

  5. 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.

  6. New Directions in Asymptotically Stable Finite-dimensional Adaptive Control of Linear Distributed Parameter Systems

    NASA Technical Reports Server (NTRS)

    Balas, M. J.

    1985-01-01

    Distributed Parameter Systems (DPS), such as systems described by partial differential equations, require infinite-dimensional state space descriptions to correctly model their dynamical behavior. However, any adaptive control algorithm must be finite-dimensional in order to be implemented via on-line digital computers. Finite-dimensional adaptive control of linear DPS requires stability analysis of nonlinear, time-varying, infinite-dimensional systems. The structure of nonadaptive finite-dimensional control of linear DPS is summarized as it relates to the existence of limiting systems for adaptive control. Two candidate schemes for finite-dimensional adaptive control of DPS are described and critical issues in infinite-dimensional stability analysis are discussed, in particular, the invariance principle, center manifold theory, and relationships between input-output and internal stability.

  7. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

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

    NASA Astrophysics Data System (ADS)

    Eberle, Albrecht

    1991-07-01

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

  10. 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.

  11. Adaptive grid finite element model of the tokamak scrapeoff layer

    SciTech Connect

    Kuprat, A.P.; Glasser, A.H.

    1995-07-01

    The authors discuss unstructured grids for application to transport in the tokamak edge SOL. They have developed a new metric with which to judge element elongation and resolution requirements. Using this method, the authors apply a standard moving finite element technique to advance the SOL equations while inserting/deleting dynamically nodes that violate an elongation criterion. In a tokamak plasma, this method achieves a more uniform accuracy, and results in highly stretched triangular finite elements, except near separatrix X-point where transport is more isotropic.

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

    NASA Astrophysics Data System (ADS)

    Springer, Paul; Klein, Bertram

    2015-10-01

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

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

    DOE PAGESBeta

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

    2015-06-24

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

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

    NASA Technical Reports Server (NTRS)

    Svard, Magnus; Gong, Jing; Nordstrom, Jan

    2006-01-01

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

  15. Large spatial, temporal, and algorithmic adaptivity for implicit nonlinear finite element analysis

    SciTech Connect

    Engelmann, B.E.; Whirley, R.G.

    1992-07-30

    The development of effective solution strategies to solve the global nonlinear equations which arise in implicit finite element analysis has been the subject of much research in recent years. Robust algorithms are needed to handle the complex nonlinearities that arise in many implicit finite element applications such as metalforming process simulation. The authors experience indicates that robustness can best be achieved through adaptive solution strategies. In the course of their research, this adaptivity and flexibility has been refined into a production tool through the development of a solution control language called ISLAND. This paper discusses aspects of adaptive solution strategies including iterative procedures to solve the global equations and remeshing techniques to extend the domain of Lagrangian methods. Examples using the newly developed ISLAND language are presented to illustrate the advantages of embedding temporal, algorithmic, and spatial adaptivity in a modem implicit nonlinear finite element analysis code.

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

    SciTech Connect

    Durlofsky, L.J. )

    1993-04-01

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

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

    NASA Astrophysics Data System (ADS)

    Nordbotten, J. M.

    2014-12-01

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

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

    NASA Astrophysics Data System (ADS)

    Jia, Jinhong; Wang, Hong

    2016-04-01

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

  19. 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.

  20. High-order central ENO finite-volume scheme for ideal MHD

    NASA Astrophysics Data System (ADS)

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

    2013-10-01

    A high-order accurate finite-volume scheme for the compressible ideal magnetohydrodynamics (MHD) equations is proposed. The high-order MHD scheme is based on a central essentially non-oscillatory (CENO) method combined with the generalized Lagrange multiplier divergence cleaning method for MHD. The CENO method uses k-exact multidimensional reconstruction together with a monotonicity procedure that switches from a high-order reconstruction to a limited low-order reconstruction in regions of discontinuous or under-resolved solution content. Both reconstructions are performed on central stencils, and the switching procedure is based on a smoothness indicator. The proposed high-order accurate MHD scheme can be used on general polygonal grids. A highly sophisticated parallel implementation of the scheme is described that is fourth-order accurate on two-dimensional dynamically-adaptive body-fitted structured grids. The hierarchical multi-block body-fitted grid permits grid lines to conform to curved boundaries. High-order accuracy is maintained at curved domain boundaries by employing high-order spline representations and constraints at the Gauss quadrature points for flux integration. Detailed numerical results demonstrate high-order convergence for smooth flows and robustness against oscillations for problems with shocks. A new MHD extension of the well-known Shu-Osher test problem is proposed to test the ability of the high-order MHD scheme to resolve small-scale flow features in the presence of shocks. The dynamic mesh adaptation capabilities of the approach are demonstrated using adaptive time-dependent simulations of the Orszag-Tang vortex problem with high-order accuracy and unprecedented effective resolution.

  1. 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.

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

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

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

  3. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2013-08-01

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

  5. Adaptive mesh refinement for time-domain electromagnetics using vector finite elements :a feasibility study.

    SciTech Connect

    Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis

    2005-12-01

    This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  7. Multi-level adaptive finite element methods. 1: Variation problems

    NASA Technical Reports Server (NTRS)

    Brandt, A.

    1979-01-01

    A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

  8. 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.

  9. 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.

  10. An adaptive finite element method for convective heat transfer with variable fluid properties

    NASA Astrophysics Data System (ADS)

    Pelletier, Dominique; Ilinca, Florin; Hetu, Jean-Francois

    1993-07-01

    This paper presents an adaptive finite element method based on remeshing to solve incompressible viscous flow problems for which fluid properties present a strong temperature dependence. Solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids. Two general purpose error estimators, that take into account fluid properties variations, are presented. The methodology is applied to a problem of practical interest: the thermal convection of corn syrup in an enclosure with localized heating. Predictions are in good agreement with experimental measurements. The method leads to improved accuracy and reliability of finite element predictions.

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

    NASA Astrophysics Data System (ADS)

    Vukovic, Mirko

    2008-10-01

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

  12. 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.

  13. 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

  14. A massively parallel adaptive finite element method with dynamic load balancing

    SciTech Connect

    Devine, K.D.; Flaherty, J.E.; Wheat, S.R.; Maccabe, A.B.

    1993-05-01

    We construct massively parallel, adaptive finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We demonstrate parallel efficiency through computations on a 1024-processor nCUBE/2 hypercube. We also present results using adaptive p-refinement to reduce the computational cost of the method. We describe tiling, a dynamic, element-based data migration system. Tiling dynamically maintains global load balance in the adaptive method by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. We demonstrate the effectiveness of the dynamic load balancing with adaptive p-refinement examples.

  15. Stress Recovery Based h-Adaptive Finite Element Simulation of Sheet Forming Operations

    NASA Astrophysics Data System (ADS)

    Ahmed, Mohd.; Singh, Devinder

    2016-05-01

    In the present work, stress recovery techniques based adaptive finite element analysis of sheet forming operations is presented. An adaptive two dimensional finite element computer code allows the analysis of sheet forming operations and results in distribution of adaptively refined mesh, effective strain, and punch load, stress and strain rate tensor in the domain that has been developed. The recovery scheme for determining more accurate stress field is based on the least squares fitting of the computed stresses in an element patch surrounding and including a particular node. The solution error is estimated on the basis of an energy norm. It is shown with the help of an illustrative example of axi-symmetric stretching of a metal blank by a hemispherical punch that the adaptive analysis may be usefully employed to predict accurately deformation process, the seats of large deformations and locations of possible instability.

  16. Stress Recovery Based h-Adaptive Finite Element Simulation of Sheet Forming Operations

    NASA Astrophysics Data System (ADS)

    Ahmed, Mohd.; Singh, Devinder

    2016-07-01

    In the present work, stress recovery techniques based adaptive finite element analysis of sheet forming operations is presented. An adaptive two dimensional finite element computer code allows the analysis of sheet forming operations and results in distribution of adaptively refined mesh, effective strain, and punch load, stress and strain rate tensor in the domain that has been developed. The recovery scheme for determining more accurate stress field is based on the least squares fitting of the computed stresses in an element patch surrounding and including a particular node. The solution error is estimated on the basis of an energy norm. It is shown with the help of an illustrative example of axi-symmetric stretching of a metal blank by a hemispherical punch that the adaptive analysis may be usefully employed to predict accurately deformation process, the seats of large deformations and locations of possible instability.

  17. 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.

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

    NASA Astrophysics Data System (ADS)

    Valkov, R.

    2012-11-01

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

  19. On discontinuous Galerkin for time integration in option pricing problems with adaptive finite differences in space

    NASA Astrophysics Data System (ADS)

    von Sydow, Lina

    2013-10-01

    The discontinuous Galerkin method for time integration of the Black-Scholes partial differential equation for option pricing problems is studied and compared with more standard time-integrators. In space an adaptive finite difference discretization is employed. The results show that the dG method are in most cases at least comparable to standard time-integrators and in some cases superior to them. Together with adaptive spatial grids the suggested pricing method shows great qualities.

  20. FEMHD: An adaptive finite element method for MHD and edge modelling

    SciTech Connect

    Strauss, H.R.

    1995-07-01

    This paper describes the code FEMHD, an adaptive finite element MHD code, which is applied in a number of different manners to model MHD behavior and edge plasma phenomena on a diverted tokamak. The code uses an unstructured triangular mesh in 2D and wedge shaped mesh elements in 3D. The code has been adapted to look at neutral and charged particle dynamics in the plasma scrape off region, and into a full MHD-particle code.

  1. Adaptive implicit-explicit finite element algorithms for fluid mechanics problems

    NASA Technical Reports Server (NTRS)

    Tezduyar, T. E.; Liou, J.

    1988-01-01

    The adaptive implicit-explicit (AIE) approach is presented for the finite-element solution of various problems in computational fluid mechanics. In the AIE approach, the elements are dynamically (adaptively) arranged into differently treated groups. The differences in treatment could be based on considerations such as the cost efficiency, the type of spatial or temporal discretization employed, the choice of field equations, etc. Several numerical tests are performed to demonstrate that this approach can achieve substantial savings in CPU time and memory.

  2. ISAARE: Information System for Adaptive, Assistive, and Recreational Equipment: Volume I: Existence; Volume II, Communication; Volume V, Adaptation.

    ERIC Educational Resources Information Center

    Melichar, Joseph F.

    Described as part of the Information System for Adaptive, Assistive and Recreational Equipment are equipment items for physically handicapped pupils in the functional areas of existence, equipment and adaptation. Reviewed in the existence section are such items as assistive food containers and container stabilizers, feeder accessories, bowel and…

  3. Higher-order adaptive finite-element methods for Kohn–Sham density functional theory

    SciTech Connect

    Motamarri, P.; Nowak, M.R.; Leiter, K.; Knap, J.; Gavini, V.

    2013-11-15

    We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688

  4. Higher-order adaptive finite-element methods for Kohn-Sham density functional theory

    NASA Astrophysics Data System (ADS)

    Motamarri, P.; Nowak, M. R.; Leiter, K.; Knap, J.; Gavini, V.

    2013-11-01

    We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss-Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100-200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn-Sham DFT problem. Our studies suggest that staggering computational savings-of the order of 1000-fold-relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn-Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using

  5. 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.

  6. The analytical solution of two interesting hyperbolic problems as a test case for a finite volume method with a new grid refinement technique

    NASA Astrophysics Data System (ADS)

    Heineken, Wolfram; Kunik, Matthias

    2008-05-01

    A finite volume method with grid adaption is applied to two hyperbolic problems: the ultra-relativistic Euler equations, and a scalar conservation law. Both problems are considered in two space dimensions and share the common feature of moving shock waves. In contrast to the classical Euler equations, the derivation of appropriate initial conditions for the ultra-relativistic Euler equations is a non-trivial problem that is solved using one-dimensional shock conditions and the Lorentz invariance of the system. The discretization of both problems is based on a finite volume method of second order in both space and time on a triangular grid. We introduce a variant of the min-mod limiter that avoids unphysical states for the Euler system. The grid is adapted during the integration process. The frequency of grid adaption is controlled automatically in order to guarantee a fine resolution of the moving shock fronts. We introduce the concept of "width refinement" which enlarges the width of strongly refined regions around the shock fronts; the optimal width is found by a numerical study. As a result we are able to improve efficiency by decreasing the number of adaption steps. The performance of the finite volume scheme is compared with several lower order methods.

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

    NASA Astrophysics Data System (ADS)

    Briceño, Raúl A.; Hansen, Maxwell T.

    2016-07-01

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

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

    DOE PAGESBeta

    Briceno, Raul A.

    2014-04-08

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

  9. 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.

  10. 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.

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

    DOE PAGESBeta

    Briceno, Raul A.; Hansen, Maxwell T.

    2016-07-13

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

  12. 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.

  13. Multiscale Simulation of Microcrack Based on a New Adaptive Finite Element Method

    NASA Astrophysics Data System (ADS)

    Xu, Yun; Chen, Jun; Chen, Dong Quan; Sun, Jin Shan

    In this paper, a new adaptive finite element (FE) framework based on the variational multiscale method is proposed and applied to simulate the dynamic behaviors of metal under loadings. First, the extended bridging scale method is used to couple molecular dynamics and FE. Then, macro damages evolvements of those micro defects are simulated by the adaptive FE method. Some auxiliary strategies, such as the conservative mesh remapping, failure mechanism and mesh splitting technique are also included in the adaptive FE computation. Efficiency of our method is validated by numerical experiments.

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

    SciTech Connect

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

    1999-07-01

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

  15. Rapid Structured Volume Grid Smoothing and Adaption Technique

    NASA Technical Reports Server (NTRS)

    Alter, Stephen J.

    2006-01-01

    A rapid, structured volume grid smoothing and adaption technique, based on signal processing methods, was developed and applied to the Shuttle Orbiter at hypervelocity flight conditions in support of the Columbia Accident Investigation. Because of the fast pace of the investigation, computational aerothermodynamicists, applying hypersonic viscous flow solving computational fluid dynamic (CFD) codes, refined and enhanced a grid for an undamaged baseline vehicle to assess a variety of damage scenarios. Of the many methods available to modify a structured grid, most are time-consuming and require significant user interaction. By casting the grid data into different coordinate systems, specifically two computational coordinates with arclength as the third coordinate, signal processing methods are used for filtering the data [Taubin, CG v/29 1995]. Using a reverse transformation, the processed data are used to smooth the Cartesian coordinates of the structured grids. By coupling the signal processing method with existing grid operations within the Volume Grid Manipulator tool, problems related to grid smoothing are solved efficiently and with minimal user interaction. Examples of these smoothing operations are illustrated for reductions in grid stretching and volume grid adaptation. In each of these examples, other techniques existed at the time of the Columbia accident, but the incorporation of signal processing techniques reduced the time to perform the corrections by nearly 60%. This reduction in time to perform the corrections therefore enabled the assessment of approximately twice the number of damage scenarios than previously possible during the allocated investigation time.

  16. Rapid Structured Volume Grid Smoothing and Adaption Technique

    NASA Technical Reports Server (NTRS)

    Alter, Stephen J.

    2004-01-01

    A rapid, structured volume grid smoothing and adaption technique, based on signal processing methods, was developed and applied to the Shuttle Orbiter at hypervelocity flight conditions in support of the Columbia Accident Investigation. Because of the fast pace of the investigation, computational aerothermodynamicists, applying hypersonic viscous flow solving computational fluid dynamic (CFD) codes, refined and enhanced a grid for an undamaged baseline vehicle to assess a variety of damage scenarios. Of the many methods available to modify a structured grid, most are time-consuming and require significant user interaction. By casting the grid data into different coordinate systems, specifically two computational coordinates with arclength as the third coordinate, signal processing methods are used for filtering the data [Taubin, CG v/29 1995]. Using a reverse transformation, the processed data are used to smooth the Cartesian coordinates of the structured grids. By coupling the signal processing method with existing grid operations within the Volume Grid Manipulator tool, problems related to grid smoothing are solved efficiently and with minimal user interaction. Examples of these smoothing operations are illustrated for reduction in grid stretching and volume grid adaptation. In each of these examples, other techniques existed at the time of the Columbia accident, but the incorporation of signal processing techniques reduced the time to perform the corrections by nearly 60%. This reduction in time to perform the corrections therefore enabled the assessment of approximately twice the number of damage scenarios than previously possible during the allocated investigation time.

  17. 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.

  18. A massively parallel adaptive finite element method with dynamic load balancing

    SciTech Connect

    Devine, K.D.; Flaherty, J.E.; Wheat, S.R.; Maccabe, A.B.

    1993-12-31

    The authors construct massively parallel adaptive finite element methods for the solution of hyperbolic conservation laws. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. The resulting method is of high order and may be parallelized efficiently on MIMD computers. They demonstrate parallel efficiency through computations on a 1024-processor nCUBE/2 hypercube. They present results using adaptive p-refinement to reduce the computational cost of the method, and tiling, a dynamic, element-based data migration system that maintains global load balance of the adaptive method by overlapping neighborhoods of processors that each perform local balancing.

  19. Finite Element Analysis of Adaptive-Stiffening and Shape-Control SMA Hybrid Composites

    NASA Technical Reports Server (NTRS)

    Gao, Xiujie; Burton, Deborah; Turner, Travis L.; Brinson, Catherine

    2005-01-01

    Shape memory alloy hybrid composites with adaptive-stiffening or morphing functions are simulated using finite element analysis. The composite structure is a laminated fiber-polymer composite beam with embedded SMA ribbons at various positions with respect to the neutral axis of the beam. Adaptive stiffening or morphing is activated via selective resistance heating of the SMA ribbons or uniform thermal loads on the beam. The thermomechanical behavior of these composites was simulated in ABAQUS using user-defined SMA elements. The examples demonstrate the usefulness of the methods for the design and simulation of SMA hybrid composites. Keywords: shape memory alloys, Nitinol, ABAQUS, finite element analysis, post-buckling control, shape control, deflection control, adaptive stiffening, morphing, constitutive modeling, user element

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

    USGS Publications Warehouse

    Naff, R.L.

    2012-01-01

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

  1. 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.

  2. 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.

  3. 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.

  4. NON-CONFORMING FINITE ELEMENTS; MESH GENERATION, ADAPTIVITY AND RELATED ALGEBRAIC MULTIGRID AND DOMAIN DECOMPOSITION METHODS IN MASSIVELY PARALLEL COMPUTING ENVIRONMENT

    SciTech Connect

    Lazarov, R; Pasciak, J; Jones, J

    2002-02-01

    Construction, analysis and numerical testing of efficient solution techniques for solving elliptic PDEs that allow for parallel implementation have been the focus of the research. A number of discretization and solution methods for solving second order elliptic problems that include mortar and penalty approximations and domain decomposition methods for finite elements and finite volumes have been investigated and analyzed. Techniques for parallel domain decomposition algorithms in the framework of PETC and HYPRE have been studied and tested. Hierarchical parallel grid refinement and adaptive solution methods have been implemented and tested on various model problems. A parallel code implementing the mortar method with algebraically constructed multiplier spaces was developed.

  5. 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

  6. Model Reference Adaptive H∞ Control for a Class of Mixed Parameter Systems by Finite Dimensional Controllers

    NASA Astrophysics Data System (ADS)

    Miyasato, Yoshihiko

    The problem of constructing model reference adaptive H∞ control for a class of mixed parameter systems is considered in this manuscript. Mixed parameter systems are complex processes composed of distributed parameter systems (infinite dimensional systems) and lumped parameter systems (finite dimensional systems). Owing to infinite dimensional modes of distributed parameter systems, control of those complex systems via finite dimensional compensators, is a difficult but important problem from both theoretical and practical viewpoints. A stabilizing control signal is added to regulate the effect of infinite dimensional modes, and it is derived as a solution of certain H∞ control problem where the effect of infinite dimensional modes are considered as external disturbances to the process.

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

    NASA Astrophysics Data System (ADS)

    Lee, Jin

    2014-05-01

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

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

    SciTech Connect

    Lazarov, R; Pasciaic, J; Vassilevski, P

    1999-07-01

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

  9. 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...

  10. Hybrid finite-volume/transported PDF method for the simulation of turbulent reactive flows

    NASA Astrophysics Data System (ADS)

    Raman, Venkatramanan

    A novel computational scheme is formulated for simulating turbulent reactive flows in complex geometries with detailed chemical kinetics. A Probability Density Function (PDF) based method that handles the scalar transport equation is coupled with an existing Finite Volume (FV) Reynolds-Averaged Navier-Stokes (RANS) flow solver. The PDF formulation leads to closed chemical source terms and facilitates the use of detailed chemical mechanisms without approximations. The particle-based PDF scheme is modified to handle complex geometries and grid structures. Grid-independent particle evolution schemes that scale linearly with the problem size are implemented in the Monte-Carlo PDF solver. A novel algorithm, in situ adaptive tabulation (ISAT) is employed to ensure tractability of complex chemistry involving a multitude of species. Several non-reacting test cases are performed to ascertain the efficiency and accuracy of the method. Simulation results from a turbulent jet-diffusion flame case are compared against experimental data. The effect of micromixing model, turbulence model and reaction scheme on flame predictions are discussed extensively. Finally, the method is used to analyze the Dow Chlorination Reactor. Detailed kinetics involving 37 species and 158 reactions as well as a reduced form with 16 species and 21 reactions are used. The effect of inlet configuration on reactor behavior and product distribution is analyzed. Plant-scale reactors exhibit quenching phenomena that cannot be reproduced by conventional simulation methods. The FV-PDF method predicts quenching accurately and provides insight into the dynamics of the reactor near extinction. The accuracy of the fractional time-stepping technique in discussed in the context of apparent multiple-steady states observed in a non-premixed feed configuration of the chlorination reactor.

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

    NASA Astrophysics Data System (ADS)

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

    2013-07-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1998-01-01

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

  13. 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

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

    NASA Astrophysics Data System (ADS)

    Ziaei-Rad, Masoud

    2010-12-01

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

  15. Model Reference Adaptive H∞ Control for Distributed Parameter Systems of Hyperbolic Type by Finite Dimensional Controllers

    NASA Astrophysics Data System (ADS)

    Miyasato, Yoshihiko

    The problem of constructing model reference adaptive H∞ control for distributed parameters systems of hyperbolic type is considered in this paper. Distributed parameters systems are infinite dimensional processes, but the proposed control scheme is constructed from finite dimensional controllers. The stabilizing control signal is added to regulate the effect of spill-over terms, and it is derived as a solution of certain H∞ control problem where spill-overs are considered as external disturbances to the process.

  16. A Lagrangian-Eulerian finite element method with adaptive gridding for advection-dispersion problems

    SciTech Connect

    Ijiri, Y.; Karasaki, K.

    1994-02-01

    In the present paper, a Lagrangian-Eulerian finite element method with adaptive gridding for solving advection-dispersion equations is described. The code creates new grid points in the vicinity of sharp fronts at every time step in order to reduce numerical dispersion. The code yields quite accurate solutions for a wide range of mesh Peclet numbers and for mesh Courant numbers well in excess of 1.

  17. Experience with automatic, dynamic load balancing and adaptive finite element computation

    SciTech Connect

    Wheat, S.R.; Devine, K.D.; Maccabe, A.B.

    1993-10-01

    Distributed memory, Massively Parallel (MP), MIMD technology has enabled the development of applications requiring computational resources previously unobtainable. Structural mechanics and fluid dynamics applications, for example, are often solved by finite element methods (FEMs) requiring, millions of degrees of freedom to accurately simulate physical phenomenon. Adaptive methods, which automatically refine or coarsen meshes and vary the order of accuracy of the numerical solution, offer greater robustness and computational efficiency than traditional FEMs by reducing the amount of computation required away from physical structures such as shock waves and boundary layers. On MP computers, FEMs frequently result in distributed processor load imbalances. To overcome load imbalance, many MP FEMs use static load balancing as a preprocessor to the finite element calculation. Adaptive methods complicate the load imbalance problem since the work per element is not uniform across the solution domain and changes as the computation proceeds. Therefore, dynamic load balancing is required to maintain global load balance. We describe a dynamic, fine-grained, element-based data migration system that maintains global load balance and is effective in the presence of changing work loads. Global load balance is achieved by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. The method utilizes an automatic element management system library to which a programmer integrates the application`s computational description. The library`s flexibility supports a large class of finite element and finite difference based applications.

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

    NASA Astrophysics Data System (ADS)

    Yan, Bo; Li, Yuguo; Liu, Ying

    2016-07-01

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

  19. 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.

  20. A vertex centred Finite Volume Jameson-Schmidt-Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics

    NASA Astrophysics Data System (ADS)

    Aguirre, Miquel; Gil, Antonio J.; Bonet, Javier; Arranz Carreño, Aurelio

    2014-02-01

    A vertex centred Finite Volume algorithm is presented for the numerical simulation of fast transient dynamics problems involving large deformations. A mixed formulation based upon the use of the linear momentum, the deformation gradient tensor and the total energy as conservation variables is discretised in space using linear triangles and tetrahedra in two-dimensional and three-dimensional computations, respectively. The scheme is implemented using central differences for the evaluation of the interface fluxes in conjunction with the Jameson-Schmidt-Turkel (JST) artificial dissipation term. The discretisation in time is performed by using a Total Variational Diminishing (TVD) two-stage Runge-Kutta time integrator. The JST algorithm is adapted in order to ensure the preservation of linear and angular momenta. The framework results in a low order computationally efficient solver for solid dynamics, which proves to be very competitive in nearly incompressible scenarios and bending dominated applications.

  1. 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.

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

    NASA Astrophysics Data System (ADS)

    Adcroft, Alistair; Hallberg, Robert; Harrison, Matthew

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

  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. 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.

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

    NASA Technical Reports Server (NTRS)

    Jou, W.-H.

    1982-01-01

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

  7. 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

  8. 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.

  9. 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.

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

    PubMed

    Johnston, Peter R

    2010-01-01

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

  11. Adaptive finite element simulation of flow and transport applications on parallel computers

    NASA Astrophysics Data System (ADS)

    Kirk, Benjamin Shelton

    The subject of this work is the adaptive finite element simulation of problems arising in flow and transport applications on parallel computers. Of particular interest are new contributions to adaptive mesh refinement (AMR) in this parallel high-performance context, including novel work on data structures, treatment of constraints in a parallel setting, generality and extensibility via object-oriented programming, and the design/implementation of a flexible software framework. This technology and software capability then enables more robust, reliable treatment of multiscale--multiphysics problems and specific studies of fine scale interaction such as those in biological chemotaxis (Chapter 4) and high-speed shock physics for compressible flows (Chapter 5). The work begins by presenting an overview of key concepts and data structures employed in AMR simulations. Of particular interest is how these concepts are applied in the physics-independent software framework which is developed here and is the basis for all the numerical simulations performed in this work. This open-source software framework has been adopted by a number of researchers in the U.S. and abroad for use in a wide range of applications. The dynamic nature of adaptive simulations pose particular issues for efficient implementation on distributed-memory parallel architectures. Communication cost, computational load balance, and memory requirements must all be considered when developing adaptive software for this class of machines. Specific extensions to the adaptive data structures to enable implementation on parallel computers is therefore considered in detail. The libMesh framework for performing adaptive finite element simulations on parallel computers is developed to provide a concrete implementation of the above ideas. This physics-independent framework is applied to two distinct flow and transport applications classes in the subsequent application studies to illustrate the flexibility of the

  12. Materials for adaptive structural acoustic control, volume 2

    NASA Astrophysics Data System (ADS)

    Cross, L. E.

    1993-04-01

    This report documents work carried out in the Materials Research Laboratory of the Pennsylvania State University over the first year of a new ONR sponsored University Research Initiative (URI) entitled Materials for Adaptive Structural Acoustic Control. For this report the activities have been grouped under the following topic headings: (1) General Summary Papers; (2) Materials Studies; (3) Composite Sensors; (4) Actuator Studies; (5) Integration Issues; (6) Processing Studies; (7) Thin Film Ferroelectrics. In material studies important advances have been made in the understanding of the evaluation of relaxor behavior in the PLZT's and of the order disorder behavior in lead scandium tantalate:lead titanate solid solutions and of the Morphotropic Phase Boundary in this system. For both composite sensors and actuators we have continued to explore and exploit the remarkable versatility of the flextensional moonie type structure. Finite element (FEA) calculations have given a clear picture of the lower order resonant modes and permitted the evaluation of various end cap metals, cap geometries and load conditions. In actuator studies multilayer structures have been combined with flextensional moonie endcaps to yield high displacement (50 micrometers) compact structures. Electrically controlled shape memory has been demonstrated in lead zirconate stannate titanate compositions, and used for controlling a simple latching relay.

  13. Materials for adaptive structural acoustic control, volume 3

    NASA Astrophysics Data System (ADS)

    Cross, L. E.

    1993-04-01

    This report documents work carried out in the Materials Research Laboratory of the Pennsylvania State University over the first year of a new ONR sponsored University Research Initiative (URI) entitled Materials for Adaptive Structural Acoustic Control. For this report the activities have been grouped under the following topic headings: (1) General Summary Papers; (2) Materials Studies; (3) Composite Sensors; (4) Actuator Studies; (5) Integration Issues; (6) Processing Studies; and (7) Thin Film Ferroelectrics. In material studies important advances have been made in the understanding of the evaluation of relaxor behavior in the PLZT's and of the order-disorder behavior in lead scandium tantalate:lead titanate solid solutions and of the Morphotropic Phase Boundary in this system. For both composite sensors and actuators, we have continued to explore and exploit the remarkable versatility of the flextensional moonie type structure. Finite element (FEA) calculations have given a clear picture of the lower order resonant modes and permitted the evaluation of various end cap metals, cap geometries, and load conditions. In actuator studies multilayer structures have been combined with flextensional moonie endcaps to yield high displacement (50 micrometers) compact structures. Electrically controlled shape memory has been demonstrated in lead zirconate stannate titanate compositions, and used for controlling a simple latching relay.

  14. Finite-approximation-error-based discrete-time iterative adaptive dynamic programming.

    PubMed

    Wei, Qinglai; Wang, Fei-Yue; Liu, Derong; Yang, Xiong

    2014-12-01

    In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite horizon discrete-time nonlinear systems with finite approximation errors. First, a new generalized value iteration algorithm of ADP is developed to make the iterative performance index function converge to the solution of the Hamilton-Jacobi-Bellman equation. The generalized value iteration algorithm permits an arbitrary positive semi-definite function to initialize it, which overcomes the disadvantage of traditional value iteration algorithms. When the iterative control law and iterative performance index function in each iteration cannot accurately be obtained, for the first time a new "design method of the convergence criteria" for the finite-approximation-error-based generalized value iteration algorithm is established. A suitable approximation error can be designed adaptively to make the iterative performance index function converge to a finite neighborhood of the optimal performance index function. Neural networks are used to implement the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the developed method. PMID:25265640

  15. 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.

  16. 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.

  17. 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

  18. An h-adaptive finite element method for turbulent heat transfer

    SciTech Connect

    Carriington, David B

    2009-01-01

    A two-equation turbulence closure model (k-{omega}) using an h-adaptive grid technique and finite element method (FEM) has been developed to simulate low Mach flow and heat transfer. These flows are applicable to many flows in engineering and environmental sciences. Of particular interest in the engineering modeling areas are: combustion, solidification, and heat exchanger design. Flows for indoor air quality modeling and atmospheric pollution transport are typical types of environmental flows modeled with this method. The numerical method is based on a hybrid finite element model using an equal-order projection process. The model includes thermal and species transport, localized mesh refinement (h-adaptive) and Petrov-Galerkin weighting for the stabilizing the advection. This work develops the continuum model of a two-equation turbulence closure method. The fractional step solution method is stated along with the h-adaptive grid method (Carrington and Pepper, 2002). Solutions are presented for 2d flow over a backward-facing step.

  19. Directionally adaptive finite element method for multidimensional Euler and Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Tan, Zhiqiang; Varghese, Philip L.

    1993-01-01

    A directionally adaptive finite element method for multidimensional compressible flows is presented. Quadrilateral and hexahedral elements are used because they have several advantages over triangular and tetrahedral elements. Unlike traditional methods that use quadrilateral/hexahedral elements, our method allows an element to be divided in each of the three directions in 3D and two directions in 2D. Some restrictions on mesh structure are found to be necessary, especially in 3D. The refining and coarsening procedures, and the treatment of constraints are given. A new implementation of upwind schemes in the constrained finite element system is presented. Some example problems, including a Mach 10 shock interaction with the walls of a 2D channel, a 2D viscous compression corner flow, and inviscid and viscous 3D flows in square channels, are also shown.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  1. 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.

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

    PubMed Central

    Xia, Guohua; Lin, Ching-Long

    2008-01-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1998-01-01

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

  4. Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration

    NASA Astrophysics Data System (ADS)

    Zhang, Y.; Key, K.; Ovall, J.; Holst, M.

    2014-12-01

    We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented

  5. Clock recovering characteristics of adaptive finite-impulse-response filters in digital coherent optical receivers.

    PubMed

    Kikuchi, Kazuro

    2011-03-14

    We analyze the clock-recovery process based on adaptive finite-impulse-response (FIR) filtering in digital coherent optical receivers. When the clock frequency is synchronized between the transmitter and the receiver, only five taps in half-symbol-spaced FIR filters can adjust the sampling phase of analog-to-digital conversion optimally, enabling bit-error rate performance independent of the initial sampling phase. Even if the clock frequency is not synchronized between them, the clock-frequency misalignment can be adjusted within an appropriate block interval; thus, we can achieve an asynchronous clock mode of operation of digital coherent receivers with block processing of the symbol sequence. PMID:21445201

  6. 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.

  7. 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.

  8. 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.

  9. MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements

    NASA Technical Reports Server (NTRS)

    Mitchell, William F.

    1993-01-01

    MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.

  10. Finite Element Analysis of Adaptive-Stiffening and Shape-Control SMA Hybrid Composites

    NASA Technical Reports Server (NTRS)

    Gao, Xiu-Jie; Turner, Travis L.; Burton, Deborah; Brinson, L. Catherine

    2005-01-01

    The usage of shape memory materials has extended rapidly to many fields, including medical devices, actuators, composites, structures and MEMS devices. For these various applications, shape memory alloys (SMAs) are available in various forms: bulk, wire, ribbon, thin film, and porous. In this work, the focus is on SMA hybrid composites with adaptive-stiffening or morphing functions. These composites are created by using SMA ribbons or wires embedded in a polymeric based composite panel/beam. Adaptive stiffening or morphing is activated via selective resistance heating or uniform thermal loads. To simulate the thermomechanical behavior of these composites, a SMA model was implemented using ABAQUS user element interface and finite element simulations of the systems were studied. Several examples are presented which show that the implemented model can be a very useful design and simulation tool for SMA hybrid composites.

  11. 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.

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

    NASA Technical Reports Server (NTRS)

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

    1981-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-05-01

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

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

    NASA Astrophysics Data System (ADS)

    Sheng, Zhiqiang; Yuan, Guangwei

    2016-06-01

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

  16. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2014-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Rizzi, A.; Eriksson, L. E.

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

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

    SciTech Connect

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

    2015-01-13

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

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

    NASA Astrophysics Data System (ADS)

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

    2012-08-01

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

  1. 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.

  2. A knowledge-based approach to the adaptive finite element analysis

    SciTech Connect

    Haghighi, K.; Kang, E.

    1995-12-31

    An automatic and knowledge-based finite element mesh generator (INTELMESH), which makes extensive use of interactive computer graphics techniques, has been developed. INTELMESH is designed for planar domains and axisymmetric 3-D structures of elasticity and heat transfer subjected to mechanical and thermal loading. It intelligently identifies the critical regions/points in the problem domain and utilizes the new concepts of substructuring and wave propagation to choose the proper mesh size for them. INTELMESH generates well-shaped triangular elements by applying triangulation and Laplacian smoothing procedures. The adaptive analysis involves the initial finite element analysis and an efficient a-posteriori error analysis and estimation. Once a problem is defined, the system automatically builds a finite element model and analyzes the problem through an automatic iterative process until the error reaches a desired level. It has been shown that the proposed approach which initiates the process with an a-priori, and near optimum mesh of the object, converges to the desired accuracy in less time and at less cost.

  3. A Newton method with adaptive finite elements for solving phase-change problems with natural convection

    NASA Astrophysics Data System (ADS)

    Danaila, Ionut; Moglan, Raluca; Hecht, Frédéric; Le Masson, Stéphane

    2014-10-01

    We present a new numerical system using finite elements with mesh adaptivity for the simulation of solid-liquid phase change systems. In the liquid phase, the natural convection flow is simulated by solving the incompressible Navier-Stokes equations with Boussinesq approximation. A variable viscosity model allows the velocity to progressively vanish in the solid phase, through an intermediate mushy region. The phase change is modeled by introducing an implicit enthalpy source term in the heat equation. The final system of equations describing the liquid-solid system by a single domain approach is solved using a Newton iterative algorithm. The space discretization is based on a P2-P1 Taylor-Hood finite elements and mesh adaptivity by metric control is used to accurately track the solid-liquid interface or the density inversion interface for water flows. The numerical method is validated against classical benchmarks that progressively add strong non-linearities in the system of equations: natural convection of air, natural convection of water, melting of a phase-change material and water freezing. Very good agreement with experimental data is obtained for each test case, proving the capability of the method to deal with both melting and solidification problems with convection. The presented numerical method is easy to implement using FreeFem++ software using a syntax close to the mathematical formulation.

  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. 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.

  6. 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.

  7. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

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

    SciTech Connect

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

    2011-01-01

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

  10. 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.

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

    SciTech Connect

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

    1999-05-01

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

  12. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2007-01-01

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

  14. 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.

  15. Digital adaptive controllers for VTOL vehicles. Volume 2: Software documentation

    NASA Technical Reports Server (NTRS)

    Hartmann, G. L.; Stein, G.; Pratt, S. G.

    1979-01-01

    The VTOL approach and landing test (VALT) adaptive software is documented. Two self-adaptive algorithms, one based on an implicit model reference design and the other on an explicit parameter estimation technique were evaluated. The organization of the software, user options, and a nominal set of input data are presented along with a flow chart and program listing of each algorithm.

  16. Effect of randomness on multi-frequency aeroelastic responses resolved by Unsteady Adaptive Stochastic Finite Elements

    SciTech Connect

    Witteveen, Jeroen A.S. Bijl, Hester

    2009-10-01

    The Unsteady Adaptive Stochastic Finite Elements (UASFE) method resolves the effect of randomness in numerical simulations of single-mode aeroelastic responses with a constant accuracy in time for a constant number of samples. In this paper, the UASFE framework is extended to multi-frequency responses and continuous structures by employing a wavelet decomposition pre-processing step to decompose the sampled multi-frequency signals into single-frequency components. The effect of the randomness on the multi-frequency response is then obtained by summing the results of the UASFE interpolation at constant phase for the different frequency components. Results for multi-frequency responses and continuous structures show a three orders of magnitude reduction of computational costs compared to crude Monte Carlo simulations in a harmonically forced oscillator, a flutter panel problem, and the three-dimensional transonic AGARD 445.6 wing aeroelastic benchmark subject to random fields and random parameters with various probability distributions.

  17. Hybrid multilevel sparse reconstruction for a whole domain bioluminescence tomography using adaptive finite element.

    PubMed

    Yu, Jingjing; He, Xiaowei; Geng, Guohua; Liu, Fang; Jiao, L C

    2013-01-01

    Quantitative reconstruction of bioluminescent sources from boundary measurements is a challenging ill-posed inverse problem owing to the high degree of absorption and scattering of light through tissue. We present a hybrid multilevel reconstruction scheme by combining the ability of sparse regularization with the advantage of adaptive finite element method. In view of the characteristics of different discretization levels, two different inversion algorithms are employed on the initial coarse mesh and the succeeding ones to strike a balance between stability and efficiency. Numerical experiment results with a digital mouse model demonstrate that the proposed scheme can accurately localize and quantify source distribution while maintaining reconstruction stability and computational economy. The effectiveness of this hybrid reconstruction scheme is further confirmed with in vivo experiments. PMID:23533542

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

    PubMed

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

    1999-02-01

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

  19. 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.

  20. Development of an adaptive hp-version finite element method for computational optimal control

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Warner, Michael S.

    1994-01-01

    In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications.

  1. Eulerian adaptive finite-difference method for high-velocity impact and penetration problems

    SciTech Connect

    Barton, Philip T.; Deiterding, Ralf; Meiron, Daniel I.; Pullin, Dale I

    2013-01-01

    Owing to the complex processes involved, faithful prediction of high-velocity impact events demands a simulation method delivering efficient calculations based on comprehensively formulated constitutive models. Such an approach is presented herein, employing a weighted essentially non-oscillatory (WENO) method within an adaptive mesh refinement (AMR) framework for the numerical solution of hyperbolic partial differential equations. Applied widely in computational fluid dynamics, these methods are well suited to the involved locally non-smooth finite deformations, circumventing any requirement for artificial viscosity functions for shock capturing. Application of the methods is facilitated through using a model of solid dynamics based upon hyper-elastic theory comprising kinematic evolution equations for the elastic distortion tensor. The model for finite inelastic deformations is phenomenologically equivalent to Maxwell s model of tangential stress relaxation. Closure relations tailored to the expected high-pressure states are proposed and calibrated for the materials of interest. Sharp interface resolution is achieved by employing level-set functions to track boundary motion, along with a ghost material method to capture the necessary internal boundary conditions for material interactions and stress-free surfaces. The approach is demonstrated for the simulation of high velocity impacts of steel projectiles on aluminium target plates in two and three dimensions.

  2. Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics.

    PubMed

    Heydari, Ali; Balakrishnan, Sivasubramanya N

    2013-01-01

    To synthesize fixed-final-time control-constrained optimal controllers for discrete-time nonlinear control-affine systems, a single neural network (NN)-based controller called the Finite-horizon Single Network Adaptive Critic is developed in this paper. Inputs to the NN are the current system states and the time-to-go, and the network outputs are the costates that are used to compute optimal feedback control. Control constraints are handled through a nonquadratic cost function. Convergence proofs of: 1) the reinforcement learning-based training method to the optimal solution; 2) the training error; and 3) the network weights are provided. The resulting controller is shown to solve the associated time-varying Hamilton-Jacobi-Bellman equation and provide the fixed-final-time optimal solution. Performance of the new synthesis technique is demonstrated through different examples including an attitude control problem wherein a rigid spacecraft performs a finite-time attitude maneuver subject to control bounds. The new formulation has great potential for implementation since it consists of only one NN with single set of weights and it provides comprehensive feedback solutions online, though it is trained offline. PMID:24808214

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

    PubMed

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

    2010-12-01

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

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

    NASA Astrophysics Data System (ADS)

    Maas, Jan; Matthes, Daniel

    2016-07-01

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

  5. 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.

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

    NASA Astrophysics Data System (ADS)

    Timofeev, Evgeny; Norouzi, Farhang

    2016-06-01

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

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

    NASA Astrophysics Data System (ADS)

    Chakrabartty, S. K.; Dhanalakshmi, K.

    1993-07-01

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

  8. 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.

  9. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

  11. 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.

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

    NASA Technical Reports Server (NTRS)

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

    1992-01-01

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

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

    NASA Technical Reports Server (NTRS)

    Damodaran, Murali; Caughey, David A.

    1987-01-01

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

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

    NASA Technical Reports Server (NTRS)

    Damodaran, Murali

    1988-01-01

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

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

    SciTech Connect

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

    1997-03-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

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

  17. 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.

  18. 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.

  19. 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.

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

    NASA Astrophysics Data System (ADS)

    Česenek, Jan

    2016-03-01

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

  1. 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.

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

    NASA Astrophysics Data System (ADS)

    Norgaard, Peter; Choueiri, Edgar; Jardin, Stephen

    2006-10-01

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

  3. 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.

  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 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

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

    PubMed

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

    2012-07-01

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

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

    NASA Technical Reports Server (NTRS)

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

    2000-01-01

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

  13. ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION

    PubMed Central

    HOLST, MICHAEL; MCCAMMON, JAMES ANDREW; YU, ZEYUN; ZHOU, YOUNGCHENG; ZHU, YUNRONG

    2011-01-01

    We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L∞ estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme

  14. 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.

  15. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2008-03-01

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

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

    NASA Astrophysics Data System (ADS)

    Li, Gang; Xing, Yulong

    2016-07-01

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

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

    SciTech Connect

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

    1999-07-01

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

  19. Digital adaptive controllers for VTOL vehicles. Volume 1: Concept evaluation

    NASA Technical Reports Server (NTRS)

    Hartmann, G. L.; Stein, G.; Pratt, S. G.

    1979-01-01

    A digital self-adaptive flight control system was developed for flight test in the VTOL approach and landing technology (VALT) research aircraft (a modified CH-47 helicopter). The control laws accept commands from an automatic on-board guidance system. The primary objective of the control laws is to provide good command-following with a minimum cross-axis response. Three attitudes and vertical velocity are separately commanded. Adaptation of the control laws is based on information from rate and attitude gyros and a vertical velocity measurement. The final design resulted from a comparison of two different adaptive concepts--one based on explicit parameter estimates from a real-time maximum-likelihood estimation algorithm, the other based on an implicit model reference adaptive system. The two designs were compared on the basis of performance and complexity.

  20. 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

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

    NASA Astrophysics Data System (ADS)

    Jahandari, H.; Farquharson, C. G.

    2015-09-01

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

  2. 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

  3. A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging.

    PubMed

    Lu, Yujie; Zhu, Banghe; Shen, Haiou; Rasmussen, John C; Wang, Ge; Sevick-Muraca, Eva M

    2010-08-21

    Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP(N)) approximations. To fully evaluate the performance of the SP(N) approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP(N) can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation. PMID:20671350

  4. Wind Forecasting Based on the HARMONIE Model and Adaptive Finite Elements

    NASA Astrophysics Data System (ADS)

    Oliver, Albert; Rodríguez, Eduardo; Escobar, José María; Montero, Gustavo; Hortal, Mariano; Calvo, Javier; Cascón, José Manuel; Montenegro, Rafael

    2015-01-01

    In this paper, we introduce a new method for wind field forecasting over complex terrain. The main idea is to use the predictions of the HARMONIE meso-scale model as the input data for an adaptive finite element mass-consistent wind model. The HARMONIE results (obtained with a maximum resolution of about 1 km) are refined in a local scale (about a few metres). An interface between both models is implemented in such a way that the initial wind field is obtained by a suitable interpolation of the HARMONIE results. Genetic algorithms are used to calibrate some parameters of the local wind field model in accordance to the HARMONIE data. In addition, measured data are considered to improve the reliability of the simulations. An automatic tetrahedral mesh generator, based on the meccano method, is applied to adapt the discretization to complex terrains. The main characteristic of the framework is a minimal user intervention. The final goal is to validate our model in several realistic applications on Gran Canaria island, Spain, with some experimental data obtained by the AEMET in their meteorological stations. The source code of the mass-consistent wind model is available online at http://www.dca.iusiani.ulpgc.es/Wind3D/.

  5. Adaptive explicit and implicit finite element methods for transient thermal analysis

    NASA Technical Reports Server (NTRS)

    Probert, E. J.; Hassan, O.; Morgan, K.; Peraire, J.

    1992-01-01

    The application of adaptive finite element methods to the solution of transient heat conduction problems in two dimensions is investigated. The computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid, using an error estimation procedure coupled to an automatic triangular mesh generator. Two alternative solution procedures are considered. In the first procedure, the solution is advanced by explicit timestepping, with domain decomposition being used to improve the computational efficiency of the method. In the second procedure, an algorithm for constructing continuous lines which pass only once through each node of the mesh is employed. The lines are used as the basis of a fully implicit method, in which the equation system is solved by line relaxation using a block tridiagonal equation solver. The numerical performance of the two procedures is compared for the analysis of a problem involving a moving heat source applied to a convectively cooled cylindrical leading edge.

  6. 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.

  7. 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

  8. 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.

  9. 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.

  10. 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.

  11. 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

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

    NASA Astrophysics Data System (ADS)

    Choi, Jung J.

    2015-08-01

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

  13. Adaptive finite elements with high aspect ratio for the computation of coalescence using a phase-field model

    NASA Astrophysics Data System (ADS)

    Burman, E.; Jacot, A.; Picasso, M.

    2004-03-01

    A multiphase-field model for the description of coalescence in a binary alloy is solved numerically using adaptive finite elements with high aspect ratio. The unknown of the multiphase-field model are the three phase fields (solid phase 1, solid phase 2, and liquid phase), a Lagrange multiplier and the concentration field. An Euler implicit scheme is used for time discretization, together with continuous, piecewise linear finite elements. At each time step, a linear system corresponding to the three phases plus the Lagrange multiplier has to be solved. Then, the linear system pertaining to concentration is solved. An adaptive finite element algorithm is proposed. In order to reduce the number of mesh vertices, the generated meshes contain elements with high aspect ratio. The refinement and coarsening criteria are based on an error indicator which has already been justified theoretically for simpler problems. Numerical results on two test cases show the efficiency of the method.

  14. An adaptive Newton continuation strategy for the fully implicit finite element immersed boundary method

    NASA Astrophysics Data System (ADS)

    Hoppe, R. H. W.; Linsenmann, C.

    2012-05-01

    The immersed boundary method (IB) is known as a powerful technique for the numerical solution of fluid-structure interaction problems as, for instance, the motion and deformation of viscoelastic bodies immersed in an external flow. It is based on the treatment of the flow equations within an Eulerian framework and of the equations of motion of the immersed bodies with respect to a Lagrangian coordinate system including interaction equations providing the transfer between both frames. The classical IB uses finite differences, but the IBM can be set up within a finite element approach in the spatial variables as well (FE-IB). The discretization in time usually relies on the Backward Euler (BE) method for the semidiscretized flow equations and the Forward Euler (FE) method for the equations of motion of the immersed bodies. The BE/FE FE-IB is subject to a CFL-type condition, whereas the fully implicit BE/BE FE-IB is unconditionally stable. The latter one can be solved numerically by Newton-type methods whose convergence properties are dictated by an appropriate choice of the time step size, in particular, if one is faced with sudden changes in the total energy of the system. In this paper, taking advantage of the well developed affine covariant convergence theory for Newton-type methods, we study a predictor-corrector continuation strategy in time with an adaptive choice of the continuation steplength. The feasibility of the approach and its superiority to BE/FE FE-IB is illustrated by two representative numerical examples.

  15. Adaptive meshless local maximum-entropy finite element method for convection-diffusion problems

    NASA Astrophysics Data System (ADS)

    Wu, C. T.; Young, D. L.; Hong, H. K.

    2014-01-01

    In this paper, a meshless local maximum-entropy finite element method (LME-FEM) is proposed to solve 1D Poisson equation and steady state convection-diffusion problems at various Peclet numbers in both 1D and 2D. By using local maximum-entropy (LME) approximation scheme to construct the element shape functions in the formulation of finite element method (FEM), additional nodes can be introduced within element without any mesh refinement to increase the accuracy of numerical approximation of unknown function, which procedure is similar to conventional p-refinement but without increasing the element connectivity to avoid the high conditioning matrix. The resulted LME-FEM preserves several significant characteristics of conventional FEM such as Kronecker-delta property on element vertices, partition of unity of shape function and exact reproduction of constant and linear functions. Furthermore, according to the essential properties of LME approximation scheme, nodes can be introduced in an arbitrary way and the continuity of the shape function along element edge is kept at the same time. No transition element is needed to connect elements of different orders. The property of arbitrary local refinement makes LME-FEM be a numerical method that can adaptively solve the numerical solutions of various problems where troublesome local mesh refinement is in general necessary to obtain reasonable solutions. Several numerical examples with dramatically varying solutions are presented to test the capability of the current method. The numerical results show that LME-FEM can obtain much better and stable solutions than conventional FEM with linear element.

  16. An Adaptive Finite Difference Method for Hyperbolic Systems in OneSpace Dimension

    SciTech Connect

    Bolstad, John H.

    1982-06-01

    Many problems of physical interest have solutions which are generally quite smooth in a large portion of the region of interest, but have local phenomena such as shocks, discontinuities or large gradients which require much more accurate approximations or finer grids for reasonable accuracy. Examples are atmospheric fronts, ocean currents, and geological discontinuities. In this thesis we develop and partially analyze an adaptive finite difference mesh refinement algorithm for the initial boundary value problem for hyperbolic systems in one space dimension. The method uses clusters of uniform grids which can ''move'' along with pulses or steep gradients appearing in the calculation, and which are superimposed over a uniform coarse grid. Such refinements are created, destroyed, merged, separated, recursively nested or moved based on estimates of the local truncation error. We use a four-way linked tree and sequentially allocated deques (double-ended queues) to perform these operations efficiently. The local truncation error in the interior of the region is estimated using a three-step Richardson extrapolation procedure, which can also be considered a deferred correction method. At the boundaries we employ differences to estimate the error. Our algorithm was implemented using a portable, extensible Fortran preprocessor, to which we added records and pointers. The method is applied to three model problems: the first order wave equation, the second order wave equation, and the inviscid Burgers equation. For the first two model problems our algorithm is shown to be three to five times more efficient (in computing time) than the use of a uniform coarse mesh, for the same accuracy. Furthermore, to our knowledge, our algorithm is the only one which adaptively treats time-dependent boundary conditions for hyperbolic systems.

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

    NASA Astrophysics Data System (ADS)

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

    2013-09-01

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

  18. 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.

  19. 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

  20. Stresses in faulted tunnel models by photoelasticity and adaptive finite element

    SciTech Connect

    Ladkany, S.G.; Huang, Y.

    1995-12-01

    Research efforts in this area continue to investigate the development of a proper technique to analyze the stresses in the Ghost Dance fault and the effect of the fault on the stability of drifts in the proposed repository. Results from two parallel techniques are being compared to each other - Photoelastic models and Finite Element (FE) models. The Photoelastic plexiglass model (88.89 mm thick & 256.1 mm long and wide) has two adjacent spare openings (57.95 mm long and wide) and a central round opening (57.95 mm diameter) placed at a clear distance approximately equal to its diameter from the square openings. The vertical loading on top of the model is 2269 N (500 lb.). Saw cuts (0.5388 mm wide), representing a fault, are being propagated from the tunnels outward with stress measurements taken at predefined locations, as the saw cuts increase in length. The FE model duplicates exactly the Photoelastic models. The adaptive mesh generation method is used to refine the FE grid at every step of the analysis. This nonlinear interactive computational techniques uses various uses various percent tolerance errors in the convergence of stress values as a measure in ending the iterative process.

  1. Finite State Machine with Adaptive Electromyogram (EMG) Feature Extraction to Drive Meal Assistance Robot

    NASA Astrophysics Data System (ADS)

    Zhang, Xiu; Wang, Xingyu; Wang, Bei; Sugi, Takenao; Nakamura, Masatoshi

    Surface electromyogram (EMG) from elbow, wrist and hand has been widely used as an input of multifunction prostheses for many years. However, for patients with high-level limb deficiencies, muscle activities in upper-limbs are not strong enough to be used as control signals. In this paper, EMG from lower-limbs is acquired and applied to drive a meal assistance robot. An onset detection method with adaptive threshold based on EMG power is proposed to recognize different muscle contractions. Predefined control commands are output by finite state machine (FSM), and applied to operate the robot. The performance of EMG control is compared with joystick control by both objective and subjective indices. The results show that FSM provides the user with an easy-performing control strategy, which successfully operates robots with complicated control commands by limited muscle motions. The high accuracy and comfortableness of the EMG-control meal assistance robot make it feasible for users with upper limbs motor disabilities.

  2. Finite time-Lyapunov based approach for robust adaptive control of wind-induced oscillations in power transmission lines

    NASA Astrophysics Data System (ADS)

    Ghabraei, Soheil; Moradi, Hamed; Vossoughi, Gholamreza

    2016-06-01

    Large amplitude oscillation of the power transmission lines, which is also known as galloping phenomenon, has hazardous consequences such as short circuiting and failure of transmission line. In this article, to suppress the undesirable vibrations of the transmission lines, first the governing equations of transmission line are derived via mode summation technique. Then, due to the occurrence of large amplitude vibrations, nonlinear quadratic and cubic terms are included in the derived linear equations. To suppress the vibrations, arbitrary number of the piezoelectric actuators is assumed to exert the actuation forces. Afterwards, a Lyapunov based approach is proposed for the robust adaptive suppression of the undesirable vibrations in the finite time. To compensate the supposed parametric uncertainties with unknown bands, proper adaption laws are introduced. To avoid the vibration devastating consequences as quickly as possible, appropriate control laws are designed. The vibration suppression in the finite time with supposed adaption and control laws is mathematically proved via Lyapunov finite time stability theory. Finally, to illustrate and validate the efficiency and robustness of the proposed finite time control scheme, a parametric case study with three piezoelectric actuators is performed. It is observed that the proposed active control strategy is more efficient and robust than the passive control methods.

  3. 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).

  4. Simulation studies of vestibular macular afferent-discharge patterns using a new, quasi-3-D finite volume method

    NASA Technical Reports Server (NTRS)

    Ross, M. D.; Linton, S. W.; Parnas, B. R.

    2000-01-01

    A quasi-three-dimensional finite-volume numerical simulator was developed to study passive voltage spread in vestibular macular afferents. The method, borrowed from computational fluid dynamics, discretizes events transpiring in small volumes over time. The afferent simulated had three calyces with processes. The number of processes and synapses, and direction and timing of synapse activation, were varied. Simultaneous synapse activation resulted in shortest latency, while directional activation (proximal to distal and distal to proximal) yielded most regular discharges. Color-coded visualizations showed that the simulator discretized events and demonstrated that discharge produced a distal spread of voltage from the spike initiator into the ending. The simulations indicate that directional input, morphology, and timing of synapse activation can affect discharge properties, as must also distal spread of voltage from the spike initiator. The finite volume method has generality and can be applied to more complex neurons to explore discrete synaptic effects in four dimensions.

  5. Axial coupling constant of the nucleon for two flavors of dynamical quarks in finite and infinite volume

    SciTech Connect

    Khan, A. Ali; Goeckeler, M.; Schaefer, A.; Haegler, Ph.; Hemmert, T. R.; Wollenweber, T.; Horsley, R.; Zanotti, J. M.; Pleiter, D.; Rakow, P. E. L.; Schierholz, G.

    2006-11-01

    We present data for the axial coupling constant g{sub A} of the nucleon obtained in lattice QCD with two degenerate flavors of dynamical nonperturbatively improved Wilson quarks. The renormalization is also performed nonperturbatively. For the analysis we give a chiral extrapolation formula for g{sub A} based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavors. Applying this formalism in a finite volume, we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattice data in finite volume, we are able to determine the axial coupling of the nucleon in the chiral limit without imposing the known value at the physical point.

  6. 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.

  7. 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.

  8. A conservative Dirichlet boundary treatment for the finite volume lattice Boltzmann method

    NASA Astrophysics Data System (ADS)

    Chen, Leitao; Schaefer, Laura

    2014-11-01

    The finite volume lattice Boltzmann method (FVLBM) enables the model to use the exact body-fitting mesh in the flow problems that involve the complex boundaries. However, the development of proper boundary treatment for the FVLBM has been outpaced. The boundary treatments designed for the conventional lattice Boltzmann method (LBM) framework are still heavily applied to the FVLBM. The largest defect of using the old boundary treatment is that, on the Dirichlet boundaries, the macroscopic variables cannot be conserved. In another word, there exist nontrivial discrepancies between the macroscopic variables defined by the boundary conditions and those yield by the numerical solutions. The errors on the boundaries will contaminate the internal solutions and even cause instability, especially on the complex boundaries. To overcome such a shortcoming, a conservative boundary treatment for the Dirichlet hydrodynamic boundary conditions is developed for the FVLBM. Through the benchmark tests, it is shown that the macroscopic conservations on the Direchlet boundaries are up to machine accuracy and completely independent of the size of relaxation time, the type of lattice model, the level of mesh resolution, the shape of boundaries and the type of internal scheme.

  9. 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.

  10. 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.

  11. 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.

  12. Simulating the Flow Dynamics in the Southern Everglades using a Finite Volume Model

    NASA Astrophysics Data System (ADS)

    Senarath, S. U.; Novoa, R. J.; Barnes, J. A.; Brion, L. M.

    2001-12-01

    The Regional Simulation Model (RSM) is a weighted, implicit, finite-volume, rainfall-runoff model and is capable of simulating two-dimensional flow in arbitrarily shaped areas using a variable mesh structure. In this study the RSM is used to investigate the effect of structural and operational water management alternatives on flow-dynamics in South Florida's southern Everglades and Big Cypress National Preserve. The model domain encompasses some of the areas earmarked for restoration under the Comprehensive Everglades Restoration Plan (CERP). The RSM will be used to assess the effect/sensitivity of flow barriers and man-made structures on flow dynamics. The RSM has the capability of simulating overland and ground water interactions, evapotranspiration, infiltration, levee seepage, and canal flow. One-dimensional canal flow and two-dimensional overland flow are simulated in the model using the diffusive wave approximation to the Saint Venant equation. The Darcy equation is used for one-dimensional canal seepage and two-dimensional groundwater flow calculations. Overland and groundwater flow components are fully coupled for a more realistic representation of runoff generation making the RSM ideally suited for simulating the high water table, highly permeable soils and relatively flat terrain, associated with the southern Everglades region of Florida.

  13. Micro Blowing Simulations Using a Coupled Finite-Volume Lattice-Boltzman n L ES Approach

    NASA Technical Reports Server (NTRS)

    Menon, S.; Feiz, H.

    1990-01-01

    Three dimensional large-eddy simulations (LES) of single and multiple jet-in-cross-flow (JICF) are conducted using the 19-bit Lattice Boltzmann Equation (LBE) method coupled with a conventional finite-volume (FV) scheme. In this coupled LBE-FV approach, the LBE-LES is employed to simulate the flow inside the jet nozzles while the FV-LES is used to simulate the crossflow. The key application area is the use of this technique is to study the micro blowing technique (MBT) for drag control similar to the recent experiments at NASA/GRC. It is necessary to resolve the flow inside the micro-blowing and suction holes with high resolution without being restricted by the FV time-step restriction. The coupled LBE-FV-LES approach achieves this objectives in a computationally efficient manner. A single jet in crossflow case is used for validation purpose and the results are compared with experimental data and full LBE-LES simulation. Good agreement with data is obtained. Subsequently, MBT over a flat plate with porosity of 25% is simulated using 9 jets in a compressible cross flow at a Mach number of 0.4. It is shown that MBT suppresses the near-wall vortices and reduces the skin friction by up to 50 percent. This is in good agreement with experimental data.

  14. Some recent finite volume schemes to compute Euler equations using real gas EOS

    NASA Astrophysics Data System (ADS)

    Gallouët, T.; Hérard, J.-M.; Seguin, N.

    2002-08-01

    This paper deals with the resolution by finite volume methods of Euler equations in one space dimension, with real gas state laws (namely, perfect gas EOS, Tammann EOS and Van Der Waals EOS). All tests are of unsteady shock tube type, in order to examine a wide class of solutions, involving Sod shock tube, stationary shock wave, simple contact discontinuity, occurrence of vacuum by double rarefaction wave, propagation of a one-rarefaction wave over vacuum, Most of the methods computed herein are approximate Godunov solvers: VFRoe, VFFC, VFRoe ncv (, u, p) and PVRS. The energy relaxation method with VFRoe ncv (, u, p) and Rusanov scheme have been investigated too. Qualitative results are presented or commented for all test cases and numerical rates of convergence on some test cases have been measured for first- and second-order (Runge-Kutta 2 with MUSCL reconstruction) approximations. Note that rates are measured on solutions involving discontinuities, in order to estimate the loss of accuracy due to these discontinuities. Copyright

  15. 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.

  16. Investigations into the applicability of adaptive finite element methods to two-dimensional infinite Prandtl number thermal and thermochemical convection

    NASA Astrophysics Data System (ADS)

    Davies, D. R.; Davies, J. H.; Hassan, O.; Morgan, K.; Nithiarasu, P.

    2007-05-01

    An adaptive finite element procedure is presented for improving the quality of solutions to convection-dominated problems in geodynamics. The method adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver, and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code ConMan. An unstructured quadrilateral mesh generator is utilized, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation-based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermochemical problems with well-established benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy while increasing computational efficiency. For thermochemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid-based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies.

  17. 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.

  18. Materials for adaptive structural acoustic control, volume 1

    NASA Astrophysics Data System (ADS)

    Cross, L. E.

    1993-04-01

    This report documents work carried out in the Materials Research Laboratory of the Pennsylvania State University over the first year of a new ONR sponsored University Research Initiative (URI) entitled Materials for Adaptive Structural Acoustic Control. For this report the activities have been grouped under the following topic headings: (1) General Summary Papers; (2) Materials Studies; (3) Composite Sensors; (4) Actuator Studies; (5) Integration Issues; (6) Processing Studies; and (7) Thin Film Ferroelectrics. In material studies important advances have been made in the understanding of the evaluation of relaxor behavior in the PLZT's and of the order disorder behavior in lead scandium tantalate:lead titanate solid solutions and of the Morphotropic Phase Boundary in this system.

  19. Survey and development of finite elements for nonlinear structural analysis. Volume 1: Handbook for nonlinear finite elements

    NASA Technical Reports Server (NTRS)

    1976-01-01

    A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity.

  20. 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

  1. 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.

  2. Three-dimensional multi bioluminescent sources reconstruction based on adaptive finite element method

    NASA Astrophysics Data System (ADS)

    Ma, Xibo; Tian, Jie; Zhang, Bo; Zhang, Xing; Xue, Zhenwen; Dong, Di; Han, Dong

    2011-03-01

    Among many optical molecular imaging modalities, bioluminescence imaging (BLI) has more and more wide application in tumor detection and evaluation of pharmacodynamics, toxicity, pharmacokinetics because of its noninvasive molecular and cellular level detection ability, high sensitivity and low cost in comparison with other imaging technologies. However, BLI can not present the accurate location and intensity of the inner bioluminescence sources such as in the bone, liver or lung etc. Bioluminescent tomography (BLT) shows its advantage in determining the bioluminescence source distribution inside a small animal or phantom. Considering the deficiency of two-dimensional imaging modality, we developed three-dimensional tomography to reconstruct the information of the bioluminescence source distribution in transgenic mOC-Luc mice bone with the boundary measured data. In this paper, to study the osteocalcin (OC) accumulation in transgenic mOC-Luc mice bone, a BLT reconstruction method based on multilevel adaptive finite element (FEM) algorithm was used for localizing and quantifying multi bioluminescence sources. Optical and anatomical information of the tissues are incorporated as a priori knowledge in this method, which can reduce the ill-posedness of BLT. The data was acquired by the dual modality BLT and Micro CT prototype system that was developed by us. Through temperature control and absolute intensity calibration, a relative accurate intensity can be calculated. The location of the OC accumulation was reconstructed, which was coherent with the principle of bone differentiation. This result also was testified by ex vivo experiment in the black 96-plate well using the BLI system and the chemiluminescence apparatus.

  3. Determination of remodeling parameters for a strain-adaptive finite element model of the distal ulna.

    PubMed

    Neuert, Mark A C; Dunning, Cynthia E

    2013-09-01

    Strain energy-based adaptive material models are used to predict bone resorption resulting from stress shielding induced by prosthetic joint implants. Generally, such models are governed by two key parameters: a homeostatic strain-energy state (K) and a threshold deviation from this state required to initiate bone reformation (s). A refinement procedure has been performed to estimate these parameters in the femur and glenoid; this study investigates the specific influences of these parameters on resulting density distributions in the distal ulna. A finite element model of a human ulna was created using micro-computed tomography (µCT) data, initialized to a homogeneous density distribution, and subjected to approximate in vivo loading. Values for K and s were tested, and the resulting steady-state density distribution compared with values derived from µCT images. The sensitivity of these parameters to initial conditions was examined by altering the initial homogeneous density value. The refined model parameters selected were then applied to six additional human ulnae to determine their performance across individuals. Model accuracy using the refined parameters was found to be comparable with that found in previous studies of the glenoid and femur, and gross bone structures, such as the cortical shell and medullary canal, were reproduced. The model was found to be insensitive to initial conditions; however, a fair degree of variation was observed between the six specimens. This work represents an important contribution to the study of changes in load transfer in the distal ulna following the implementation of commercial orthopedic implants. PMID:23804949

  4. Direct numerical simulations of particle-laden density currents with adaptive, discontinuous finite elements

    NASA Astrophysics Data System (ADS)

    Parkinson, S. D.; Hill, J.; Piggott, M. D.; Allison, P. A.

    2014-05-01

    High resolution direct numerical simulations (DNS) are an important tool for the detailed analysis of turbidity current dynamics. Models that resolve the vertical structure and turbulence of the flow are typically based upon the Navier-Stokes equations. Two-dimensional simulations are known to produce unrealistic cohesive vortices that are not representative of the real three-dimensional physics. The effect of this phenomena is particularly apparent in the later stages of flow propagation. The ideal solution to this problem is to run the simulation in three dimensions but this is computationally expensive. This paper presents a novel finite-element (FE) DNS turbidity current model that has been built within Fluidity, an open source, general purpose, computational fluid dynamics code. The model is validated through re-creation of a lock release density current at a Grashof number of 5 × 106 in two, and three-dimensions. Validation of the model considers the flow energy budget, sedimentation rate, head speed, wall normal velocity profiles and the final deposit. Conservation of energy in particular is found to be a good metric for measuring mesh performance in capturing the range of dynamics. FE models scale well over many thousands of processors and do not impose restrictions on domain shape, but they are computationally expensive. Use of discontinuous discretisations and adaptive unstructured meshing technologies, which reduce the required element count by approximately two orders of magnitude, results in high resolution DNS models of turbidity currents at a fraction of the cost of traditional FE models. The benefits of this technique will enable simulation of turbidity currents in complex and large domains where DNS modelling was previously unachievable.

  5. A Finite Element Based Constrained Mixture Implementation for Arterial Growth, Remodeling, and Adaptation: Theory and Numerical Verification

    PubMed Central

    Valentín, A.; Humphrey, J. D.; Holzapfel, G. A.

    2013-01-01

    We implemented a constrained mixture model of arterial growth and remodeling (G&R) in a nonlinear finite element framework to facilitate numerical analyses of diverse cases of arterial adaptation and maladaptation, including disease progression, resulting in complex evolving geometries and compositions. This model enables hypothesis testing by predicting consequences of postulated characteristics of cell and matrix turnover, including evolving quantities and orientations of fibrillar constituents and non-homogenous degradation of elastin or loss of smooth muscle function. The non-linear finite element formulation is general within the context of arterial mechanics, but we restricted our present numerical verification to cylindrical geometries to allow comparisons to prior results for two special cases: uniform transmural changes in mass and differential G&R within a two-layered cylindrical model of the human aorta. The present finite element model recovers the results of these simplified semi-inverse analyses with good agreement. PMID:23713058

  6. Model Reference Adaptive H∞ Control for Distributed Parameter Systems of Hyperbolic Type with Input Nonlinearity by Finite Dimensional Controllers

    NASA Astrophysics Data System (ADS)

    Miyasato, Yoshihiko

    The problem of constructing model reference adaptive H∞ control for distributed parameter systems of hyperbolic type preceded by unknown input nonlinearity such as dead zone or backlash, is considered in this paper. Distributed parameter systems are infinite dimensional processes, but the proposed control scheme is constructed from finite dimensional controllers. An adaptive inverse model is introduced to estimate and compensate the input nonlinearity. The stabilizing control signal is added to regulate the effect of spill-over terms, and it is derived as a solution of certain H∞ control problem where the residual part of the inverse model and the spill-over term are considered as external disturbances to the process.

  7. 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

  8. 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

  9. Glacial isostatic adjustment on 3-D Earth models: a finite-volume formulation

    NASA Astrophysics Data System (ADS)

    Latychev, Konstantin; Mitrovica, Jerry X.; Tromp, Jeroen; Tamisiea, Mark E.; Komatitsch, Dimitri; Christara, Christina C.

    2005-05-01

    We describe and present results from a finite-volume (FV) parallel computer code for forward modelling the Maxwell viscoelastic response of a 3-D, self-gravitating, elastically compressible Earth to an arbitrary surface load. We implement a conservative, control volume discretization of the governing equations using a tetrahedral grid in Cartesian geometry and a low-order, linear interpolation. The basic starting grid honours all major radial discontinuities in the Preliminary Reference Earth Model (PREM), and the models are permitted arbitrary spatial variations in viscosity and elastic parameters. These variations may be either continuous or discontinuous at a set of grid nodes forming a 3-D surface within the (regional or global) modelling domain. In the second part of the paper, we adopt the FV methodology and a spherically symmetric Earth model to generate a suite of predictions sampling a broad class of glacial isostatic adjustment (GIA) data types (3-D crustal motions, long-wavelength gravity anomalies). These calculations, based on either a simple disc load history or a global Late Pleistocene ice load reconstruction (ICE-3G), are benchmarked against predictions generated using the traditional normal-mode approach to GIA. The detailed comparison provides a guide for future analyses (e.g. what grid resolution is required to obtain a specific accuracy?) and it indicates that discrepancies in predictions of 3-D crustal velocities less than 0.1 mm yr-1 are generally obtainable for global grids with ~3 × 106 nodes; however, grids of higher resolution are required to predict large-amplitude (>1 cm yr-1) radial velocities in zones of peak post-glacial uplift (e.g. James bay) to the same level of absolute accuracy. We conclude the paper with a first application of the new formulation to a 3-D problem. Specifically, we consider the impact of mantle viscosity heterogeneity on predictions of present-day 3-D crustal motions in North America. In these tests, the

  10. 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

  11. 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.

  12. Finite volume numerical scheme for high-resolution gravity field modelling and its parallel implementation

    NASA Astrophysics Data System (ADS)

    Fašková, Z.; Macák, M.; Čunderlík, R.; Mikula, K.

    2012-04-01

    The paper discusses a numerical solution of the geodetic boundary value problem (GBVP) by the finite volume method (FVM). The FVM is a numerical method where numerical flux is conserved from one discretization cell to its neighbour, so it's very appropriate for solving GBVP with the Neumann and the Dirichlet BCs. Our numerical scheme is developed for 3D computational domain above an ellipsoid. It is shown that a refinement of the discretization in height's direction leads to more precise numerical results. In order to achieve high-resolution numerical results, parallel implementations of algorithms using the MPI procedures were developed and computations on parallel computers were successfully performed. This basis includes the splitting of all arrays in meridian's direction, usage of an implementation of the Bi-CGSTAB non-stationary iterative solver instead of the standard SOR and an optimization of communications on parallel computers with the NUMA architecture. This gives us higher speed up in comparison to standard approaches and enables us to develop an efficient tool for high-resolution global or regional gravity field modelling in huge areas. Numerical experiments present global modelling with the resolution comparable with EGM2008 and detailed regional modelling in the Pacific Ocean with the resolution 2x2 arc min. Input gravity disturbances are generated from the DTU10-GRAV gravity field model and the disturbing potential is computed from the GOCE_DIR2 satellite geopotential model up to degree 240. Finally, the obtained disturbing potential is used to evaluate the geopotential on the DTU10 mean sea surface and the achieved mean dynamic topography is compared with the ECCO oceanographic model.

  13. 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.

  14. 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.

  15. Adaptive Computer-Assisted Tutorials: A Cybernetic Approach Optimization with Finite-State Machines.

    ERIC Educational Resources Information Center

    Offir, Joseph

    This paper presents the concepts of a computer-directed system to improve human performance in structured learning situations. Attention is focused on finite-state systems in order to provide a systematic method for constructing training systems and to assist in analysis of problem solving and curriculum planning. The finite-state approach allows…

  16. Online adaptive radiotherapy of the bladder: Small bowel irradiated-volume reduction

    SciTech Connect

    Burridge, Nichola . E-mail: nichola.burridge@physics.cr.man.ac.uk; Amer, Ali; Marchant, Tom; Sykes, Jonathan; Stratford, Julie; Henry, Ann; McBain, Catherine; Price, Pat; Moore, Chris

    2006-11-01

    Purpose: To assess the potential reduction of small bowel volume receiving high-dose radiation by using kilovoltage X-ray cone beam computed tomography (CBCT) and quantized margin selection for adaptive bladder cancer treatment. Methods and Materials: Twenty bladder patients were planned conformally using a four-field, 15-mm uniform margin technique. Two additional planning target volumes (PTVs) were created using margins quantized to 5 and 10 mm in the superior direction only. CBCTs ({approx}8 scans/patient) were acquired during treatment. CBCT volumes were registered with CT planning scans to determine setup errors and to select the appropriate PTV of the day. Margin reduction in other directions was considered. Outlining of small bowel in every fraction is required to properly quantify the volume of small bowel spared from high doses. In the case of CBCT this is not always possible owing to artifacts created by small bowel movement and the presence of gas. A simpler method was adopted by considering the volume difference between PTVs created using uniform and adapted margins, which corresponds to the potential volume of small bowel sparing. Results: The average small bowel volume that can be spared by this form of adaptive radiotherapy is 31 {+-} 23 cm{sup 3} ({+-}1 SD). The bladder for 1 patient was systematically smaller than the planning scan and hence demonstrated the largest average reduction of 76 cm{sup 3}. The clinical target volume to PTV margins in other directions can be safely reduced to 10 mm except in the anterior direction where, like the superior direction, the bladder showed significant variation. Conclusions: Online CBCT-assisted plan selection based on quantized margins can significantly reduce the volume of small bowel receiving high doses for some bladder patients. CBCT allows the 15-mm margins used in some directions to be safely reduced to 10 mm.

  17. 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.

  18. 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

  19. SER-LARS, Volume 6. Instructional Materials, Teacher Made and Commercially Adapted. 1975-76 Edition.

    ERIC Educational Resources Information Center

    Montgomery County Intermediate Unit 23, Blue Bell, PA.

    The sixth of nine volumes in the Special Education Resources Location Analysis and Retrieval System (SER-LARS), a diagnostic-prescriptive instructional data bank for teachers of handicapped children, presents an inventory of teacher-made and commercially adapted instructional materials. The instructional materials are organized by accession number…

  20. ISAARE: Information System for Adaptive, Assistive and Recreational Equipment: Volume III, Insitu Motion; Volume IV, Travel; Volume VI, Rehabilitation.

    ERIC Educational Resources Information Center

    Melichar, Joseph F.

    In a continuation of the Information System for Adaptive, Assistive and Recreational Equipment, described are aids for physically handicapped pupils in the functional areas of insitu motion, travel, and rehabilitation. Insitu motion equipment items are seen to include static positioning devices (such as tilt tables, stand-in tables, and protective…

  1. Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

    A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach.

  2. 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.

  3. Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale.

    PubMed

    Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

    2016-02-01

    Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions. PMID:26986440

  4. Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale

    NASA Astrophysics Data System (ADS)

    Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

    2016-02-01

    Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

  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. 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.

  7. Dynamic adaptive finite element analysis of acoustic wave propagation due to underwater explosion for fluid-structure interaction problems

    NASA Astrophysics Data System (ADS)

    Emamzadeh, Seyed Shahab; Ahmadi, Mohammad Taghi; Mohammadi, Soheil; Biglarkhani, Masoud

    2015-07-01

    In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes: a) calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b) fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c) adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.

  8. H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows

    NASA Technical Reports Server (NTRS)

    Chang, H. J.; Bass, J. M.; Tworzydlo, W.; Oden, J. T.

    1993-01-01

    The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).

  9. A Godunov-type Finite Volume Scheme for Meso- and Micro-scale Flows in Three Dimensions

    NASA Astrophysics Data System (ADS)

    Ahmad, Nash'at; Lindeman, John

    2008-10-01

    This short note reports the extension of the f-waves approximate Riemann solver (A hmad and L indeman, 2007; L eV eque, 2002; B ale et al., 2002) for three-dimensional meso- and micro-scale atmospheric flows. The Riemann solver employs flux-based wave decomposition for the calculation of Godunov fluxes and does not require the explicit definition of the Roe matrix to enforce conservation. The other important feature of the Riemann solver is its ability to incorporate source term due to gravity without introducing discretization errors. The resulting finite volume scheme is second-order accurate in space and time. The finite-difference schemes currently used in atmospheric flow models are neither conservative nor able to resolve regions of sharp gradients. The finite volume scheme described in this paper is fully conservative and has the ability to resolve regions of sharp gradients without introducing spurious oscillations in the solution. The scheme shows promise in accurately resolving flows on the meso- and micro-scales and should be considered for implementation in the dynamical cores of next generation meso- and micro-scale atmospheric flow models.

  10. Parallelization of an Adaptive Multigrid Algorithm for Fast Solution of Finite Element Structural Problems

    SciTech Connect

    Crane, N K; Parsons, I D; Hjelmstad, K D

    2002-03-21

    Adaptive mesh refinement selectively subdivides the elements of a coarse user supplied mesh to produce a fine mesh with reduced discretization error. Effective use of adaptive mesh refinement coupled with an a posteriori error estimator can produce a mesh that solves a problem to a given discretization error using far fewer elements than uniform refinement. A geometric multigrid solver uses increasingly finer discretizations of the same geometry to produce a very fast and numerically scalable solution to a set of linear equations. Adaptive mesh refinement is a natural method for creating the different meshes required by the multigrid solver. This paper describes the implementation of a scalable adaptive multigrid method on a distributed memory parallel computer. Results are presented that demonstrate the parallel performance of the methodology by solving a linear elastic rocket fuel deformation problem on an SGI Origin 3000. Two challenges must be met when implementing adaptive multigrid algorithms on massively parallel computing platforms. First, although the fine mesh for which the solution is desired may be large and scaled to the number of processors, the multigrid algorithm must also operate on much smaller fixed-size data sets on the coarse levels. Second, the mesh must be repartitioned as it is adapted to maintain good load balancing. In an adaptive multigrid algorithm, separate mesh levels may require separate partitioning, further complicating the load balance problem. This paper shows that, when the proper optimizations are made, parallel adaptive multigrid algorithms perform well on machines with several hundreds of processors.

  11. A chimera grid scheme. [multiple overset body-conforming mesh system for finite difference adaptation to complex aircraft configurations

    NASA Technical Reports Server (NTRS)

    Steger, J. L.; Dougherty, F. C.; Benek, J. A.

    1983-01-01

    A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.

  12. Tumor Volume-Adapted Dosing in Stereotactic Ablative Radiotherapy of Lung Tumors

    SciTech Connect

    Trakul, Nicholas; Chang, Christine N.; Harris, Jeremy; Chapman, Christopher; Rao, Aarti; Shen, John; Quinlan-Davidson, Sean; Filion, Edith J.; Wakelee, Heather A.; Colevas, A. Dimitrios; Whyte, Richard I.; and others

    2012-09-01

    Purpose: Current stereotactic ablative radiotherapy (SABR) protocols for lung tumors prescribe a uniform dose regimen irrespective of tumor size. We report the outcomes of a lung tumor volume-adapted SABR dosing strategy. Methods and Materials: We retrospectively reviewed the outcomes in 111 patients with a total of 138 primary or metastatic lung tumors treated by SABR, including local control, regional control, distant metastasis, overall survival, and treatment toxicity. We also performed subset analysis on 83 patients with 97 tumors treated with a volume-adapted dosing strategy in which small tumors (gross tumor volume <12 mL) received single-fraction regimens with biologically effective doses (BED) <100 Gy (total dose, 18-25 Gy) (Group 1), and larger tumors (gross tumor volume {>=}12 mL) received multifraction regimens with BED {>=}100 Gy (total dose, 50-60 Gy in three to four fractions) (Group 2). Results: The median follow-up time was 13.5 months. Local control for Groups 1 and 2 was 91.4% and 92.5%, respectively (p = 0.24) at 12 months. For primary lung tumors only (excluding metastases), local control was 92.6% and 91.7%, respectively (p = 0.58). Regional control, freedom from distant metastasis, and overall survival did not differ significantly between Groups 1 and 2. Rates of radiation pneumonitis, chest wall toxicity, and esophagitis were low in both groups, but all Grade 3 toxicities developed in Group 2 (p = 0.02). Conclusion: A volume-adapted dosing approach for SABR of lung tumors seems to provide excellent local control for both small- and large-volume tumors and may reduce toxicity.

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

    NASA Astrophysics Data System (ADS)

    Dutta, Vimala

    1993-07-01

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

  14. 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.

  15. Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids

    SciTech Connect

    Ragusa, Jean C.

    2015-01-01

    In this paper, we propose a piece-wise linear discontinuous (PWLD) finite element discretization of the diffusion equation for arbitrary polygonal meshes. It is based on the standard diffusion form and uses the symmetric interior penalty technique, which yields a symmetric positive definite linear system matrix. A preconditioned conjugate gradient algorithm is employed to solve the linear system. Piece-wise linear approximations also allow a straightforward implementation of local mesh adaptation by allowing unrefined cells to be interpreted as polygons with an increased number of vertices. Several test cases, taken from the literature on the discretization of the radiation diffusion equation, are presented: random, sinusoidal, Shestakov, and Z meshes are used. The last numerical example demonstrates the application of the PWLD discretization to adaptive mesh refinement.

  16. 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.)

  17. 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.

  18. A preconditioned fast finite volume scheme for a fractional differential equation discretized on a locally refined composite mesh

    NASA Astrophysics Data System (ADS)

    Jia, Jinhong; Wang, Hong

    2015-10-01

    Numerical methods for fractional differential equations generate full stiffness matrices, which were traditionally solved via Gaussian type direct solvers that require O (N3) of computational work and O (N2) of memory to store where N is the number of spatial grid points in the discretization. We develop a preconditioned fast Krylov subspace iterative method for the efficient and faithful solution of finite volume schemes defined on a locally refined composite mesh for fractional differential equations to resolve boundary layers of the solutions. Numerical results are presented to show the utility of the method.

  19. Finite-volume scheme for transonic potential flow about airfoils and bodies in an arbitrarily-shaped channel

    NASA Technical Reports Server (NTRS)

    South, J. C., Jr.; Green, L. L.; Doria, M. L.

    1985-01-01

    A conservative finite-volume difference scheme is developed for the potential equation to solve transonic flow about airfoils and bodies in an arbitrary channel. The scheme employs a mesh which is a nearly-conformal 'O' mesh about the airfoil and nearly orthogonal at the channel walls. The mesh extends to infinity upstream and downstream, where the mapping is singular. Special procedures are required to treat the singularities at infinity, including computation of the metrics near those points. Channels with exit areas different from inlet areas are solved; a body with a sting mount is an example of such a case.

  20. Finite-volume scheme for transonic potential flow about airfoils and bodies in an arbitrarily shaped channel

    NASA Technical Reports Server (NTRS)

    South, Jerry C., Jr.; Doria, Michael L.; Green, Lawrence L.

    1986-01-01

    A conservative finite-volume difference scheme is developed for the potential equation to solve transonic flow about airfoils and bodies in an arbitrarily shaped channel. The scheme employs a mesh which is a nearly conformal O mesh about the airfoil and nearly orthogonal at the channel walls. The mesh extends to infinity upstream and downstream, where the mapping is singular. Special procedures are required to treat the singularities at infinity, including computation of the metrics near those points. Channels with exit areas different from inlet areas are solved; a body with a sting mount is an example of such a case.

  1. Incorporation of modified dynamic inverse Jiles-Atherton model in finite volume time domain for nonlinear electromagnetic field computation

    NASA Astrophysics Data System (ADS)

    Hamimid, M.; Mimoune, S. M.; Feliachi, M.

    2013-01-01

    In this paper, a time stepping finite volume method (FVM) associated with the modified inverse Jiles-Atherton model for the nonlinear electromagnetic field computation is presented. To describe the dynamic behavior in the conducting media, the effective field is modified by adding two counter-fields associated respectively to the eddy current and excess losses. The hysteresis loss can be estimated by the integration over the obtained hysteresis loop at each frequency. To examine the validity of the proposed dynamic model coupled with FVM, the computed total losses and hysteresis loops are compared to experiments.

  2. Rapid Adaptive Optical Recovery of Optimal Resolution over LargeVolumes

    PubMed Central

    Wang, Kai; Milkie, Dan; Saxena, Ankur; Engerer, Peter; Misgeld, Thomas; Bronner, Marianne E.; Mumm, Jeff; Betzig, Eric

    2014-01-01

    Using a de-scanned, laser-induced guide star and direct wavefront sensing, we demonstrate adaptive correction of complex optical aberrations at high numerical aperture and a 14 ms update rate. This permits us to compensate for the rapid spatial variation in aberration often encountered in biological specimens, and recover diffraction-limited imaging over large (> 240 μm)3 volumes. We applied this to image fine neuronal processes and subcellular dynamics within the zebrafish brain. PMID:24727653

  3. Updating a finite element model to the real experimental setup by thermographic measurements and adaptive regression optimization

    NASA Astrophysics Data System (ADS)

    Peeters, J.; Arroud, G.; Ribbens, B.; Dirckx, J. J. J.; Steenackers, G.

    2015-12-01

    In non-destructive evaluation the use of finite element models to evaluate structural behavior and experimental setup optimization can complement with the inspector's experience. A new adaptive response surface methodology, especially adapted for thermal problems, is used to update the experimental setup parameters in a finite element model to the state of the test sample measured by pulsed thermography. Poly Vinyl Chloride (PVC) test samples are used to examine the results for thermal insulator models. A comparison of the achieved results is made by changing the target values from experimental pulsed thermography data to a fixed validation model. Several optimizers are compared and discussed with the focus on speed and accuracy. A time efficiency increase of over 20 and an accuracy of over 99.5% are achieved by the choice of the correct parameter sets and optimizer. Proper parameter set selection criteria are defined and the influence of the choice of the optimization algorithm and parameter set on the accuracy and convergence time are investigated.

  4. Relationship between sample volumes and modulus of human vertebral trabecular bone in micro-finite element analysis.

    PubMed

    Wen, Xin-Xin; Xu, Chao; Zong, Chun-Lin; Feng, Ya-Fei; Ma, Xiang-Yu; Wang, Fa-Qi; Yan, Ya-Bo; Lei, Wei

    2016-07-01

    Micro-finite element (μFE) models have been widely used to assess the biomechanical properties of trabecular bone. How to choose a proper sample volume of trabecular bone, which could predict the real bone biomechanical properties and reduce the calculation time, was an interesting problem. Therefore, the purpose of this study was to investigate the relationship between different sample volumes and apparent elastic modulus (E) calculated from μFE model. 5 Human lumbar vertebral bodies (L1-L5) were scanned by micro-CT. Cubic concentric samples of different lengths were constructed as the experimental groups and the largest possible volumes of interest (VOI) were constructed as the control group. A direct voxel-to-element approach was used to generate μFE models and steel layers were added to the superior and inferior surface to mimic axial compression tests. A 1% axial strain was prescribed to the top surface of the model to obtain the E values. ANOVA tests were performed to compare the E values from the different VOIs against that of the control group. Nonlinear function curve fitting was performed to study the relationship between volumes and E values. The larger cubic VOI included more nodes and elements, and more CPU times were needed for calculations. E values showed a descending tendency as the length of cubic VOI decreased. When the volume of VOI was smaller than (7.34mm(3)), E values were significantly different from the control group. The fit function showed that E values approached an asymptotic values with increasing length of VOI. Our study demonstrated that apparent elastic modulus calculated from μFE models were affected by the sample volumes. There was a descending tendency of E values as the length of cubic VOI decreased. Sample volume which was not smaller than (7.34mm(3)) was efficient enough and timesaving for the calculation of E. PMID:26999702

  5. 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.

  6. A p-adaptive stabilized finite element method for fluid dynamics

    NASA Astrophysics Data System (ADS)

    Karanam, Anil Kumar

    2008-10-01

    Stabilized finite element methods have been shown to yield robust, accurate numerical solutions to both the compressible and incompressible Navier-Stokes equations for laminar and turbulent flows. This work presents an application of mesh entity based, hierarchical basis functions to a new stabilized finite element formulation, exploiting the capability to grade polynomial order while maintaining C0 continuity while using traditional finite element data structures. The hierarchical basis accomplishes this by starting with vertex interpolants (a linear basis) and then allowing the polynomial order to vary on each entity (edges, faces, and regions) in the mesh which are then multiplied by blends within each element to build a composite function that is locally higher order but still globally continuous. Details of this formulation and its efficient implementation will be presented. Partition weighting schemes were developed to achieve optimal load balance and scalability for parallel simulations. An application is presented, of p-refinement applied to a laminar flow past a surface mounted unit cube placed in a channel. Finally, post-processing techniques are also described for the effective visualization of higher order solutions.

  7. PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual

    NASA Technical Reports Server (NTRS)

    Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.

    1977-01-01

    The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.

  8. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2006-09-01

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

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

    DOE PAGESBeta

    Hansen, Maxwell; Briceno, Raul

    2015-10-01

    We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volumemore » $$\\textbf{0}\\rightarrow\\textbf{2}$$ and $$\\textbf{1}\\rightarrow\\textbf{2}$$ transition amplitudes. Our result accommodates theories in which the final two-particle state is coupled to any number of other two-body channels, with all angular momentum states included. The derivation uses generic, fully relativistic field theory, and is exact up to exponentially suppressed corrections in the lightest particle mass times the box size. This work distinguishes itself from previous studies by accommodating particles with any intrinsic spin. To illustrate the utility of our general result, we discuss how it can be implemented for studies of $$N+\\mathcal{J}~\\rightarrow~(N\\pi,N\\eta,N\\eta',\\Sigma K,\\Lambda K)$$ transitions, where $$\\mathcal{J}$$ is a generic external current. The reduction of rotational symmetry, due to the cubic finite volume, manifests in this example through the mixing of S- and P-waves when the system has nonzero total momentum.« less

  11. Generalization of the CCLADS method for modeling anisotropic diffusion tensors on three-dimensional finite-volume grids

    NASA Astrophysics Data System (ADS)

    Provost, A.; Langevin, C.

    2012-12-01

    A number of numerical methods exist for incorporating anisotropic diffusion tensors, such as hydraulic or thermal conductivity, into two- and three-dimensional numerical models. The methods vary in mathematical approach, complexity, performance, and applicability to different types of model grids. The CCLADS variant of the CCLAD (Cell-Centered LAgrangian Diffusion) method of Maire & Breil (2011) is applicable to two-dimensional, unstructured, cell-centered finite-volume grids. It has a local stencil and exhibits nearly second-order accuracy on smooth distorted grids. As originally derived, CCLADS is not directly generalizable to three dimensions, and the derivation breaks down when adjacent cell edges meet at 180 degrees. Here, we rederive CCLADS to overcome these limitations and investigate the performance of the generalized method in a suite of three-dimensional test problems on structured, rectangular grids. As in two dimensions, the generalized method should be applicable to unstructured grids. Maire, P.-H., and Breil J., 2012, A nominally second-order accurate finite volume cell-centered scheme for anisotropic diffusion on two-dimensional unstructured grids, J. Comput. Phys., 231 (5), 2259-2299.

  12. 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.

  13. Adaptation of a program for nonlinear finite element analysis to the CDC STAR 100 computer

    NASA Technical Reports Server (NTRS)

    Pifko, A. B.; Ogilvie, P. L.

    1978-01-01

    The conversion of a nonlinear finite element program to the CDC STAR 100 pipeline computer is discussed. The program called DYCAST was developed for the crash simulation of structures. Initial results with the STAR 100 computer indicated that significant gains in computation time are possible for operations on gloval arrays. However, for element level computations that do not lend themselves easily to long vector processing, the STAR 100 was slower than comparable scalar computers. On this basis it is concluded that in order for pipeline computers to impact the economic feasibility of large nonlinear analyses it is absolutely essential that algorithms be devised to improve the efficiency of element level computations.

  14. An adaptive-mesh finite-difference solution method for the Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Luchini, Paolo

    1987-02-01

    An adjustable variable-spacing grid is presented which permits the addition or deletion of single points during iterative solutions of the Navier-Stokes equations by finite difference methods. The grid is designed for application to two-dimensional steady-flow problems which can be described by partial differential equations whose second derivatives are constrained to the Laplacian operator. An explicit Navier-Stokes equations solution technique defined for use with the grid incorporates a hybrid form of the convective terms. Three methods are developed for automatic modifications of the mesh during calculations.

  15. Muscular adaptations after two different volumes of blood flow-restricted training.

    PubMed

    Martín-Hernández, J; Marín, P J; Menéndez, H; Ferrero, C; Loenneke, J P; Herrero, A J

    2013-03-01

    This study aimed to gain an insight into the adaptations of muscle strength and skeletal muscle thickness after two different volumes of blood flow restriction training (BFRT), and compare them with high-intensity training. The sample was divided into four groups: low-volume, low-intensity BFRT (BFRT LV); high-volume, low-intensity BFRT (BFRT HV); traditional high-intensity resistance training (HIT); and a control group, which maintained their routine activities (CON). Leg extension one repetition maximum (1RM), isokinetic peak knee extension, and flexion torques at 60°/s and 180°/s as well as muscle thickness of the rectus femoris (RF) and vastus lateralis (VL) were assessed at baseline and after 5 weeks of training BFRT LV (7.03%, P < 0.05), BFRT HV (6.24%, P < 0.05) and HIT (18.86%, P < 0.001) groups increased 1RM performance, while no changes were observed in the CON group. Muscle thickness of the RF and VL was increased irrespective of the training group (7.5%, P < 0.001; and 9.9%, P < 0.001, respectively). We conclude that doubling the exercise volume with BFRT causes no further benefit with muscular size or strength. Although similar increases in muscle thickness were observed between training groups, HIT increased 1RM performance to a greater extent compared to either volume of BFRT. PMID:23278841

  16. IMRT planning on adaptive volume structures--a decisive reduction in computational complexity.

    PubMed

    Scherrer, Alexander; Küfer, Karl-Heinz; Bortfeld, Thomas; Monz, Michael; Alonso, Fernando

    2005-05-01

    The objective of radiotherapy planning is to find a compromise between the contradictive goals of delivering a sufficiently high dose to the target volume while widely sparing critical structures. The search for such a compromise requires the computation of several plans, which mathematically means solving several optimization problems. In the case of intensity modulated radiotherapy (IMRT) these problems are large-scale, hence the accumulated computational expense is very high. The adaptive clustering method presented in this paper overcomes this difficulty. The main idea is to use a preprocessed hierarchy of aggregated dose-volume information as a basis for individually adapted approximations of the original optimization problems. This leads to a decisively reduced computational expense: numerical experiments on several sets of real clinical data typically show computation times decreased by a factor of about 10. In contrast to earlier work in this field, this reduction in computational complexity will not lead to a loss in accuracy: the adaptive clustering method produces the optimum of the original optimization problem. PMID:15843735

  17. Three-dimensional region-based adaptive image processing techniques for volume visualization applications

    NASA Astrophysics Data System (ADS)

    de Deus Lopes, Roseli; Zuffo, Marcelo K.; Rangayyan, Rangaraj M.

    1996-04-01

    Recent advances in three-dimensional (3D) imaging techniques have expanded the scope of applications of volume visualization to many areas such as medical imaging, scientific visualization, robotic vision, and virtual reality. Advanced image filtering, enhancement, and analysis techniques are being developed in parallel in the field of digital image processing. Although the fields cited have many aspects in common, it appears that many of the latest developments in image processing are not being applied to the fullest extent possible in visualization. It is common to encounter the use of rather simple and elementary image pre- processing operations being used in visualization and 3D imaging applications. The purpose of this paper is to present an overview of selected topics from recent developments in adaptive image processing and demonstrate or suggest their applications in volume visualization. The techniques include adaptive noise removal; improvement of contrast and visibility of objects; space-variant deblurring and restoration; segmentation-based lossless coding for data compression; and perception-based measures for analysis, enhancement, and rendering. The techniques share the common base of identification of adaptive regions by region growing, which lends them a perceptual basis related to the human visual system. Preliminary results obtained with some of the techniques implemented so far are used to illustrate the concepts involved, and to indicate potential performance capabilities of the methods.

  18. An a-posteriori finite element error estimator for adaptive grid computation of viscous incompressible flows

    NASA Astrophysics Data System (ADS)

    Wu, Heng

    2000-10-01

    In this thesis, an a-posteriori error estimator is presented and employed for solving viscous incompressible flow problems. In an effort to detect local flow features, such as vortices and separation, and to resolve flow details precisely, a velocity angle error estimator e theta which is based on the spatial derivative of velocity direction fields is designed and constructed. The a-posteriori error estimator corresponds to the antisymmetric part of the deformation-rate-tensor, and it is sensitive to the second derivative of the velocity angle field. Rationality discussions reveal that the velocity angle error estimator is a curvature error estimator, and its value reflects the accuracy of streamline curves. It is also found that the velocity angle error estimator contains the nonlinear convective term of the Navier-Stokes equations, and it identifies and computes the direction difference when the convective acceleration direction and the flow velocity direction have a disparity. Through benchmarking computed variables with the analytic solution of Kovasznay flow or the finest grid of cavity flow, it is demonstrated that the velocity angle error estimator has a better performance than the strain error estimator. The benchmarking work also shows that the computed profile obtained by using etheta can achieve the best matching outcome with the true theta field, and that it is asymptotic to the true theta variation field, with a promise of fewer unknowns. Unstructured grids are adapted by employing local cell division as well as unrefinement of transition cells. Using element class and node class can efficiently construct a hierarchical data structure which provides cell and node inter-reference at each adaptive level. Employing element pointers and node pointers can dynamically maintain the connection of adjacent elements and adjacent nodes, and thus avoids time-consuming search processes. The adaptive scheme is applied to viscous incompressible flow at different

  19. 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.

  20. Finite volume method for radiative heat transfer in an unstructured flow solver for emitting, absorbing and scattering media

    NASA Astrophysics Data System (ADS)

    Gazdallah, Moncef; Feldheim, Véronique; Claramunt, Kilian; Hirsch, Charles

    2012-06-01

    This paper presents the implementation of the finite volume method to solve the radiative transfer equation in a commercial code. The particularity of this work is that the method applied on unstructured hexahedral meshes does not need a pre-processing step establishing a particular marching order to visit all the control volumes. The solver simply visits the faces of the control volumes as numbered in the hexahedral unstructured mesh. A cell centred mesh and a spatial differencing step scheme to relate facial radiative intensities to nodal intensities is used. The developed computer code based on FVM has been integrated in the CFD solver FINE™/Open from NUMECA Int. Radiative heat transfer can be evaluated within systems containing uniform, grey, emitting, absorbing and/or isotropically or linear anisotropically scattering medium bounded by diffuse grey walls. This code has been validated for three test cases. The first one is a three dimensional rectangular enclosure filled with emitting, absorbing and anisotropically scattering media. The second is the differentially heated cubic cavity. The third one is the L-shaped enclosure. For these three test cases a good agreement has been observed when temperature and heat fluxes predictions are compared with references taken, from literature.

  1. Digging adaptation in insectivorous subterranean eutherians. The enigma of Mesoscalops montanensis unveiled by geometric morphometrics and finite element analysis.

    PubMed

    Piras, Paolo; Sansalone, Gabriele; Teresi, Luciano; Moscato, Marco; Profico, Antonio; Eng, Ronald; Cox, Timothy C; Loy, Anna; Colangelo, Paolo; Kotsakis, Tassos

    2015-10-01

    The enigmatic Early Miocene fossorial mammal Mesoscalops montanensis shows one of the most modified humeri among terrestrial mammals. It has been suggested, on qualitative considerations, that this species has no extant homologues for humerus kinematics and that, functionally, the closest extant group is represented by Chrysochloridae. We combine here three dimensional geometric morphometrics, finite element analysis and phylogenetic comparative methods to explore the shape and mechanical stress states of Mesoscalops montanensis as well as of extant and extinct Talpidae and Chrysochloridae under realistic digging simulations. Evolutionary convergence analyses reveal that the shape of Mesoscalops montanensis represents a unique morphology in the context of fossorial mammals and that its functional performance, albeit superficially similar to that of extant Chrysochloridae, still represents a nonconvergent optimum for adaptation to digging. PMID:26134243

  2. Continuum Diffusion Reaction Rate Calculations of Wild-Type and Mutant Mouse Acetylcholinesterase: Adaptive Finite Element Analysis

    PubMed Central

    Song, Yuhua; Zhang, Yongjie; Bajaj, Chandrajit L.; Baker, Nathan A.

    2004-01-01

    As described previously, continuum models, such as the Smoluchowski equation, offer a scalable framework for studying diffusion in biomolecular systems. This work presents new developments in the efficient solution of the continuum diffusion equation. Specifically, we present methods for adaptively refining finite element solutions of the Smoluchowski equation based on a posteriori error estimates. We also describe new, molecular-surface-based models, for diffusional reaction boundary criteria and compare results obtained from these models with the traditional spherical criteria. The new methods are validated by comparison of the calculated reaction rates with experimental values for wild-type and mutant forms of mouse acetylcholinesterase. The results show good agreement with experiment and help to define optimal reactive boundary conditions. PMID:15345536

  3. Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound.

    PubMed

    Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai

    2011-01-01

    In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method. PMID:20876014

  4. Crystal plasticity finite element analysis for René88DT statistical volume element generation

    NASA Astrophysics Data System (ADS)

    Tucker, Joseph C.; Cerrone, Albert R., III; Ingraffea, Anthony R.; Rollett, Anthony D.

    2015-04-01

    This work focuses on the major cause of life limiting behavior in Ni-based superalloys for high pressure and temperature turbine disks applications in low cycle fatigue. Specific ideas of local microstructure features, such as the role of as large as (ALA) grains, in promoting slip localization in directly measured 3D microstructures were tested with finite element method (FEM) simulations with crystal plasticity. Synthetic microstructures with experimentally determined microstructurally small fatigue crack weakest link features of ALA grains comprise the test cases. A René88 damage tolerant (R88DT) dataset, from electron backscatter diffraction, was used to instantiate approximately 1.5 million elements and 200 grains from FEM sensitivity studies. Changing mesh resolution minimally impacted global damage response, but local convergence required the maximum resolution. The present results help to quantify the deleterious impact of ALA grains in Ni-based superalloys to extend service life.

  5. Two-dimensional geomagnetic forward modeling using adaptive finite element method and investigation of the topographic effect

    NASA Astrophysics Data System (ADS)

    Jeshvaghani, Mehdi Shahmirzae; Darijani, Mehrdad

    2014-06-01

    Forward modeling approach is a major concept in geophysical exploration and also a key factor in the development of inversion algorithms. Finite element method for two-dimensional (2-D) geomagnetic forward modeling is based on numerical solution of the Laplace equation. In this paper we present a fast and accurate adaptive finite element algorithm for forward modeling of 2-D geomagnetic structures. Our method is stable and is reliable to recover 2-D magnetization distribution with complex shapes. It uses an unstructured triangular grid which allows modeling the complex geometry with the presence of topography. The Galerkin's method is used to derive the systems of equations. Then, the conjugate gradient solver with incomplete LU decomposition as the pre-conditioner is used to solve the system of equations. To ensure numerical accuracy, iterative mesh refinement is guided by a posteriori error estimator. We validate our algorithm in simple geometry by analytical technique. The tests on synthetic data illustrate a good performance of the method in mapping the complex geometry of the magnetic sources with topography. The magnetic responses of the model have proved to be different in the presence of topography. Therefore, it is highly recommended to consider the effects of topography on interpretation. Finally, we applied numerical FEM algorithm to real data set providing fine recovery model of the shallow high mineralized crustal setting of Soltanieh region, Iran.

  6. A simple adaptive mesh generator for 2-D finite element calculations

    SciTech Connect

    Fernandez, F.A.; Yong, Y.C.; Ettinger, R.D. )

    1993-03-01

    A strategy for adaptive mesh generation is proposed. The method consists of the use of a suitably defined density function', which can either be defined by the user or be calculated from a previous approximate solution, to guide the generation of a new mesh. This new mesh is built starting from a minimal number of triangular elements which are then in several sweeps, repeatedly refined according to the density function. The Delaunay algorithm is used in each stage to keep the shape of the triangles as equilateral as possible.

  7. Multiphase flow modelling using non orthogonal collocated finite volumes : application to fluid catalytical cracking and large scale geophysical flows.

    NASA Astrophysics Data System (ADS)

    Martin, R. M.; Nicolas, A. N.

    2003-04-01

    A modeling approach of gas solid flow, taking into account different physical phenomena such as gas turbulence and inter-particle interactions is presented. Moment transport equations are derived for the second order fluctuating velocity tensor which allow to involve practical closures based on single phase turbulence modeling on one hand and kinetic theory of granular media on the other hand. The model is applied to fluid catalytic cracking processes and explosive volcanism. In the industry as well as in the geophysical community, multiphase flows are modeled using a finite volume approach and a multicorrector algorithm in time in order to determine implicitly the pressures, velocities and volume fractions for each phase. Pressures, and velocities are generally determined at mid-half mesh step from each other following the staggered grid approach. This ensures stability and prevents oscillations in pressure. It allows to treat almost all the Reynolds number ranges for all speeds and viscosities. The disadvantages appear when we want to treat more complex geometries or if a generalized curvilinear formulation of the conservation equations is considered. Too many interpolations have to be done and accuracy is then lost. In order to overcome these problems, we use here a similar algorithm in time and a Rhie and Chow interpolation (1983) of the collocated variables and essentially the velocities at the interface. The Rhie and Chow interpolation of the velocities at the finite volume interfaces allows to have no oscillations of the pressure without checkerboard effects and to stabilize all the algorithm. In a first predictor step, fluxes at the interfaces of the finite volumes are then computed using 2nd and 3rd order shock capturing schemes of MUSCL/TVD or Van Leer type, and the orthogonal stress components are treated implicitly while cross viscous/diffusion terms are treated explicitly. Pentadiagonal linear systems are solved in each geometrical direction (the so

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. A finite volume method and experimental study of a stator of a piezoelectric traveling wave rotary ultrasonic motor.

    PubMed

    Bolborici, V; Dawson, F P; Pugh, M C

    2014-03-01

    Piezoelectric traveling wave rotary ultrasonic motors are motors that generate torque by using the friction force between a piezoelectric composite ring (or disk-shaped stator) and a metallic ring (or disk-shaped rotor) when a traveling wave is excited in the stator. The motor speed is proportional to the amplitude of the traveling wave and, in order to obtain large amplitudes, the stator is excited at frequencies close to its resonance frequency. This paper presents a non-empirical partial differential equations model for the stator, which is discretized using the finite volume method. The fundamental frequency of the discretized model is computed and compared to the experimentally-measured operating frequency of the stator of Shinsei USR60 piezoelectric motor. PMID:24210273

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Women with Anorexia Nervosa: Finite Element and Trabecular Structure Analysis by Using Flat-Panel Volume CT

    PubMed Central

    Phan, Catherine M.; Misra, Madhusmita; Bredella, Miriam A.; Miller, Karen K.; Fazeli, Pouneh K.; Bayraktar, Harun H.; Klibanski, Anne; Gupta, Rajiv

    2010-01-01

    Purpose: To use finite element modeling based on flat-panel volume computed tomography (CT) and bone mineral density (BMD) provided by dual-energy x-ray absorptiometry (DXA) to compare bone failure load, stiffness, and trabecular structure in women with anorexia nervosa (AN) and age-matched normal-weight control subjects. Materials and Methods: The study was approved by the institutional review board and complied with HIPAA guidelines. Informed consent was obtained. Fourteen women, eight with AN (mean age, 26.6 years) and six control subjects (mean age, 26.3 years), underwent flat-panel volume CT of the distal radius to determine apparent trabecular bone volume fraction (BV/TV), apparent trabecular number (TbN), apparent trabecular thickness (TbTh), and apparent trabecular separation (TbSp). Bone strength and stiffness were calculated from uniaxial compression tests by using finite element models created from flat-panel volume CT. DXA was used to determine BMD of the radius, lumbar spine, and hip. Means ± standard deviations of all variables were calculated for both groups and compared (Student t test). Univariate regression analysis and stepwise regression modeling were performed. Results: Patients with AN had lower values for stiffness (284.77 kN/mm ± 76.14 vs 389.97 kN/mm ± 84.90, P = .04), failure load (4.98 kN ± 1.23 vs 7.01 kN ± 1.52, P = .02), BV/TV (0.32% ± 0.09 vs 0.44% ± 0.02, P = .007), and TbN (1.15 mm−3 ± 0.20 vs 1.43 mm−3 ± 0.13, P = .008) and higher values for TbSp (0.62 mm ± 0.20 vs 0.40 mm ± 0.04, P = .02) compared with normal-weight control subjects. TbTh was lower in women with AN (P = .1). BMD measurements were significantly lower for the AN group. BMD measurements and trabecular parameters (except TbTh) correlated with stiffness and failure load (r = 0.58 to 0.83). Conclusion: Failure load and stiffness are abnormal in women with AN compared with those in normal-weight control subjects and correlate with BMD and trabecular

  19. 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.

  20. The role of computational fluid dynamics in aeronautical engineering (5). Improvements and applications of implicit TVD finite volume code

    NASA Astrophysics Data System (ADS)

    Shima, Eiji; Yoshida, Kenji; Amano, Kanichi

    1987-11-01

    An automatic grid generator for multiple element airfoils was developed and the existing implicit Total Variation Diminishing (TVD) finite volume code was improved in both accuracy and efficiency, in order to make the Navier-Stokes solver a practical design tool for high lift devices. Utilizing these codes, Navier-Stokes analysis of the single slotted flap was carried out. The automatic grid generator utilizes the elliptic equation solver using the finite difference method combined with the panel method. The flow field is divided into subregions by the dividing stream lines which are calculated by the panel method and the computational grid in each subregion is generated by solving the elliptic equations (Thompson's method). Since the panel method can solve the potential flow around any number of arbitrary shaped bodies, this grid generator can generate a H-type computational grid around such bodies automatically. To obtain a high accuracy on a rapidly stretching grid, the flow solver uses the TVD formulation containing an explicit treatment of nonuniform grid spacing. Converging rate and numerical stability of the flow solver is augmented by the relaxation approach using Symmetric Point Gauss Seidel method in matrix inversion process which is necessary for an implicit scheme.

  1. A new high-resolution unstructured grid finite volume Arctic Ocean model (AO-FVCOM): An application for tidal studies

    NASA Astrophysics Data System (ADS)

    Chen, Changsheng; Gao, Guoping; Qi, Jianhua; Proshutinsky, Andrey; Beardsley, Robert C.; Kowalik, Zygmunt; Lin, Huichan; Cowles, Geoffrey

    2009-08-01

    A spherical coordinate version of the unstructured grid 3-D FVCOM (finite volume coastal ocean model) has been applied to the Arctic Ocean to simulate tides with a horizontal resolution ranging from 1 km in the near-coastal areas to 15 km in the deep ocean. By accurately resolving the irregular coastlines and bathymetry in the Arctic Ocean coastal regions, this model reproduces the diurnal (K1 and O1) and semidiurnal (M2 and S2) tidal wave dynamics and captures the complex tidal structure along the coast, particularly in the narrow straits of the Canadian Archipelago. The simulated tidal parameters (harmonic constituents of sea surface elevation and currents) agree well with the available observational data. High-resolution meshes over the continental shelf and slope capture the detailed spatial structure of topographic trapped shelf waves, which are quite energetic along the Greenland, Siberia, and Spitsbergen continental slope and shelf break areas. Water stratification influences the vertical distribution of tidal currents but not the water transport and thus tidal elevation. The comparison with previous finite difference models suggests that horizontal resolution and geometric fitting are two prerequisites to simulate realistically the tidal energy flux in the Arctic Ocean, particularly in the Canadian Archipelago.

  2. Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction

    NASA Astrophysics Data System (ADS)

    Kidanemariam, Aman G.; Chan-Braun, Clemens; Doychev, Todor; Uhlmann, Markus

    2013-02-01

    We have performed direct numerical simulation of turbulent open channel flow over a smooth horizontal wall in the presence of finite-size, heavy particles. The spherical particles have a diameter of approximately 7 wall units, a density of 1.7 times the fluid density and a solid volume fraction of 5 × 10-4. The value of the Galileo number is set to 16.5, while the Shields parameter measures approximately 0.2. Under these conditions, the particles are predominantly located in the vicinity of the bottom wall, where they exhibit strong preferential concentration which we quantify by means of Voronoi analysis and by computing the particle-conditioned concentration field. As observed in previous studies with similar parameter values, the mean streamwise particle velocity is smaller than that of the fluid. We propose a new definition of the fluid velocity ‘seen’ by finite-size particles based on an average over a spherical surface segment, from which we deduce in the present case that the particles are instantaneously lagging the fluid only by a small amount. The particle-conditioned fluid velocity field shows that the particles preferentially reside in the low-speed streaks, leading to the observed apparent lag. Finally, a vortex eduction study reveals that spanwise particle motion is significantly correlated with the presence of vortices with the corresponding sense of rotation which are located in the immediate vicinity of the near-wall particles.

  3. 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

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

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

  5. 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.

  6. Improving peri-prosthetic bone adaptation around cementless hip stems: a clinical and finite element study.

    PubMed

    ten Broeke, René H M; Tarala, Maria; Arts, Jacobus J; Janssen, Dennis W; Verdonschot, Nico; Geesink, Rudolph G T

    2014-03-01

    This study assessed whether the Symax™ implant, a modification of the Omnifit(®) stem (in terms of shape, proximal coating and distal surface treatment), would yield improved bone remodelling in a clinical DEXA study, and if these results could be predicted in a finite element (FE) simulation study. In a randomized clinical trial, 2 year DEXA measurements between the uncemented Symax™ and Omnifit(®) stem (both n=25) showed bone mineral density (BMD) loss in Gruen zone 7 of 14% and 20%, respectively (p<0.05). In contrast, the FE models predicted a 28% (Symax™) and 26% (Omnifit(®)) bone loss. When the distal treatment to the Symax™ was not modelled in the simulation, bone loss of 35% was predicted, suggesting the benefit of this surface treatment for proximal bone maintenance. The theoretical concept for enhanced proximal bone loading by the Symax™, and the predicted remodelling pattern were confirmed by DEXA-results, but there was no quantitative match between clinical and FE findings. This was due to a simulation based on incomplete assumptions concerning the yet unknown biological and mechanical effects of the new coating and surface treatment. Study listed under ClinicalTrials.gov with number NCT01695213. PMID:24378381

  7. Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation

    NASA Astrophysics Data System (ADS)

    Wang, Cheng; Dong, XinZhuang; Shu, Chi-Wang

    2015-10-01

    For numerical simulation of detonation, computational cost using uniform meshes is large due to the vast separation in both time and space scales. Adaptive mesh refinement (AMR) is advantageous for problems with vastly different scales. This paper aims to propose an AMR method with high order accuracy for numerical investigation of multi-dimensional detonation. A well-designed AMR method based on finite difference weighted essentially non-oscillatory (WENO) scheme, named as AMR&WENO is proposed. A new cell-based data structure is used to organize the adaptive meshes. The new data structure makes it possible for cells to communicate with each other quickly and easily. In order to develop an AMR method with high order accuracy, high order prolongations in both space and time are utilized in the data prolongation procedure. Based on the message passing interface (MPI) platform, we have developed a workload balancing parallel AMR&WENO code using the Hilbert space-filling curve algorithm. Our numerical experiments with detonation simulations indicate that the AMR&WENO is accurate and has a high resolution. Moreover, we evaluate and compare the performance of the uniform mesh WENO scheme and the parallel AMR&WENO method. The comparison results provide us further insight into the high performance of the parallel AMR&WENO method.

  8. Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients

    SciTech Connect

    Kalchev, D

    2012-04-02

    This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-{rho}AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the

  9. 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.

  10. 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.

  11. Accurate, finite-volume methods for three dimensional magneto-hydrodynamics on Lagrangian meshes

    SciTech Connect

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

    1999-07-01

    Recently developed algorithms for ideal and resistive, 3D MHD calculations on Lagrangian hexahedral meshes have been generalized to work with a lagrangian mesh composed of arbitrary polyhedral cells. this allows for mesh refinement during a calculation to prevent the well known problem of tangling in a Lagrangian mesh. Arbitrary polyhedral cells are decomposed into tetrahedrons. The action of the magnetic vector potential, A {sm_bullet} {delta}1, is centered on all faces edges of this extended mesh. Thus, {triangledown} {sm_bullet} B = 0 is maintained to round-off error. For ideal flow, (E = v x B), vertex forces are derived by the variation of magnetic energy with respect to vertex positions, F = {minus}{partial_derivative}W{sub B}/{partial_derivative}r. This assures symmetry as well as magnetic flux, momentum, and energy conservation. The method is local so that parallelization by domain decomposition is natural for large meshes. In addition, a simple, ideal-gas, finite pressure term has been included. The resistive diffusion, (E = {minus}{eta}J), is treated with a support operator method, to obtain an energy conservative, symmetric method on an arbitrary polyhedral mesh. The equation of motion is time-step-split. First, the ideal term is treated explicitly. Next, the diffusion is solved implicitly with a preconditioned conjugate gradient method. Results of convergence tests are presented. Initial results of an annular Z-pinch implosion problem illustrate the application of these methods to multi-material problems.

  12. Small Sample Properties of an Adaptive Filter with Application to Low Volume Statistical Process Control

    SciTech Connect

    CROWDER, STEPHEN V.

    1999-09-01

    In many manufacturing environments such as the nuclear weapons complex, emphasis has shifted from the regular production and delivery of large orders to infrequent small orders. However, the challenge to maintain the same high quality and reliability standards while building much smaller lot sizes remains. To meet this challenge, specific areas need more attention, including fast and on-target process start-up, low volume statistical process control, process characterization with small experiments, and estimating reliability given few actual performance tests of the product. In this paper we address the issue of low volume statistical process control. We investigate an adaptive filtering approach to process monitoring with a relatively short time series of autocorrelated data. The emphasis is on estimation and minimization of mean squared error rather than the traditional hypothesis testing and run length analyses associated with process control charting. We develop an adaptive filtering technique that assumes initial process parameters are unknown, and updates the parameters as more data become available. Using simulation techniques, we study the data requirements (the length of a time series of autocorrelated data) necessary to adequately estimate process parameters. We show that far fewer data values are needed than is typically recommended for process control applications. We also demonstrate the techniques with a case study from the nuclear weapons manufacturing complex.

  13. Small sample properties of an adaptive filter with application to low volume statistical process control

    SciTech Connect

    Crowder, S.V.; Eshleman, L.

    1998-08-01

    In many manufacturing environments such as the nuclear weapons complex, emphasis has shifted from the regular production and delivery of large orders to infrequent small orders. However, the challenge to maintain the same high quality and reliability standards white building much smaller lot sizes remains. To meet this challenge, specific areas need more attention, including fast and on-target process start-up, low volume statistical process control, process characterization with small experiments, and estimating reliability given few actual performance tests of the product. In this paper the authors address the issue of low volume statistical process control. They investigate an adaptive filtering approach to process monitoring with a relatively short time series of autocorrelated data. The emphasis is on estimation and minimization of mean squared error rather than the traditional hypothesis testing and run length analyses associated with process control charting. The authors develop an adaptive filtering technique that assumes initial process parameters are unknown, and updates the parameters as more data become available. Using simulation techniques, they study the data requirements (the length of a time series of autocorrelated data) necessary to adequately estimate process parameters. They show that far fewer data values are needed than is typically recommended for process control applications. And they demonstrate the techniques with a case study from the nuclear weapons manufacturing complex.

  14. Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study

    NASA Astrophysics Data System (ADS)

    Grayver, Alexander V.

    2015-07-01

    This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated

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

    SciTech Connect

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

    1998-10-01

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

  16. Application of adaptive and neural network computational techniques to Traffic Volume and Classification Monitoring

    SciTech Connect

    Mead, W.C.; Fisher, H.N.; Jones, R.D.; Bisset, K.R.; Lee, L.A.

    1993-09-01

    We are developing a Traffic Volume and Classification Monitoring (TVCM) system based on adaptive and neural network computational techniques. The value of neutral networks in this application lies in their ability to learn from data and to form a mapping of arbitrary topology. The piezoelectric strip and magnetic loop sensors typically used for TVCM provide signals that are complicated and variable, and that correspond in indirect ways with the desired FWHA 13-class classification system. Further, the wide variety of vehicle configurations adds to the complexity of the classification task. Our goal is to provide a TVCM system featuring high accuracy, adaptability to wide sensor and envirorunental variations, and continuous fault detection. We have instrumented an experimental TVCM site, developed PC-based on-line data acquisition software, collected a large database of vehicles` signals together with accurate ground truth determination, and analyzed the data off-line with a neural net classification system that can distinguish between class 2 (automobiles) and class 3 (utility vehicles) with better than 90% accuracy. The neural network used, called the Connectionist Hyperprism Classification (CHC) network, features simple basis functions; rapid, linear training algorithms for basis function amplitudes and widths; and basis function elimination that enhances network speed and accuracy. Work is in progress to extend the system to other classes, to quantify the system`s adaptability, and to develop automatic fault detection techniques.

  17. 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.

  18. Blood Volume: Importance and Adaptations to Exercise Training, Environmental Stresses and Trauma/Sickness

    NASA Technical Reports Server (NTRS)

    Sawka, Michael N.; Convertino, Victor A.; Eichner, E. Randy; Schnieder, Suzanne M.; Young, Andrew J.

    2000-01-01

    This paper reviews the influence of several perturbations (physical exercise, heat stress, terrestrial altitude, microgravity, and trauma/sickness) on adaptations of blood volume (BV), erythrocyte volume (EV), and plasma volume (PV). Exercise training can induced BV expansion; PV expansion usually occurs immediately, but EV expansion takes weeks. EV and PV expansion contribute to aerobic power improvements associated with exercise training. Repeated heat exposure induces PV expansion but does not alter EV. PV expansion does not improve thermoregulation, but EV expansion improves thermoregulation during exercise in the heat. Dehydration decreases PV (and increases plasma tonicity) which elevates heat strain and reduces exercise performance. High altitude exposure causes rapid (hours) plasma loss. During initial weeks at altitude, EV is unaffected, but a gradual expansion occurs with extended acclimatization. BV adjustments contribute, but are not key, to altitude acclimatization. Microgravity decreases PV and EV which contribute to orthostatic intolerance and decreased exercise capacity in astronauts. PV decreases may result from lower set points for total body water and central venous pressure, which EV decrease bay result form increased erythrocyte destruction. Trauma, renal disease, and chronic diseases cause anemia from hemorrhage and immune activation, which suppressions erythropoiesis. The re-establishment of EV is associated with healing, improved life quality, and exercise capabilities for these injured/sick persons.

  19. Onset of Time-Dependent 3-D spherical Mantle Convection using a Radial Basis Function-Pseudospectral Method ; Spectral-Finite Volume ; Spectral Higher-Order Finite- Difference Methods

    NASA Astrophysics Data System (ADS)

    Wright, G.; Flyer, N.; Yuen, D. A.; Monnereau, M.; Zhang, S.; Wang, S. M.

    2009-05-01

    Many numerical methods, such as finite-differences, finite-volume, their yin-yang variants, finite-elements and spectral methods have been employed to study 3-D mantle convection. All have their own strengths, but also serious weaknesses. Spectrally accurate methods do not practically allow for node refinement and often involve cumbersome algebra while finite difference, volume, or element methods are generally low-order, adding excessive numerical diffusion to the model. For the 3-D mantle convection problem, we have introduced a new mesh-free approach, using radial basis functions (RBF). This method has the advantage of being algorithmic simple, spectrally accurate for arbitrary node layouts in multi-dimensions and naturally allows for node-refinement. One virtue of the RBF scheme allows the user to use a simple Cartesian geometry, while implementing the required boundary conditions for the temperature, velocities and stress components on a spherical surface at both the planetary surface and the core-mantle boundary. We have studied time- dependent mantle convection, using both a RBF-pseudospectral code and a code which uses spherical- harmonics in the angular direction and second-order finite volume in the radial direction. We have employed a third code , which uses spherical harmonics and higher-order finite-difference method a la Fornberg in the radial coordinate.We first focus on the onset of time-dependence at Rayleigh number Ra of 70,000. We follow the development of stronger time-dependence to a Ra of one million, using high enough resolution with 120 to 200 points in the radial direction and 128 to 256 spherical harmonics.

  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. The Adaptive Significance of Enamel Loss in the Mandibular Incisors of Cercopithecine Primates (Mammalia: Cercopithecidae): A Finite Element Modelling Study

    PubMed Central

    Kupczik, Kornelius; Lev-Tov Chattah, Netta

    2014-01-01

    In several primate groups enamel is reduced or absent from the lingual (tongue) side of the mandibular incisor crowns akin to other placental and marsupial mammalian groups such as rodents, lagomorphs and wombats. Here we investigate the presumed adaptation of crowns with unilateral enamel to the incision of tough foods in cercopithecines, an Old World monkey subfamily, using a simulation approach. We developed and validated a finite element model of the lower central incisor of the rhesus macaque (Macaca mulatta) with labial enamel only to compute three-dimensional displacements and maximum principal stresses on the crown subjected to compressive loads varying in orientation. Moreover, we developed a model of a macaque incisor with enamel present on both labial and lingual aspects, thus resembling the ancestral condition found in the sister taxon, the leaf-eating colobines. The results showed that, concomitant with experimental results, the cercopithecine crown with unilateral enamel bends predominantly towards the inside of the mouth, while displacements decreased when both labial and lingual enamel are present. Importantly, the cercopithecine incisor crown experienced lower maximum principal stress on the lingual side compared to the incisor with enamel on the lingual and labial aspects under non-axial loads directed either towards the inside or outside of the mouth. These findings suggest that cercopithecine mandibular incisors are adapted to a wide range of ingestive behaviours compared to colobines. We conclude that the evolutionary loss of lingual enamel in cercopithecines has conferred a safeguard against crown failure under a loading regime assumed for the ingestion (peeling, scraping) of tough-skinned fruits. PMID:24831704

  2. Radiative transfer equation for predicting light propagation in biological media: comparison of a modified finite volume method, the Monte Carlo technique, and an exact analytical solution.

    PubMed

    Asllanaj, Fatmir; Contassot-Vivier, Sylvain; Liemert, André; Kienle, Alwin

    2014-01-01

    We examine the accuracy of a modified finite volume method compared to analytical and Monte Carlo solutions for solving the radiative transfer equation. The model is used for predicting light propagation within a two-dimensional absorbing and highly forward-scattering medium such as biological tissue subjected to a collimated light beam. Numerical simulations for the spatially resolved reflectance and transmittance are presented considering refractive index mismatch with Fresnel reflection at the interface, homogeneous and two-layered media. Time-dependent as well as steady-state cases are considered. In the steady state, it is found that the modified finite volume method is in good agreement with the other two methods. The relative differences between the solutions are found to decrease with spatial mesh refinement applied for the modified finite volume method obtaining <2.4%. In the time domain, the fourth-order Runge-Kutta method is used for the time semi-discretization of the radiative transfer equation. An agreement among the modified finite volume method, Runge-Kutta method, and Monte Carlo solutions are shown, but with relative differences higher than in the steady state. PMID:24390371

  3. Two coupled particle-finite volume methods using Delaunay-Voronoie meshes for the approximation of Vlasov-Poisson and Vlasov-Maxwell equations

    SciTech Connect

    Hermeline, F. )

    1993-05-01

    This paper deals with the approximation of Vlasov-Poisson and Vlasov-Maxwell equations. We present two coupled particle-finite volume methods which use the properties of Delaunay-Voronoi meshes. These methods are applied to benchmark calculations and engineering problems such as simulation of electron injector devices. 42 refs., 13 figs.

  4. 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

  5. Pulmonary airways tree segmentation from CT examinations using adaptive volume of interest

    NASA Astrophysics Data System (ADS)

    Park, Sang Cheol; Kim, Won Pil; Zheng, Bin; Leader, Joseph K.; Pu, Jiantao; Tan, Jun; Gur, David

    2009-02-01

    Airways tree segmentation is an important step in quantitatively assessing the severity of and changes in several lung diseases such as chronic obstructive pulmonary disease (COPD), asthma, and cystic fibrosis. It can also be used in guiding bronchoscopy. The purpose of this study is to develop an automated scheme for segmenting the airways tree structure depicted on chest CT examinations. After lung volume segmentation, the scheme defines the first cylinder-like volume of interest (VOI) using a series of images depicting the trachea. The scheme then iteratively defines and adds subsequent VOIs using a region growing algorithm combined with adaptively determined thresholds in order to trace possible sections of airways located inside the combined VOI in question. The airway tree segmentation process is automatically terminated after the scheme assesses all defined VOIs in the iteratively assembled VOI list. In this preliminary study, ten CT examinations with 1.25mm section thickness and two different CT image reconstruction kernels ("bone" and "standard") were selected and used to test the proposed airways tree segmentation scheme. The experiment results showed that (1) adopting this approach affectively prevented the scheme from infiltrating into the parenchyma, (2) the proposed method reasonably accurately segmented the airways trees with lower false positive identification rate as compared with other previously reported schemes that are based on 2-D image segmentation and data analyses, and (3) the proposed adaptive, iterative threshold selection method for the region growing step in each identified VOI enables the scheme to segment the airways trees reliably to the 4th generation in this limited dataset with successful segmentation up to the 5th generation in a fraction of the airways tree branches.

  6. Adapted fan-beam volume reconstruction for stationary digital breast tomosynthesis

    NASA Astrophysics Data System (ADS)

    Wu, Gongting; Inscoe, Christine; Calliste, Jabari; Lee, Yueh Z.; Zhou, Otto; Lu, Jianping

    2015-03-01

    Digital breast tomosynthesis (DBT) provides 3D images which remove tissue overlapping and enables better cancer detection. Stationary DBT (s-DBT) uses a fixed X-ray source array to eliminate image blur associated with the x-ray tube motion and provides better image quality as well as faster scanning speed. For limited angle tomography, it is known that iterative reconstructions generally produces better images with fewer artifacts. However classical iterative tomosynthesis reconstruction methods are considerably slower than the filtered back-projection (FBP) reconstruction. The linear x-ray source array used in s-DBT enables a computationally more efficient volume reconstruction using adapted fan beam slice sampling, which transforms the 3-D cone beam reconstruction to a series of 2-D fan beam slice reconstructions. In this paper, we report the first results of the adapted fan-beam volume reconstruction (AFVR) for the s-DBT system currently undergoing clinical trial at UNC, using a simultaneous algebraic reconstruction technique (SART). An analytic breast phantom is used to quantitatively analyze the performance of the AFVR. Image quality of a CIRS biopsy phantom reconstructed using the AFVR method are compared to that using FBP algorithm with a commercial package. Our results show a significant reduction in memory usage and an order of magnitude speed increase in reconstructing speed using AFVR compared to that of classical 3-D cone beam reconstruction. We also observed that images reconstructed by AFVR with SART had a better sharpness and contrast compared to that using FBP. Preliminary results on patient images demonstrates the improved detectability of the s-DBT system over the mammography. By utilizing parallel computing with graphics processing unit (GPU), it is expected that the AFVR method will enable iterative reconstruction technique to be practical for clinical applications.

  7. Adaptive volume rendering of cardiac 3D ultrasound images: utilizing blood pool statistics

    NASA Astrophysics Data System (ADS)

    Åsen, Jon Petter; Steen, Erik; Kiss, Gabriel; Thorstensen, Anders; Rabben, Stein Inge

    2012-03-01

    In this paper we introduce and investigate an adaptive direct volume rendering (DVR) method for real-time visualization of cardiac 3D ultrasound. DVR is commonly used in cardiac ultrasound to visualize interfaces between tissue and blood. However, this is particularly challenging with ultrasound images due to variability of the signal within tissue as well as variability of noise signal within the blood pool. Standard DVR involves a global mapping of sample values to opacity by an opacity transfer function (OTF). While a global OTF may represent the interface correctly in one part of the image, it may result in tissue dropouts, or even artificial interfaces within the blood pool in other parts of the image. In order to increase correctness of the rendered image, the presented method utilizes blood pool statistics to do regional adjustments of the OTF. The regional adaptive OTF was compared with a global OTF in a dataset of apical recordings from 18 subjects. For each recording, three renderings from standard views (apical 4-chamber (A4C), inverted A4C (IA4C) and mitral valve (MV)) were generated for both methods, and each rendering was tuned to the best visual appearance by a physician echocardiographer. For each rendering we measured the mean absolute error (MAE) between the rendering depth buffer and a validated left ventricular segmentation. The difference d in MAE between the global and regional method was calculated and t-test results are reported with significant improvements for the regional adaptive method (dA4C = 1.5 +/- 0.3 mm, dIA4C = 2.5 +/- 0.4 mm, dMV = 1.7 +/- 0.2 mm, d.f. = 17, all p < 0.001). This improvement by the regional adaptive method was confirmed through qualitative visual assessment by an experienced physician echocardiographer who concluded that the regional adaptive method produced rendered images with fewer tissue dropouts and less spurious structures inside the blood pool in the vast majority of the renderings. The algorithm has been

  8. An adaptive extended finite element method for the analysis of agglomeration of colloidal particles in a flowing fluid

    SciTech Connect

    Choi, Young Joon; Jorshari, Razzi Movassaghi; Djilali, Ned

    2015-03-10

    Direct numerical simulations of the flow-nanoparticle interaction in a colloidal suspension are presented using an extended finite element method (XFEM) in which the dynamics of the nanoparticles is solved in a fully-coupled manner with the flow. The method is capable of accurately describing solid-fluid interfaces without the need of boundary-fitted meshes to investigate the dynamics of particles in complex flows. In order to accurately compute the high interparticle shear stresses and pressures while minimizing computing costs, an adaptive meshing technique is incorporated with the fluid-structure interaction algorithm. The particle-particle interaction at the microscopic level is modeled using the Lennard-Jones (LJ) potential and the corresponding potential parameters are determined by a scaling procedure. The study is relevant to the preparation of inks used in the fabrication of catalyst layers for fuel cells. In this paper, we are particularly interested in investigating agglomeration of the nanoparticles under external shear flow in a sliding bi-periodic Lees-Edwards frame. The results indicate that the external shear has a crucial impact on the structure formation of colloidal particles in a suspension.

  9. Fractal behavior of traffic volume on urban expressway through adaptive fractal analysis

    NASA Astrophysics Data System (ADS)

    He, Hong-di; Wang, Jun-li; Wei, Hai-rui; Ye, Cheng; Ding, Yi

    2016-02-01

    In this paper, we investigate the fractal behavior of traffic volume in urban expressway based on a newly developed adaptive fractal analysis (AFA), which has a number of advantages over traditional method of detrended fluctuation analysis (DFA). Before fractal analysis, autocorrelation function was first adopted on traffic volume data and the long-range correlation behavior was found to be existed in both on-ramp and off-ramp situations. Then AFA as well as DFA was applied to further examine the fractal behavior. The results showed that the multifractality and the long-range anti-persistent behavior existed on both on-ramp and off-ramp. Additionally, multifractal analysis on weekdays and weekends are performed respectively and the results show that the degree of multifractality on weekdays is higher than that on weekends, implying that long-range correlation behaviors were more obvious on weekdays. Finally, the source of multifractality is examined with randomly shuffled and the surrogated series. Long-range correlation behaviors are identified in both on-ramp and off-ramp situations and fat-tail distributions were found to make little in the contributions of multifractality.

  10. 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.

  11. Global energy and water balance: Characteristics from finite-volume atmospheric model of the IAP/LASG (FAMIL1)

    SciTech Connect

    Zhou, Linjiong; Bao, Qing; Liu, Yimin; Wu, Guoxiong; Wang, Wei-Chyung; Wang, Xiaocong; He, Bian; Yu, Haiyang; Li, Jiandong

    2015-03-01

    This paper documents version 1 of the Finite-volume Atmospheric Model of the IAP/LASG (FAMIL1), which has a flexible horizontal resolution up to a quarter of 1°. The model, currently running on the ‘‘Tianhe 1A’’ supercomputer, is the atmospheric component of the third-generation Flexible Global Ocean-Atmosphere-Land climate System model (FGOALS3) which will participate in the Coupled Model Intercomparison Project Phase 6 (CMIP6). In addition to describing the dynamical core and physical parameterizations of FAMIL1, this paper describes the simulated characteristics of energy and water balances and compares them with observational/reanalysis data. The comparisons indicate that the model simulates well the seasonal and geographical distributions of radiative fluxes at the top of the atmosphere and at the surface, as well as the surface latent and sensible heat fluxes. A major weakness in the energy balance is identified in the regions where extensive and persistent marine stratocumulus is present. Analysis of the global water balance also indicates realistic seasonal and geographical distributions with the global annual mean of evaporation minus precipitation being approximately 10⁻⁵ mm d⁻¹. We also examine the connections between the global energy and water balance and discuss the possible link between the two within the context of the findings from the reanalysis data. Finally, the model biases as well as possible solutions are discussed.

  12. Global energy and water balance: Characteristics from finite-volume atmospheric model of the IAP/LASG (FAMIL1)

    DOE PAGESBeta

    Zhou, Linjiong; Bao, Qing; Liu, Yimin; Wu, Guoxiong; Wang, Wei-Chyung; Wang, Xiaocong; He, Bian; Yu, Haiyang; Li, Jiandong

    2015-03-01

    This paper documents version 1 of the Finite-volume Atmospheric Model of the IAP/LASG (FAMIL1), which has a flexible horizontal resolution up to a quarter of 1°. The model, currently running on the ‘‘Tianhe 1A’’ supercomputer, is the atmospheric component of the third-generation Flexible Global Ocean-Atmosphere-Land climate System model (FGOALS3) which will participate in the Coupled Model Intercomparison Project Phase 6 (CMIP6). In addition to describing the dynamical core and physical parameterizations of FAMIL1, this paper describes the simulated characteristics of energy and water balances and compares them with observational/reanalysis data. The comparisons indicate that the model simulates well the seasonalmore » and geographical distributions of radiative fluxes at the top of the atmosphere and at the surface, as well as the surface latent and sensible heat fluxes. A major weakness in the energy balance is identified in the regions where extensive and persistent marine stratocumulus is present. Analysis of the global water balance also indicates realistic seasonal and geographical distributions with the global annual mean of evaporation minus precipitation being approximately 10⁻⁵ mm d⁻¹. We also examine the connections between the global energy and water balance and discuss the possible link between the two within the context of the findings from the reanalysis data. Finally, the model biases as well as possible solutions are discussed.« less

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

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

    SciTech Connect

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

    2007-04-10

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

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

    NASA Astrophysics Data System (ADS)

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

    2013-03-01

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

  2. Adaptive beamlet-based finite-size pencil beam dose calculation for independent verification of IMRT and VMAT

    SciTech Connect

    Park, Justin C.; Li, Jonathan G.; Arhjoul, Lahcen; Yan, Guanghua; Lu, Bo; Fan, Qiyong; Liu, Chihray

    2015-04-15

    Purpose: The use of sophisticated dose calculation procedure in modern radiation therapy treatment planning is inevitable in order to account for complex treatment fields created by multileaf collimators (MLCs). As a consequence, independent volumetric dose verification is time consuming, which affects the efficiency of clinical workflow. In this study, the authors present an efficient adaptive beamlet-based finite-size pencil beam (AB-FSPB) dose calculation algorithm that minimizes the computational procedure while preserving the accuracy. Methods: The computational time of finite-size pencil beam (FSPB) algorithm is proportional to the number of infinitesimal and identical beamlets that constitute an arbitrary field shape. In AB-FSPB, dose distribution from each beamlet is mathematically modeled such that the sizes of beamlets to represent an arbitrary field shape no longer need to be infinitesimal nor identical. As a result, it is possible to represent an arbitrary field shape with combinations of different sized and minimal number of beamlets. In addition, the authors included the model parameters to consider MLC for its rounded edge and transmission. Results: Root mean square error (RMSE) between treatment planning system and conventional FSPB on a 10 × 10 cm{sup 2} square field using 10 × 10, 2.5 × 2.5, and 0.5 × 0.5 cm{sup 2} beamlet sizes were 4.90%, 3.19%, and 2.87%, respectively, compared with RMSE of 1.10%, 1.11%, and 1.14% for AB-FSPB. This finding holds true for a larger square field size of 25 × 25 cm{sup 2}, where RMSE for 25 × 25, 2.5 × 2.5, and 0.5 × 0.5 cm{sup 2} beamlet sizes were 5.41%, 4.76%, and 3.54% in FSPB, respectively, compared with RMSE of 0.86%, 0.83%, and 0.88% for AB-FSPB. It was found that AB-FSPB could successfully account for the MLC transmissions without major discrepancy. The algorithm was also graphical processing unit (GPU) compatible to maximize its computational speed. For an intensity modulated radiation therapy (

  3. Adaptation of an unstructured-mesh, finite-element ocean model to the simulation of ocean circulation beneath ice shelves

    NASA Astrophysics Data System (ADS)

    Kimura, Satoshi; Candy, Adam S.; Holland, Paul R.; Piggott, Matthew D.; Jenkins, Adrian

    2013-07-01

    Several different classes of ocean model are capable of representing floating glacial ice shelves. We describe the incorporation of ice shelves into Fluidity-ICOM, a nonhydrostatic finite-element ocean model with the capacity to utilize meshes that are unstructured and adaptive in three dimensions. This geometric flexibility offers several advantages over previous approaches. The model represents melting and freezing on all ice-shelf surfaces including vertical faces, treats the ice shelf topography as continuous rather than stepped, and does not require any smoothing of the ice topography or any of the additional parameterisations of the ocean mixed layer used in isopycnal or z-coordinate models. The model can also represent a water column that decreases to zero thickness at the 'grounding line', where the floating ice shelf is joined to its tributary ice streams. The model is applied to idealised ice-shelf geometries in order to demonstrate these capabilities. In these simple experiments, arbitrarily coarsening the mesh outside the ice-shelf cavity has little effect on the ice-shelf melt rate, while the mesh resolution within the cavity is found to be highly influential. Smoothing the vertical ice front results in faster flow along the smoothed ice front, allowing greater exchange with the ocean than in simulations with a realistic ice front. A vanishing water-column thickness at the grounding line has little effect in the simulations studied. We also investigate the response of ice shelf basal melting to variations in deep water temperature in the presence of salt stratification.

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

    DOE PAGESBeta

    Charest, Marc R.J.; Canfield, Thomas R.; Morgan, Nathaniel R.; Waltz, Jacob; Wohlbier, John G.

    2015-03-11

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

  6. Robust adaptive transient damping in power systems. Volume 1, System identification and decentralized adaptive control with applications to power systems: Final report

    SciTech Connect

    Pierre, D.A.; Sadighi, I.; Trudnowski, D.J.; Smith, J.R.; Nehrir, M.H.

    1992-09-01

    This Volume 1 of the final report on RP2665-1 contains two parts. part 1 consists of the following: (1) a literature review of real-time parameter identification algorithms which may be used in self-tuning adaptive control; (2) a description of mathematical discrete-time models that are linear in the parameters and that are useful for self-tuning adaptive control; (3) detailed descriptions of several variations of recursive-least-squares algorithms (RLS algorithms) and a unified representation of some of these algorithms; (4) a new variation of RLS called Corrector Least Squares (CLS); (5) a set of practical issues that need to be addressed in the implementation of RLS-based algorithms; (6) a set of simulation examples that illustrate properties of the identification methods; and (7) appendices With FORTRAN listings of several identification codes. Part 2 of this volume addresses the problem of damping electromechanical oscillations in power systems using advanced control theory. Two control strategies are developed. Controllers are then applied to a power system as power system stabilizer (PSS) units. The primary strategy is a decentralized indirect adaptive control scheme where multiple self-tuning adaptive controllers are coordinated. This adaptive scheme is presented in a general format and the stabilizing properties are demonstrated using examples. Both the adaptive and the conventional strategies are applied to a 17-machine computer-simulated power system. PSS units are applied to four generators in the system. Detailed simulation results are presented that show the feasibility and properties of both control schemes. FORTRAN codes for the control simulations are given in appendices of Part 2, as also are FORTRAN codes for the Prony identification method.

  7. Expansion and improvement of the FORMA system for response and load analysis. Volume 2C: Listings, finite element FORMA subroutines

    NASA Technical Reports Server (NTRS)

    Wohlen, R. L.

    1976-01-01

    A listing of the source deck of each finite element FORMA subroutine is given to remove the 'black-box' aura of the subroutines so that the analyst may better understand the detailed operations of each subroutine. The FORTRAN 4 programming language is used in all finite element FORMA subroutines.

  8. 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.

  9. A conservative finite volume scheme with time-accurate local time stepping for scalar transport on unstructured grids

    NASA Astrophysics Data System (ADS)

    Cavalcanti, José Rafael; Dumbser, Michael; Motta-Marques, David da; Fragoso Junior, Carlos Ruberto

    2015-12-01

    In this article we propose a new conservative high resolution TVD (total variation diminishing) finite volume scheme with time-accurate local time stepping (LTS) on unstructured grids for the solution of scalar transport problems, which are typical in the context of water quality simulations. To keep the presentation of the new method as simple as possible, the algorithm is only derived in two space dimensions and for purely convective transport problems, hence neglecting diffusion and reaction terms. The new numerical method for the solution of the scalar transport is directly coupled to the hydrodynamic model of Casulli and Walters (2000) that provides the dynamics of the free surface and the velocity vector field based on a semi-implicit discretization of the shallow water equations. Wetting and drying is handled rigorously by the nonlinear algorithm proposed by Casulli (2009). The new time-accurate LTS algorithm allows a different time step size for each element of the unstructured grid, based on an element-local Courant-Friedrichs-Lewy (CFL) stability condition. The proposed method does not need any synchronization between different time steps of different elements and is by construction locally and globally conservative. The LTS scheme is based on a piecewise linear polynomial reconstruction in space-time using the MUSCL-Hancock method, to obtain second order of accuracy in both space and time. The new algorithm is first validated on some classical test cases for pure advection problems, for which exact solutions are known. In all cases we obtain a very good level of accuracy, showing also numerical convergence results; we furthermore confirm mass conservation up to machine precision and observe an improved computational efficiency compared to a standard second order TVD scheme for scalar transport with global time stepping (GTS). Then, the new LTS method is applied to some more complex problems, where the new scalar transport scheme has also been coupled to

  10. 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.

  11. Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations

    NASA Astrophysics Data System (ADS)

    Hawken, D. F.; Gottlieb, J. J.; Hansen, J. S.

    1991-08-01

    Results are presented from a search of the literature on adaptive numerical methods for the solution of PDEs, using node-movements to yield low truncation-solution error levels while minimizing the number of nodes required in the calculation. The applications in question encompass nonstationary flow problems containing moving regions of rapid flow-variable change, amid regions of comparatively smooth variation. Flows involving shock waves, contact surfaces, slipstreams, boundary layers, and phase-change interfaces, are shown to be modeled with both great precision and economy of execution, if the nodes are moved so that they are concentrated in the rapid flow-variable change regions.

  12. Implementation and efficiency analysis of an adaptive hp-finite element method for solving boundary value problems for the stationary reaction-diffusion equation

    NASA Astrophysics Data System (ADS)

    Zolotareva, N. D.; Nikolaev, E. S.

    2016-05-01

    An iterative process implementing an adaptive hp-version of the finite element method (FEM) previously proposed by the authors for the approximate solution of boundary value problems for the stationary reaction-diffusion equation is described. The method relies on piecewise polynomial basis functions and makes use of an adaptive strategy for constructing a sequence of finite-dimensional subspaces based on the computation of correction indicators. Singularly perturbed boundary value test problems with smooth and not very smooth solutions are used to analyze the efficiency of the method in the situation when an approximate solution has to be found with high accuracy. The convergence of the approximate solution to the exact one is investigated depending on the value of the small parameter multiplying the highest derivative, on the family of basis functions and the quadrature formulas used, and on the internal parameters of the method. The method is compared with an adaptive h-version of FEM that also relies on correction indicators and with its nonadaptive variant based on the bisection of grid intervals.

  13. Three-dimensional modeling of a thermal dendrite using the phase field method with automatic anisotropic and unstructured adaptive finite element meshing

    NASA Astrophysics Data System (ADS)

    Sarkis, C.; Silva, L.; Gandin, Ch-A.; Plapp, M.

    2016-03-01

    Dendritic growth is computed with automatic adaptation of an anisotropic and unstructured finite element mesh. The energy conservation equation is formulated for solid and liquid phases considering an interface balance that includes the Gibbs-Thomson effect. An equation for a diffuse interface is also developed by considering a phase field function with constant negative value in the liquid and constant positive value in the solid. Unknowns are the phase field function and a dimensionless temperature, as proposed by [1]. Linear finite element interpolation is used for both variables, and discretization stabilization techniques ensure convergence towards a correct non-oscillating solution. In order to perform quantitative computations of dendritic growth on a large domain, two additional numerical ingredients are necessary: automatic anisotropic unstructured adaptive meshing [2,[3] and parallel implementations [4], both made available with the numerical platform used (CimLib) based on C++ developments. Mesh adaptation is found to greatly reduce the number of degrees of freedom. Results of phase field simulations for dendritic solidification of a pure material in two and three dimensions are shown and compared with reference work [1]. Discussion on algorithm details and the CPU time will be outlined.

  14. 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).

  15. 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.

  16. Adaptation.

    PubMed

    Broom, Donald M

    2006-01-01

    The term adaptation is used in biology in three different ways. It may refer to changes which occur at the cell and organ level, or at the individual level, or at the level of gene action and evolutionary processes. Adaptation by cells, especially nerve cells helps in: communication within the body, the distinguishing of stimuli, the avoidance of overload and the conservation of energy. The time course and complexity of these mechanisms varies. Adaptive characters of organisms, including adaptive behaviours, increase fitness so this adaptation is evolutionary. The major part of this paper concerns adaptation by individuals and its relationships to welfare. In complex animals, feed forward control is widely used. Individuals predict problems and adapt by acting before the environmental effect is substantial. Much of adaptation involves brain control and animals have a set of needs, located in the brain and acting largely via motivational mechanisms, to regulate life. Needs may be for resources but are also for actions and stimuli which are part of the mechanism which has evolved to obtain the resources. Hence pigs do not just need food but need to be able to carry out actions like rooting in earth or manipulating materials which are part of foraging behaviour. The welfare of an individual is its state as regards its attempts to cope with its environment. This state includes various adaptive mechanisms including feelings and those which cope with disease. The part of welfare which is concerned with coping with pathology is health. Disease, which implies some significant effect of pathology, always results in poor welfare. Welfare varies over a range from very good, when adaptation is effective and there are feelings of pleasure or contentment, to very poor. A key point concerning the concept of individual adaptation in relation to welfare is that welfare may be good or poor while adaptation is occurring. Some adaptation is very easy and energetically cheap and

  17. Finite-difference modeling with variable grid-size and adaptive time-step in porous media

    NASA Astrophysics Data System (ADS)

    Liu, Xinxin; Yin, Xingyao; Wu, Guochen

    2014-04-01

    Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However, the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap, combined with variable grid-size and time-step, this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.

  18. Determining the Hydrologic Impacts of Climate Variability on Florida's Everglades Through the Use of a Finite Volume Hydrologic Model

    NASA Astrophysics Data System (ADS)

    Senarath, S. U.; Novoa, R. J.; Niedzialek, J. M.; Zheng, F.

    2006-12-01

    A good understanding of climate variability and its impacts on the regional water budget are crucial for the restoration of Florida's Everglades. This is investigated by varying the two most sensitive climatic data sets, namely rainfall and evapotranspiration of a regional-scale hydrologic model. A 36-year long record, spanning from 1965 to 2000 is used in these assessments. Although not comprehensive, these data sets include several seasons with extremely high and low rainfall and evapotranspiration. The Everglades National Park, the Big Cypress National Preserve, and the Water Conservation Areas 3A and 3B are included in the study area. These watersheds jointly encompass an area of 10,158 square kilometers, and are home to many endangered and threatened species of fauna and flora. The Regional Simulation Model (RSM) developed by the South Florida Water Management District (SFWMD) is used in this study to evaluate and quantify the hydrologic responses caused due to climate variability. RSM is a finite-volume, regional-scale, distributed, continuous hydrologic model with fully coupled groundwater, canal and overland flow components. This model uses a variable triangular mesh that conforms to levees, canals and sub-basin boundaries. RSM can adequately simulate the low-relief topography, and high water tables, saturated hydraulic conductivities and surface roughnesses that exist in Florida's Everglades. The model uses the diffusive wave approximation of Saint-Venant's equation to simulate canal and overland flows. The Southern Everglades implementation of the RSM (hereafter, Southern Everglades Model or SEM) is calibrated and verified using stage data from 1988 to 1995, and 1996 to 2000, respectively. An irregular triangular mesh with 52,817 cells and a one-day time step are used in this implementation. For all simulations and assessments the model boundary conditions are obtained from the South Florida Water Management Model developed by the SFWMD. Two types of

  19. Use of a Distributed, Finite-Volume, Hydrologic Model to Assess the Sensitivity of the Everglades to De-compartmentalization

    NASA Astrophysics Data System (ADS)

    Senarath, S. U.

    2002-12-01

    The Everglades, the only remaining subtropical wilderness in the continental USA, is the home to a number of threatened and endangered species. Although the pre-drainage Everglades covered an area of approximately 11,048 km2, urbanization and farming have reduced its area by approximately 50%. The remaining Everglades has also changed as a result of drainage and compartmentalization by over 2,200 km of levees and canals. This area is also adversely affected by exotic species, nutrient enrichment, contaminants and altered freshwater flows. The \\8 billion Comprehensive Everglades Restoration Plan provides a ``framework and guide to restore, protect, and preserve the water resources of central and southern Florida, including the Everglades.'' The success of this project, one of the largest eco-system restoration projects in the world, depends heavily on our understanding of the quantity, quality, timing and distribution of South Florida's pre-drainage freshwater flow. Consequently, accurate hydrologic modeling is crucial for the restoration of the greater Everglades ecosystem. The Regional Simulation Model (RSM) developed by the South Florida Water Management District is currently being used to investigate the effect of de-compartmentalization on freshwater flow dynamics in parts of the remaining Everglades which includes the Everglades National Park and the Big Cypress National Preserve. The RSM is an implicit, finite-volume, continuous, distributed, integrated surface/ground-water model, capable of simulating one-dimensional canal flow and two-dimensional overland flow in arbitrarily shaped areas using a variable triangular mesh. It has physically-based formulations for the simulation of overland and groundwater flow, evapo-transpiration, infiltration, levee seepage, and canal and structure flows. It is capable of simulating features that are unique to South Florida such as low-relief topography, high water tables, saturation-excess runoff, depth

  20. 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.

  1. 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.

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

    NASA Astrophysics Data System (ADS)

    Key, K.

    2013-12-01

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

  3. On-board multispectral classification study. Volume 2: Supplementary tasks. [adaptive control

    NASA Technical Reports Server (NTRS)

    Ewalt, D.

    1979-01-01

    The operational tasks of the onboard multispectral classification study were defined. These tasks include: sensing characteristics for future space applications; information adaptive systems architectural approaches; data set selection criteria; and onboard functional requirements for interfacing with global positioning satellites.

  4. 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.

  5. Adapt

    NASA Astrophysics Data System (ADS)

    Bargatze, L. F.

    2015-12-01

    Active Data Archive Product Tracking (ADAPT) is a collection of software routines that permits one to generate XML metadata files to describe and register data products in support of the NASA Heliophysics Virtual Observatory VxO effort. ADAPT is also a philosophy. The ADAPT concept is to use any and all available metadata associated with scientific data to produce XML metadata descriptions in a consistent, uniform, and organized fashion to provide blanket access to the full complement of data stored on a targeted data server. In this poster, we present an application of ADAPT to describe all of the data products that are stored by using the Common Data File (CDF) format served out by the CDAWEB and SPDF data servers hosted at the NASA Goddard Space Flight Center. These data servers are the primary repositories for NASA Heliophysics data. For this purpose, the ADAPT routines have been used to generate data resource descriptions by using an XML schema named Space Physics Archive, Search, and Extract (SPASE). SPASE is the designated standard for documenting Heliophysics data products, as adopted by the Heliophysics Data and Model Consortium. The set of SPASE XML resource descriptions produced by ADAPT includes high-level descriptions of numerical data products, display data products, or catalogs and also includes low-level "Granule" descriptions. A SPASE Granule is effectively a universal access metadata resource; a Granule associates an individual data file (e.g. a CDF file) with a "parent" high-level data resource description, assigns a resource identifier to the file, and lists the corresponding assess URL(s). The CDAWEB and SPDF file systems were queried to provide the input required by the ADAPT software to create an initial set of SPASE metadata resource descriptions. Then, the CDAWEB and SPDF data repositories were queried subsequently on a nightly basis and the CDF file lists were checked for any changes such as the occurrence of new, modified, or deleted

  6. An adaptive quadrature-free implementation of the high-order spectral volume method on unstructured grids

    NASA Astrophysics Data System (ADS)

    Harris, Robert Evan

    2008-10-01

    An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and nonlinear advection equations, and the Euler equations. The new quadrature-free approach is then extended to handle local adaptive hp-refinement (grid and order refinement). Efficient edge-based adaptation utilizing a binary tree search algorithm is employed. Several different adaptation criteria which focus computational effort near high gradient regions are presented. Both h- and p-refinements are presented in a general framework where it is possible to perform either or both on any grid cell at any time. Several well-known inviscid flow test cases, subjected to various levels of adaptation, are utilized to demonstrate the effectiveness of the method. An analysis of the accuracy and stability properties of the spectral volume (SV) method is then presented. The current work seeks to address the issue of stability, as well as polynomial quality, in the design of SV partitions. A new approach is presented, which efficiently locates stable partitions by means of constrained minimization. Once stable partitions are located, a

  7. Cell type-specific adaptation of cellular and nuclear volume in micro-engineered 3D environments.

    PubMed

    Greiner, Alexandra M; Klein, Franziska; Gudzenko, Tetyana; Richter, Benjamin; Striebel, Thomas; Wundari, Bayu G; Autenrieth, Tatjana J; Wegener, Martin; Franz, Clemens M; Bastmeyer, Martin

    2015-11-01

    Bio-functionalized three-dimensional (3D) structures fabricated by direct laser writing (DLW) are structurally and mechanically well-defined and ideal for systematically investigating the influence of three-dimensionality and substrate stiffness on cell behavior. Here, we show that different fibroblast-like and epithelial cell lines maintain normal proliferation rates and form functional cell-matrix contacts in DLW-fabricated 3D scaffolds of different mechanics and geometry. Furthermore, the molecular composition of cell-matrix contacts forming in these 3D micro-environments and under conventional 2D culture conditions is identical, based on the analysis of several marker proteins (paxillin, phospho-paxillin, phospho-focal adhesion kinase, vinculin, β1-integrin). However, fibroblast-like and epithelial cells differ markedly in the way they adapt their total cell and nuclear volumes in 3D environments. While fibroblast-like cell lines display significantly increased cell and nuclear volumes in 3D substrates compared to 2D substrates, epithelial cells retain similar cell and nuclear volumes in 2D and 3D environments. Despite differential cell volume regulation between fibroblasts and epithelial cells in 3D environments, the nucleus-to-cell (N/C) volume ratios remain constant for all cell types and culture conditions. Thus, changes in cell and nuclear volume during the transition from 2D to 3D environments are strongly cell type-dependent, but independent of scaffold stiffness, while cells maintain the N/C ratio regardless of culture conditions. PMID:26283159

  8. Physiological and health-related adaptations to low-volume interval training: influences of nutrition and sex.

    PubMed

    Gibala, Martin J; Gillen, Jenna B; Percival, Michael E

    2014-11-01

    Interval training refers to the basic concept of alternating periods of relatively intense exercise with periods of lower-intensity effort or complete rest for recovery. Low-volume interval training refers to sessions that involve a relatively small total amount of exercise (i.e. ≤10 min of intense exercise), compared with traditional moderate-intensity continuous training (MICT) protocols that are generally reflected in public health guidelines. In an effort to standardize terminology, a classification scheme was recently proposed in which the term 'high-intensity interval training' (HIIT) be used to describe protocols in which the training stimulus is 'near maximal' or the target intensity is between 80 and 100 % of maximal heart rate, and 'sprint interval training' (SIT) be used for protocols that involve 'all out' or 'supramaximal' efforts, in which target intensities correspond to workloads greater than what is required to elicit 100 % of maximal oxygen uptake (VO2max). Both low-volume SIT and HIIT constitute relatively time-efficient training strategies to rapidly enhance the capacity for aerobic energy metabolism and elicit physiological remodeling that resembles changes normally associated with high-volume MICT. Short-term SIT and HIIT protocols have also been shown to improve health-related indices, including cardiorespiratory fitness and markers of glycemic control in both healthy individuals and those at risk for, or afflicted by, cardiometabolic diseases. Recent evidence from a limited number of studies has highlighted potential sex-based differences in the adaptive response to SIT in particular. It has also been suggested that specific nutritional interventions, in particular those that can augment muscle buffering capacity, such as sodium bicarbonate, may enhance the adaptive response to low-volume interval training. PMID:25355187

  9. Volume and dosimetric variations during two-phase adaptive intensity-modulated radiotherapy for locally advanced nasopharyngeal carcinoma.

    PubMed

    Wang, Rui-hao; Zhang, Shu-xu; Zhou, Ling-hong; Zhang, Guo-qian; Yu, Hui; Lin, Xiao-dan; Lin, Shengqu

    2014-01-01

    The aims of this study were to evaluate the volume and dosimetric variations during IMRT for locally advanced NPC and to identify the benefits of a two-phase adaptive IMRT method. Twenty patients with locally advanced NPC having received IMRT treatment were included. Each patient had both an initial planning CT (CT-1) and a repeated CT scan (CT-2) after treatment at a dose of 40 Gy. Three IMRT planning scenarios were compared: (1) the initial plan on the CT-1 (plan-1); (2) the hybrid plan recalculated the initial plan on the CT-2 (plan-2); (3) the replan generated on the CT-2 being used to complete the course of IMRT (plan-3). The mean gross target volume and mean volumes of the positive neck lymph nodes, high-risk clinical target volume, and the left and right parotid glands significantly decreased by 30.2%, 45.1%, 21.1%, 14.7% and 18.2%, respectively on the CT-2. Comparing plan-2 with plan-1, the dose coverage of the targets remained unchanged, whereas the dose delivered to the parotid glands and spinal cord increased significantly. These patients with locally advanced NPC might benefit from replanning because of the sparing of the parotid glands and spinal cord. PMID:24212016

  10. Moving and adaptive grid methods for compressible flows

    NASA Technical Reports Server (NTRS)

    Trepanier, Jean-Yves; Camarero, Ricardo

    1995-01-01

    This paper describes adaptive grid methods developed specifically for compressible flow computations. The basic flow solver is a finite-volume implementation of Roe's flux difference splitting scheme or arbitrarily moving unstructured triangular meshes. The grid adaptation is performed according to geometric and flow requirements. Some results are included to illustrate the potential of the methodology.

  11. Adaptive wavelet simulation of global ocean dynamics using a new Brinkman volume penalization

    NASA Astrophysics Data System (ADS)

    Kevlahan, N. K.-R.; Dubos, T.; Aechtner, M.

    2015-12-01

    In order to easily enforce solid-wall boundary conditions in the presence of complex coastlines, we propose a new mass and energy conserving Brinkman penalization for the rotating shallow water equations. This penalization does not lead to higher wave speeds in the solid region. The error estimates for the penalization are derived analytically and verified numerically for linearized one-dimensional equations. The penalization is implemented in a conservative dynamically adaptive wavelet method for the rotating shallow water equations on the sphere with bathymetry and coastline data from NOAA's ETOPO1 database. This code could form the dynamical core for a future global ocean model. The potential of the dynamically adaptive ocean model is illustrated by using it to simulate the 2004 Indonesian tsunami and wind-driven gyres.

  12. Solving the chemical master equation by a fast adaptive finite state projection based on the stochastic simulation algorithm.

    PubMed

    Sidje, R B; Vo, H D

    2015-11-01

    The mathematical framework of the chemical master equation (CME) uses a Markov chain to model the biochemical reactions that are taking place within a biological cell. Computing the transient probability distribution of this Markov chain allows us to track the composition of molecules inside the cell over time, with important practical applications in a number of areas such as molecular biology or medicine. However the CME is typically difficult to solve, since the state space involved can be very large or even countably infinite. We present a novel way of using the stochastic simulation algorithm (SSA) to reduce the size of the finite state projection (FSP) method. Numerical experiments that demonstrate the effectiveness of the reduction are included. PMID:26319118

  13. Predictors of individual adaptation to high-volume or high-intensity endurance training in recreational endurance runners.

    PubMed

    Vesterinen, V; Häkkinen, K; Laine, T; Hynynen, E; Mikkola, J; Nummela, A

    2016-08-01

    The aim of this study was to investigate factors that can predict individual adaptation to high-volume or high-intensity endurance training. After the first 8-week preparation period, 37 recreational endurance runners were matched into the high-volume training group (HVT) and high-intensity training group (HIT). During the next 8-week training period, HVT increased their running training volume and HIT increased training intensity. Endurance performance characteristics, heart rate variability (HRV), and serum hormone concentrations were measured before and after the training periods. While HIT improved peak treadmill running speed (RSpeak ) 3.1 ± 2.8% (P < 0.001), no significant changes occurred in HVT (RSpeak : 0.5 ± 1.9%). However, large individual variation was found in the changes of RSpeak in both groups (HVT: -2.8 to 4.1%; HIT: 0-10.2%). A negative relationship was observed between baseline high-frequency power of HRV (HFPnight ) and the individual changes of RSpeak (r = -0.74, P = 0.006) in HVT and a positive relationship (r = 0.63, P = 0.039) in HIT. Individuals with lower HFP showed greater change of RSpeak in HVT, while individuals with higher HFP responded well in HIT. It is concluded that nocturnal HRV can be used to individualize endurance training in recreational runners. PMID:26247789

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

    PubMed

    Shrestha, Kalyan; Mompean, Gilmar; Calzavarini, Enrico

    2016-02-01

    A finite-volume (FV) discretization method for the lattice Boltzmann (LB) equation, which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard streaming lattice Boltzmann equation algorithm. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken as the method of choice in fluid-dynamics LB simulations. For this reason the comparative analysis is further extended to the case of realistic flows, in particular thermally driven flows in turbulent conditions. We report the successful simulation of high-Rayleigh number convective flow performed by a lattice Boltzmann FV-based algorithm with wall grid refinement. PMID:26986438

  15. 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.

  16. Investigation of a matrix-model for the artificial dissipation in a cell vertex finite volume scheme for solving the Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Brodersen, Olaf

    1992-06-01

    A matrix dissipation model is evaluated for the numerical solution of the Navier-Stokes equations. The numerical approach, a finite volume scheme with central differencing, was outlined and the necessity of artificially added dissipation was shown. The design of the dissipation term for modeling an upwind scheme is described for the one dimensional linear wave equation. Following this approach results in time consuming matrix multiplications for two dimensional and three dimensional cases. Because of a new splitting technique of the matrices found in the literature, it is now possible to use this dissipation model in a more efficient way. The basic effects were analyzed for viscous flow around the RAE 2822 airfoil. The results show a higher resolution of shocks and the boundary layer. Thus, it is possible to use coarser meshes so that CPU (Central Processing Unit) time is reduced by about a factor of three.

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

    NASA Astrophysics Data System (ADS)

    Shrestha, Kalyan; Mompean, Gilmar; Calzavarini, Enrico

    2016-02-01

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

  18. 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.

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

    NASA Astrophysics Data System (ADS)

    Sahin, Mehmet

    2005-11-01

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

  20. 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.

  1. 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.

  2. Simulating the interaction of the heliosphere with the local interstellar medium: MHD results from a finite volume approach, first bidimensional results

    NASA Technical Reports Server (NTRS)

    Chanteur, G.; Khanfir, R.

    1995-01-01

    We have designed a full compressible MHD code working on unstructured meshes in order to be able to compute accurately sharp structures embedded in large scale simulations. The code is based on a finite volume method making use of a kinetic flux splitting. A bidimensional version of the code has been used to simulate the interaction of a moving interstellar medium, magnetized or unmagnetized with a rotating and magnetized heliopspheric plasma source. Being aware that these computations are not realistic due to the restriction to two dimensions, we present it to demonstrate the ability of this new code to handle this problem. An axisymetric version, now under development, will be operational in a few months. Ultimately we plan to run a full 3d version.

  3. 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.

  4. First-principles study of intrinsic point defects in ZnO: Role of band structure, volume relaxation, and finite-size effects

    NASA Astrophysics Data System (ADS)

    Erhart, Paul; Albe, Karsten; Klein, Andreas

    2006-05-01

    Density-functional theory (DFT) calculations of intrinsic point defect properties in zinc oxide were performed in order to remedy the influence of finite-size effects and the improper description of the band structure. The generalized gradient approximation (GGA) with empirical self-interaction corrections (GGA+U) was applied to correct for the overestimation of covalency intrinsic to GGA-DFT calculations. Elastic as well as electrostatic image interactions were accounted for by application of extensive finite-size scaling and compensating charge corrections. Size-corrected formation enthalpies and volumes as well as their charge state dependence have been deduced. Our results partly confirm earlier calculations but reveal a larger number of transition levels: (1) For both the zinc interstitial as well as the oxygen vacancy, transition levels are close to the conduction band minimum. (2) The zinc vacancy shows a transition rather close to the valence band maximum and another one near the middle of the calculated band gap. (3) For the oxygen interstitials, transition levels occur both near the valence band maximum and the conduction band minimum.

  5. Assimilation of Cloud- and Land-Affected TOVS/ATOVS Level 1B Radiances in DAO's Next Generation Finite-Volume Data Assimilation System

    NASA Technical Reports Server (NTRS)

    Joiner, J.; daSilva, A.; Einaudi, Franco (Technical Monitor)

    2001-01-01

    The Physical-space/Finite-volume Data Assimilation System (fvDAS) is the next generation global atmospheric data assimilation system in development at the Data Assimilation Office (DAO) at NASA's Goddard Space Flight Center. It is based on a new finite-volume general circulation model jointly developed by NASA and NCAR, and on the Physical-Space Statistical Analysis System (PSAS) developed at the DAO. In this talk we will focus on the assimilation of data from the (Advanced) TIROS Operational Vertical Sounder (ATOVS), with emphasis on the impact of cloud- and land-affected level 1B radiances. Recently, it has been shown that the use of observations from satellite-borne microwave and infrared radiometers in data assimilation systems consistently increases forecast skill. Considerable effort has been expended over the past two decades, particularly with the (Advanced) TIROS Operational Vertical Sounder (ATOVS), to achieve this result. The positive impact on forecast skill has resulted from improvements in quality control algorithms, systematic error correction schemes, and more sophisticated data assimilation algorithms. Despite these advances, there are still many issues regarding the use of satellite data in data assimilation systems that remain unresolved. In particular, most operational centers still do not assimilate cloud- and land-affected TOVS data. In this study, we evaluate the impact of assimilating cloud-and land-affected TOVS/ATOVS level 1B data in DAO's next generation fvDAS, using a 1D variational scheme. We will discuss the impact of these data on both tropospheric and stratospheric forecasts, as well as on the general aspects of the earth climate system.

  6. A new numerical framework to simulate viscoelastic free-surface flows with the finite-volume method

    NASA Astrophysics Data System (ADS)

    Comminal, R.; Spangenberg, J.; Hattel, J. H.

    2015-04-01

    A new method for the simulation of 2D viscoelastic flow is presented. Numerical stability is obtained by the logarithmic-conformation change of variable, and a fully-implicit pure-streamfunction flow formulation, without use of any artificial diffusion. As opposed to other simulation results, our calculations predict a hydrodynamic instability in the 4:1 contraction geometry at a Weissenberg number of order 4. This new result is in qualitative agreement with the prediction of a non-linear subcritical elastic instability in Poiseuille flow. Our viscoelastic flow solver is coupled with a volume-of-fluid solver in order to predict free- surfaces in extrusion.

  7. 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. Structural and functional adaptation in the rat myocardium and coronary vascular bed caused by changes in pressure and volume load.

    PubMed

    Friberg, P

    1985-01-01

    The structural and functional characteristics of the myocardium and coronary vessels are major determinants of cardiac function. Both can be influenced by long-term hemodynamic changes, such as sustained alterations of pressure and/or volume load on the heart. The diastolic pressure-volume relationship of the left ventricle (LV) was evaluated in arrested isolated hearts from spontaneously hypertensive rats (SHR), Wistar Kyoto normotensive rats (WKY), pregnant and hyperthyroid SHR and WKY. Such measurements of the LV dimensions were also performed after antihypertensive therapy by hydralazine, felodipine, metoprolol and alpha-methyldopa. Cardiac function was studied in a perfusion system in which external work could be measured at various pre- and afterloads. Coronary flow and O2-extraction could also be determined. LV function was examined in young and aged SHR and WKY, in metoprolol-felodipine treated SHR and in two-kidney, one clip hypertension before and after its reversal by renal artery unclipping. The SHR LV in early established primary hypertension mainly showed eccentric hypertrophy, with increased LV enddiastolic volume for a given filling pressure and a marginal reduction of wall to lumen ratio (w/ri). Hence, a higher stroke volume could be delivered for a given myocardial fibre shortening. Nevertheless, when challenged by high afterloads, LV function in SHR was considerably augmented compared with WKY. The antihypertensive drugs used reduce arterial pressure in different ways, which may differently affect cardiac design. Generally, the results suggest that wall thickness was structurally adapted to keep w/ri balanced to the prevailing blood pressure, while internal radius was adapted to long-term changes in diastolic filling. Thus sympatholytic drugs which lowered arterial pressure by reducing cardiac output, induced a reduction of wall thickness at a minor change of internal radius, while drugs which reduced pressure by systemic vasodilation increased

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

    NASA Astrophysics Data System (ADS)

    Boscheri, Walter; Dumbser, Michael

    2014-10-01

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

  10. Effects of different volume-equated resistance training loading strategies on muscular adaptations in well-trained men.

    PubMed

    Schoenfeld, Brad J; Ratamess, Nicholas A; Peterson, Mark D; Contreras, Bret; Sonmez, G T; Alvar, Brent A

    2014-10-01

    Regimented resistance training has been shown to promote marked increases in skeletal muscle mass. Although muscle hypertrophy can be attained through a wide range of resistance training programs, the principle of specificity, which states that adaptations are specific to the nature of the applied stimulus, dictates that some programs will promote greater hypertrophy than others. Research is lacking, however, as to the best combination of variables required to maximize hypertophic gains. The purpose of this study was to investigate muscular adaptations to a volume-equated bodybuilding-type training program vs. a powerlifting-type routine in well-trained subjects. Seventeen young men were randomly assigned to either a hypertrophy-type resistance training group that performed 3 sets of 10 repetition maximum (RM) with 90 seconds rest or a strength-type resistance training (ST) group that performed 7 sets of 3RM with a 3-minute rest interval. After 8 weeks, no significant differences were noted in muscle thickness of the biceps brachii. Significant strength differences were found in favor of ST for the 1RM bench press, and a trend was found for greater increases in the 1RM squat. In conclusion, this study showed that both bodybuilding- and powerlifting-type training promote similar increases in muscular size, but powerlifting-type training is superior for enhancing maximal strength. PMID:24714538

  11. CALCULATION OF DELTA I = 3/2 KAON WEAK MATRIX ELEMENTS INCLUDING TWO-PION INTERACTION EFFECTS IN FINITE VOLUME.

    SciTech Connect

    YAMAZAKI, T.

    2006-07-23

    We calculate {Delta}I = 3/2 kaon decay matrix elements using domain wall fermions and the DBW2 gauge action at one coarse lattice spacing corresponding to a{sup -1} = 1.3 GeV. We employ the Lellouch and Luescher formula and its extension for non-zero total momentum to extract the infinite volume, center-of-mass frame decay amplitudes. The decay amplitudes obtained from the methods correspond to those from the indirect method with full order chiral perturbation theory. We confirm that the result is consistent with the previous result calculated with H-parity (anti-periodic) boundary condition by investigating the relative momentum dependence. We evaluate the decay amplitude ReA{sub 2} at the physical point by a chiral extrapolation with a polynomial function of m{sub {pi}}{sup 2} and the relative momentum as well as the {Delta}I = 3/2 electroweak penguin contributions to {var_epsilon}{prime}/{var_epsilon}. We found that the result of ReA{sub 2} reasonably agrees with the experiment.

  12. 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

  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. Unified Modeling Language description of the object-oriented multi-scale adaptive finite element method for Step-and-Flash Imprint Lithography Simulations

    NASA Astrophysics Data System (ADS)

    Paszyński, Maciej; Gurgul, Piotr; Sieniek, Marcin; Pardo, David

    2010-06-01

    In the first part of the paper we present the multi-scale simulation of the Step-and-Flash Imprint Lithography (SFIL), a modern patterning process. The simulation utilizes the hp adaptive Finite Element Method (hp-FEM) coupled with Molecular Statics (MS) model. Thus, we consider the multi-scale problem, with molecular statics applied in the areas of the mesh where the highest accuracy is required, and the continuous linear elasticity with thermal expansion coefficient applied in the remaining part of the domain. The degrees of freedom from macro-scale element's nodes located on the macro-scale side of the interface have been identified with particles from nano-scale elements located on the nano-scale side of the interface. In the second part of the paper we present Unified Modeling Language (UML) description of the resulting multi-scale application (hp-FEM coupled with MS). We investigated classical, procedural codes from the point of view of the object-oriented (O-O) programming paradigm. The discovered hierarchical structure of classes and algorithms makes the UML project as independent on the spatial dimension of the problem as possible. The O-O UML project was defined at an abstract level, independent on the programming language used.

  15. Impact of protein and carbohydrate supplementation on plasma volume expansion and thermoregulatory adaptation by aerobic training in older men.

    PubMed

    Okazaki, Kazunobu; Ichinose, Takashi; Mitono, Hiroyuki; Chen, Mian; Masuki, Shizue; Endoh, Hiroshi; Hayase, Hideki; Doi, Tatsuya; Nose, Hiroshi

    2009-09-01

    We examined whether protein-carbohydrate (CHO) supplementation immediately after exercise each day during aerobic training facilitated plasma volume (PV) expansion and thermoregulatory and cardiovascular adaptations in older men. Fourteen moderately active older men [68 +/- 5 (SD) yr] were divided into two groups so as to have no significant differences in anthropometric measures, PV, and peak oxygen consumption rate (Vo(2peak)). Each group was provided with a mixture of protein and CHO (3.2 kcal, 0.18 g protein/kg body wt, Pro-CHO, n = 7) or a non-protein and low-calorie placebo (0.5 kcal, 0 g protein/kg body wt, CNT, n = 7) immediately after cycling exercise (60-75% Vo(2peak), 60 min/day, 3 days/wk) each day for 8 wk at approximately 19 degrees C ambient temperature (T(a)) and approximately 43% relative humidity (RH). Before and after training, we measured PV, cardiac stroke volume (SV), and esophageal temperature (T(es)) during 20-min exercise at 60% of pretraining Vo(2peak) at 30 degrees C T(a) and 50% RH. Moreover, we determined the sensitivity of the chest sweat rate (DeltaSR/DeltaT(es)) and forearm vascular conductance (DeltaFVC/DeltaT(es)) in response to increased T(es) during exercise. After training, PV increased by approximately 6% in Pro-CHO (P < 0.001), with an approximately 10% increase in SV during exercise (P < 0.001), but not in CNT (P > 0.07). DeltaFVC/DeltaT(es) increased by 80% and DeltaSR/DeltaT(es) by 18% in Pro-CHO (both P < 0.01) but not in CNT (P > 0.07). Moreover, we found a significant interactive effect of group x training on PV, SV, and DeltaFVC/DeltaT(es) (all P < 0.02) but with no significant effect of group (P > 0.4), suggesting that the supplement enhanced these responses to aerobic training. Thus postexercise protein-CHO supplementation during training caused PV expansion and facilitated thermoregulatory and cardiovascular adaptations, possibly providing a new training regimen for older men. PMID:19608927

  16. Volume-equated high- and low-repetition daily undulating programming strategies produce similar hypertrophy and strength adaptations.

    PubMed

    Klemp, Alex; Dolan, Chad; Quiles, Justin M; Blanco, Rocky; Zoeller, Robert F; Graves, B Sue; Zourdos, Michael C

    2016-07-01

    The overarching aim of this study was to compare volume-equated high-repetition daily undulating periodization (DUPHR) versus a low-repetition daily undulating periodization (DUPLR) program for muscle performance. Sixteen college-aged (23 ± 3 years) resistance-trained males were counterbalanced into 2 groups: (i) DUPHR (n = 8), with a weekly training order of 12 repetitions (Day 1), 10 repetitions (Day 2), and 8 repetitions (Day 3); and (ii) DUPLR (n = 8), with a weekly training order of 6 repetitions (Day 1), 4 repetitions (Day 2), and 2 repetitions (Day 3). Both groups trained 3 times/week for 8 weeks on nonconsecutive days, with pre- and post-training testing during weeks 1 and 8. Participants performed only squat and bench press exercises each session. Changes in one-repetition maximum (1RM) strength, muscle thickness (MT), and muscular endurance (ME) were assessed. Both groups significantly increased 1RM strength for both squat and bench press (p < 0.01), and no group differences existed (p > 0.05). Similarly, both groups experienced significant increases in chest, lateral quadriceps distal, and anterior quadriceps MT (p < 0.05), but no change was present in either group for lateral quadriceps mid MT (p < 0.05). No group differences were discovered for changes in MT (p > 0.05). ME did not significantly change in the squat or bench press for either group (p > 0.05); however, for squat ME, a moderate effect size was observed for DUPHR (0.57) versus a trivial effect size for DUPLR (0.17). Our findings suggest that in previously trained males, training volume is a significant contributor to strength and hypertrophy adaptations, which occur independently of specific repetition ranges. PMID:27218448

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

    NASA Astrophysics Data System (ADS)

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

    2015-10-01

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

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

    SciTech Connect

    Norman, Matthew R

    2014-01-01

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

  19. Application of the high-resolution finite-volume NASA/NCAR Climate Model for Medium-Range Weather Prediction Experiments

    NASA Astrophysics Data System (ADS)

    Lin, S. J. L.; Shen, B. W. S.; Putman, W. P.; Chern, J. D. C.

    2003-04-01

    A high-resolution version of the finite-volume climate model (fvGCM) jointly developed by NASA/DAO and NCAR/CGD has been used operationally at NASA/DAO for data assimilation and stratospheric re-analysis. The fvGCM has been regarded as a climate model because the physics packages were originally developed and tuned for low-resolution climate simulations. It was therefore unclear if the fvGCM would do well for medium-range weather predictions. In this study we carried out the so-called transplant experiment in which the forecasts from fvGCM were initialized, not with its own data assimilation system, the fvDAS, but with foreign data from the NCEP's operational system. The forecasts from fvGCM were then compared to that from NCEP's Global Forecasts system (GFS) using the same initial conditions. Despite some initial problems and disadvantages (e.g., initial shocks due to different physics, incompatible land initial conditions, different vertical/horizontal resolution, and different terrain), it is found that the forecasts from fvGCM using NCEP initial conditions are very competitive, particularly for the winter hemisphere.

  20. 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.