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Sample records for high-order finite volume

  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. 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.

  3. 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.

  4. 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

  5. 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.

  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. 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

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

  16. 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.

  17. 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

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  19. 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

  20. 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.

  1. 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.

  2. 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.

  3. 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

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

  6. 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

  7. High-order finite element methods for cardiac monodomain simulations.

    PubMed

    Vincent, Kevin P; Gonzales, Matthew J; Gillette, Andrew K; Villongco, Christopher T; Pezzuto, Simone; Omens, Jeffrey H; Holst, Michael J; McCulloch, Andrew D

    2015-01-01

    Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783

  8. High-order finite element methods for cardiac monodomain simulations

    PubMed Central

    Vincent, Kevin P.; Gonzales, Matthew J.; Gillette, Andrew K.; Villongco, Christopher T.; Pezzuto, Simone; Omens, Jeffrey H.; Holst, Michael J.; McCulloch, Andrew D.

    2015-01-01

    Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783

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

    NASA Technical Reports Server (NTRS)

    Fisher, Travis C.; Carpenter, Mark H.

    2013-01-01

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

  10. High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains

    NASA Astrophysics Data System (ADS)

    Fisher, Travis C.; Carpenter, Mark H.

    2013-11-01

    Nonlinear entropy stability is used to derive provably stable high-order finite difference operators including boundary closure stencils, for the compressible Navier-Stokes equations. A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks. Viscous terms are approximated using conservative, entropy stable, narrow-stencil finite difference operators. The efficacy of the new discrete operators is demonstrated using both smooth and discontinuous test cases.

  11. High Order Finite Difference Methods for Multiscale Complex Compressible Flows

    NASA Technical Reports Server (NTRS)

    Sjoegreen, Bjoern; Yee, H. C.

    2002-01-01

    The classical way of analyzing finite difference schemes for hyperbolic problems is to investigate as many as possible of the following points: (1) Linear stability for constant coefficients; (2) Linear stability for variable coefficients; (3) Non-linear stability; and (4) Stability at discontinuities. We will build a new numerical method, which satisfies all types of stability, by dealing with each of the points above step by step.

  12. Geometric conservation law and applications to high-order finite difference schemes with stationary grids

    NASA Astrophysics Data System (ADS)

    Deng, Xiaogang; Mao, Meiliang; Tu, Guohua; Liu, Huayong; Zhang, Hanxin

    2011-02-01

    The geometric conservation law (GCL) includes the volume conservation law (VCL) and the surface conservation law (SCL). Though the VCL is widely discussed for time-depending grids, in the cases of stationary grids the SCL also works as a very important role for high-order accurate numerical simulations. The SCL is usually not satisfied on discretized grid meshes because of discretization errors, and the violation of the SCL can lead to numerical instabilities especially when high-order schemes are applied. In order to fulfill the SCL in high-order finite difference schemes, a conservative metric method (CMM) is presented. This method is achieved by computing grid metric derivatives through a conservative form with the same scheme applied for fluxes. The CMM is proven to be a sufficient condition for the SCL, and can ensure the SCL for interior schemes as well as boundary and near boundary schemes. Though the first-level difference operators δ3 have no effects on the SCL, no extra errors can be introduced as δ3 = δ2. The generally used high-order finite difference schemes are categorized as central schemes (CS) and upwind schemes (UPW) based on the difference operator δ1 which are used to solve the governing equations. The CMM can be applied to CS and is difficult to be satisfied by UPW. Thus, it is critical to select the difference operator δ1 to reduce the SCL-related errors. Numerical tests based on WCNS-E-5 show that the SCL plays a very important role in ensuring free-stream conservation, suppressing numerical oscillations, and enhancing the robustness of the high-order scheme in complex grids.

  13. Finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems

    NASA Astrophysics Data System (ADS)

    Xie, Xue-Jun; Zhang, Xing-Hui; Zhang, Kemei

    2016-07-01

    This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a ? Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.

  14. Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel; Wang, Z. J.

    2004-01-01

    A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of

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

    NASA Technical Reports Server (NTRS)

    Nordstrom, Jan; Carpenter, Mark H.

    1999-01-01

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

  16. High order curvilinear finite elements for elastic–plastic Lagrangian dynamics

    SciTech Connect

    Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.

    2014-01-15

    This paper presents a high-order finite element method for calculating elastic–plastic flow on moving curvilinear meshes and is an extension of our general high-order curvilinear finite element approach for solving the Euler equations of gas dynamics in a Lagrangian frame [1,2]. In order to handle transition to plastic flow, we formulate the stress–strain relation in rate (or incremental) form and augment our semi-discrete equations for Lagrangian hydrodynamics with an additional evolution equation for the deviatoric stress which is valid for arbitrary order spatial discretizations of the kinematic and thermodynamic variables. The semi-discrete equation for the deviatoric stress rate is developed for 2D planar, 2D axisymmetric and full 3D geometries. For each case, the strain rate is approximated via a collocation method at zone quadrature points while the deviatoric stress is approximated using an L{sub 2} projection onto the thermodynamic basis. We apply high order, energy conserving, explicit time stepping methods to the semi-discrete equations to develop the fully discrete method. We conclude with numerical results from an extensive series of verification tests that demonstrate several practical advantages of using high-order finite elements for elastic–plastic flow.

  17. 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.

  18. High-order nite volume WENO schemes for the shallow water equations with dry states

    SciTech Connect

    Xing, Yulong; Shu, Chi-wang

    2011-01-01

    The shallow water equations are used to model flows in rivers and coastal areas, and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. These equations have still water steady state solutions in which the flux gradients are balanced by the source term. It is desirable to develop numerical methods which preserve exactly these steady state solutions. Another main difficulty usually arising from the simulation of dam breaks and flood waves flows is the appearance of dry areas where no water is present. If no special attention is paid, standard numerical methods may fail near dry/wet front and produce non-physical negative water height. A high-order accurate finite volume weighted essentially non-oscillatory (WENO) scheme is proposed in this paper to address these difficulties and to provide an efficient and robust method for solving the shallow water equations. A simple, easy-to-implement positivity-preserving limiter is introduced. One- and two-dimensional numerical examples are provided to verify the positivity-preserving property, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.

  19. High order finite difference methods with subcell resolution for advection equations with stiff source terms

    SciTech Connect

    Wang, Wei; Shu, Chi-Wang; Yee, H.C.; Sjögreen, Björn

    2012-01-01

    A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with the computed flow variables in the shock region modified by the Harten subcell resolution idea. For numerical experiments, a fifth-order finite-difference WENO scheme and its anti-diffusion WENO variant are considered. A wide range of 1D and 2D scalar and Euler system test cases are investigated. Studies indicate that for the considered test cases, the new method maintains high order accuracy in space for smooth flows, and for stiff source terms with discontinuities, it can capture the correct propagation speed of discontinuities in very coarse meshes with reasonable CFL numbers.

  20. Efficient simulation of cardiac electrical propagation using high order finite elements

    NASA Astrophysics Data System (ADS)

    Arthurs, Christopher J.; Bishop, Martin J.; Kay, David

    2012-05-01

    We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

  1. Direct Simulations of Transition and Turbulence Using High-Order Accurate Finite-Difference Schemes

    NASA Technical Reports Server (NTRS)

    Rai, Man Mohan

    1997-01-01

    In recent years the techniques of computational fluid dynamics (CFD) have been used to compute flows associated with geometrically complex configurations. However, success in terms of accuracy and reliability has been limited to cases where the effects of turbulence and transition could be modeled in a straightforward manner. Even in simple flows, the accurate computation of skin friction and heat transfer using existing turbulence models has proved to be a difficult task, one that has required extensive fine-tuning of the turbulence models used. In more complex flows (for example, in turbomachinery flows in which vortices and wakes impinge on airfoil surfaces causing periodic transitions from laminar to turbulent flow) the development of a model that accounts for all scales of turbulence and predicts the onset of transition may prove to be impractical. Fortunately, current trends in computing suggest that it may be possible to perform direct simulations of turbulence and transition at moderate Reynolds numbers in some complex cases in the near future. This seminar will focus on direct simulations of transition and turbulence using high-order accurate finite-difference methods. The advantage of the finite-difference approach over spectral methods is that complex geometries can be treated in a straightforward manner. Additionally, finite-difference techniques are the prevailing methods in existing application codes. In this seminar high-order-accurate finite-difference methods for the compressible and incompressible formulations of the unsteady Navier-Stokes equations and their applications to direct simulations of turbulence and transition will be presented.

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

    NASA Astrophysics Data System (ADS)

    Wu, Kailiang; Tang, Huazhong

    2015-10-01

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

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

    NASA Technical Reports Server (NTRS)

    Rai, Man M.; Chakrvarthy, Sukumar

    1993-01-01

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

  4. High-order lattice Boltzmann models for wall-bounded flows at finite Knudsen numbers

    NASA Astrophysics Data System (ADS)

    Feuchter, C.; Schleifenbaum, W.

    2016-07-01

    We analyze a large number of high-order discrete velocity models for solving the Boltzmann-Bhatnagar-Gross-Krook equation for finite Knudsen number flows. Using the Chapman-Enskog formalism, we prove for isothermal flows a relation identifying the resolved flow regimes for low Mach numbers. Although high-order lattice Boltzmann models recover flow regimes beyond the Navier-Stokes level, we observe for several models significant deviations from reference results. We found this to be caused by their inability to recover the Maxwell boundary condition exactly. By using supplementary conditions for the gas-surface interaction it is shown how to systematically generate discrete velocity models of any order with the inherent ability to fulfill the diffuse Maxwell boundary condition accurately. Both high-order quadratures and an exact representation of the boundary condition turn out to be crucial for achieving reliable results. For Poiseuille flow, we can reproduce the mass flow and slip velocity up to the Knudsen number of 1. Moreover, for small Knudsen numbers, the Knudsen layer behavior is recovered.

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

    SciTech Connect

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

    2012-01-01

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

  6. Multi-Dimensional High Order Essentially Non-Oscillatory Finite Difference Methods in Generalized Coordinates

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang

    1998-01-01

    This project is about the development of high order, non-oscillatory type schemes for computational fluid dynamics. Algorithm analysis, implementation, and applications are performed. Collaborations with NASA scientists have been carried out to ensure that the research is relevant to NASA objectives. The combination of ENO finite difference method with spectral method in two space dimension is considered, jointly with Cai [3]. The resulting scheme behaves nicely for the two dimensional test problems with or without shocks. Jointly with Cai and Gottlieb, we have also considered one-sided filters for spectral approximations to discontinuous functions [2]. We proved theoretically the existence of filters to recover spectral accuracy up to the discontinuity. We also constructed such filters for practical calculations.

  7. High-order cyclo-difference techniques: An alternative to finite differences

    NASA Technical Reports Server (NTRS)

    Carpenter, Mark H.; Otto, John C.

    1993-01-01

    The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.

  8. A fast high-order finite difference algorithm for pricing American options

    NASA Astrophysics Data System (ADS)

    Tangman, D. Y.; Gopaul, A.; Bhuruth, M.

    2008-12-01

    We describe an improvement of Han and Wu's algorithm [H. Han, X.Wu, A fast numerical method for the Black-Scholes equation of American options, SIAM J. Numer. Anal. 41 (6) (2003) 2081-2095] for American options. A high-order optimal compact scheme is used to discretise the transformed Black-Scholes PDE under a singularity separating framework. A more accurate free boundary location based on the smooth pasting condition and the use of a non-uniform grid with a modified tridiagonal solver lead to an efficient implementation of the free boundary value problem. Extensive numerical experiments show that the new finite difference algorithm converges rapidly and numerical solutions with good accuracy are obtained. Comparisons with some recently proposed methods for the American options problem are carried out to show the advantage of our numerical method.

  9. Combined Immersed-Boundary/High-Order Finite Difference Methods For Simulations of Acoustic Scattering

    NASA Astrophysics Data System (ADS)

    Arias-Ramirez, Walter; Olson, Britton; Wolf, William; Lawrence Livermore National Laboratory Team; University of Campinas Team

    2015-11-01

    The suitability of a continuing forcing immersed boundary method (IBM) combined with a high-order finite difference method is examined on several acoustic scattering problems. A suite of two-dimensional numerical simulations of canonical cases are conducted with the aim of analyzing the error behavior associated with the IBM, through wave reflection, wave diffraction, and the shock-boundary layer interaction phenomena. The compressible Navier-Stokes equations are solved using the Miranda code developed at Lawrence Livermore National Laboratory. Comparison of analytical solution against numerical results is shown for different flow parameters. Preliminary results indicate that the continuing forcing approach has the largest error in wave reflection compared to analytical solution. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.

  10. A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

    DOE PAGESBeta

    Guerra, Jorge E.; Ullrich, Paul A.

    2016-06-01

    Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy alsomore » eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Lastly, our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less

  11. A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

    NASA Astrophysics Data System (ADS)

    Guerra, Jorge E.; Ullrich, Paul A.

    2016-06-01

    Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.

  12. A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

    DOE PAGESBeta

    Guerra, Jorge E.; Ullrich, Paul A.

    2016-06-01

    Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy alsomore » eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less

  13. A High-order Eulerian-Lagrangian Finite Element Method for Coupled Electro-mechanical Systems

    NASA Astrophysics Data System (ADS)

    Brandstetter, Gerd

    The main focus of this work is on the development of a high-order Eulerian-Lagrangian finite element method for the simulation of electro-mechanical systems. The coupled problem is solved by a staggered scheme, where the mechanical motion is discretized by standard Lagrangian finite elements, and the electrical field is solved on a fixed Eulerian grid with embedded boundary conditions. Traditional Lagrangian-Lagrangian or arbitrary Lagrangian-Eulerian (ALE) methods encounter deficiencies, for example, when dealing with mesh distortion due to large deformations, or topology changes due to contacting bodies. The presented Eulerian-Lagrangian approach addresses these issues in a natural way. Within this context we develop a high-order immersed boundary discontinuous-Galerkin (IB-DG) method, which is shown to be necessary for (i) the accurate representation of the electrical gradient along nonlinear boundary features such as singular corners, and (ii) to achieve full convergence during the iterative global solution. We develop an implicit scheme based on the mid-point rule, as well as an explicit scheme based on the centered-difference method, with the incorporation of energy conserving, frictionless contact algorithms for an elastic-to-rigid-surface contact. The performance of the proposed method is assessed for several benchmark tests: the electro-static force vector around a singular corner, the quasi-static pull-in of an electro-mechanically actuated switch, the excitation of a carbon nanotube at resonance, and the cyclic impact simulation of a micro-electro-mechanical resonant-switch. We report improved accuracy for the high-order method as compared to low-order methods, and linear convergence in the iterative solution of the staggered scheme. Additionally, we investigate a Newton-Krylov shooting scheme in order to directly find cyclic steady states of electro-mechanical devices excited at resonance-- as opposed to a naive time-stepping from zero initial

  14. Modeling fragmentation with new high order finite element technology and node splitting

    NASA Astrophysics Data System (ADS)

    Olovsson, Lars; Limido, Jérôme; Lacome, Jean-Luc; Grønsund Hanssen, Arve; Petit, Jacques

    2015-09-01

    The modeling of fragmentation has historically been linked to the weapons industry where the main goal is to optimize a bomb or to design effective blast shields. Numerical modeling of fragmentation from dynamic loading has traditionally been modeled by legacy finite element solvers that rely on element erosion to model material failure. However this method results in the removal of too much material. This is not realistic as retaining the mass of the structure is critical to modeling the event correctly. We propose a new approach implemented in the IMPETUS AFEA SOLVER® based on the following: New High Order Finite Elements that can easily deal with very large deformations; Stochastic distribution of initial damage that allows for a non homogeneous distribution of fragments; and a Node Splitting Algorithm that allows for material fracture without element erosion that is mesh independent. The approach is evaluated for various materials and scenarios: -Titanium ring electromagnetic compression; Hard steel Taylor bar impact, Fused silica Taylor bar impact, Steel cylinder explosion, The results obtained from the simulations are representative of the failure mechanisms observed experimentally. The main benefit of this approach is good energy conservation (no loss of mass) and numerical robustness even in complex situations.

  15. 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.

  16. A block interface flux reconstruction method for numerical simulation with high order finite difference scheme

    NASA Astrophysics Data System (ADS)

    Gao, Junhui

    2013-05-01

    Overlap grid is usually used in numerical simulation of flow with complex geometry by high order finite difference scheme. It is difficult to generate overlap grid and the connectivity information between adjacent blocks, especially when interpolation is required for non-coincident overlap grids. In this study, an interface flux reconstruction (IFR) method is proposed for numerical simulation using high order finite difference scheme with multi-block structured grids. In this method the neighboring blocks share a common face, and the fluxes on each block are matched to set the boundary conditions for each interior block. Therefore this method has the promise of allowing discontinuous grids on either side of an interior block interface. The proposed method is proven to be stable for 7-point central DRP scheme coupled with 4-point and 5-point boundary closure schemes, as well as the 4th order compact scheme coupled with 3rd order boundary closure scheme. Four problems are numerically solved with the developed code to validate the interface flux reconstruction method in this study. The IFR method coupled with the 4th order DRP scheme or compact scheme is validated to be 4th order accuracy with one and two dimensional waves propagation problems. Two dimensional pulse propagation in mean flow is computed with wavy mesh to demonstrate the ability of the proposed method for non-uniform grid. To demonstrate the ability of the proposed method for complex geometry, sound scattering by two cylinders is simulated and the numerical results are compared with the analytical data. It is shown that the numerical results agree well with the analytical data. Finally the IFR method is applied to simulate viscous flow pass a cylinder at Reynolds number 150 to show its capability for viscous problem. The computed pressure coefficient on the cylinder surface, the frequency of vortex shedding, the lift and drag coefficients are presented. The numerical results are compared with the data

  17. Characterization of high order spatial discretizations and lumping techniques for discontinuous finite element SN transport

    SciTech Connect

    Maginot, P. G.; Ragusa, J. C.; Morel, J. E.

    2013-07-01

    We examine several possible methods of mass matrix lumping for discontinuous finite element discrete ordinates transport using a Lagrange interpolatory polynomial trial space. Though positive outflow angular flux is guaranteed with traditional mass matrix lumping in a purely absorbing 1-D slab cell for the linear discontinuous approximation, we show that when used with higher degree interpolatory polynomial trial spaces, traditional lumping does yield strictly positive outflows and does not increase in accuracy with an increase in trial space polynomial degree. As an alternative, we examine methods which are 'self-lumping'. Self-lumping methods yield diagonal mass matrices by using numerical quadrature restricted to the Lagrange interpolatory points. Using equally-spaced interpolatory points, self-lumping is achieved through the use of closed Newton-Cotes formulas, resulting in strictly positive outflows in pure absorbers for odd power polynomials in 1-D slab geometry. By changing interpolatory points from the traditional equally-spaced points to the quadrature points of the Gauss-Legendre or Lobatto-Gauss-Legendre quadratures, it is possible to generate solution representations with a diagonal mass matrix and a strictly positive outflow for any degree polynomial solution representation in a pure absorber medium in 1-D slab geometry. Further, there is no inherent limit to local truncation error order of accuracy when using interpolatory points that correspond to the quadrature points of high order accuracy numerical quadrature schemes. (authors)

  18. A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations

    NASA Technical Reports Server (NTRS)

    Gerritsen, Margot; Olsson, Pelle

    1996-01-01

    We derive a high-order finite difference scheme for the Euler equations that satisfies a semi-discrete energy estimate, and present an efficient strategy for the treatment of discontinuities that leads to sharp shock resolution. The formulation of the semi-discrete energy estimate is based on a symmetrization of the Euler equations that preserves the homogeneity of the flux vector, a canonical splitting of the flux derivative vector, and the use of difference operators that satisfy a discrete analogue to the integration by parts procedure used in the continuous energy estimate. Around discontinuities or sharp gradients, refined grids are created on which the discrete equations are solved after adding a newly constructed artificial viscosity. The positioning of the sub-grids and computation of the viscosity are aided by a detection algorithm which is based on a multi-scale wavelet analysis of the pressure grid function. The wavelet theory provides easy to implement mathematical criteria to detect discontinuities, sharp gradients and spurious oscillations quickly and efficiently.

  19. Landing-gear noise prediction using high-order finite difference schemes

    NASA Astrophysics Data System (ADS)

    Liu, Wen; Wook Kim, Jae; Zhang, Xin; Angland, David; Caruelle, Bastien

    2013-07-01

    Aerodynamic noise from a generic two-wheel landing-gear model is predicted by a CFD/FW-H hybrid approach. The unsteady flow-field is computed using a compressible Navier-Stokes solver based on high-order finite difference schemes and a fully structured grid. The calculated time history of the surface pressure data is used in an FW-H solver to predict the far-field noise levels. Both aerodynamic and aeroacoustic results are compared to wind tunnel measurements and are found to be in good agreement. The far-field noise was found to vary with the 6th power of the free-stream velocity. Individual contributions from three components, i.e. wheels, axle and strut of the landing-gear model are also investigated to identify the relative contribution to the total noise by each component. It is found that the wheels are the dominant noise source in general. Strong vortex shedding from the axle is the second major contributor to landing-gear noise. This work is part of Airbus LAnding Gear nOise database for CAA validatiON (LAGOON) program with the general purpose of evaluating current CFD/CAA and experimental techniques for airframe noise prediction.

  20. Matched interface and boundary (MIB) for the implementation of boundary conditions in high-order central finite differences

    PubMed Central

    Zhao, Shan; Wei, G. W.

    2010-01-01

    SUMMARY High-order central finite difference schemes encounter great difficulties in implementing complex boundary conditions. This paper introduces the matched interface and boundary (MIB) method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high-order central finite difference schemes. To attain arbitrarily high order, the MIB method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions. The proposed approach is extensively validated via boundary value problems, initial-boundary value problems, eigenvalue problems, and high-order differential equations. Successful implementations are given to not only Dirichlet, Neumann, and Robin boundary conditions, but also more general ones, such as multiple boundary conditions in high-order differential equations and time-dependent boundary conditions in evolution equations. Detailed stability analysis of the MIB method is carried out. The MIB method is shown to be able to deliver high-order accuracy, while maintaining the same or similar stability conditions of the standard high-order central difference approximations. The application of the proposed MIB method to the boundary treatment of other non-standard high-order methods is also considered. PMID:20485574

  1. Convergency analysis of the high-order mimetic finite difference method

    SciTech Connect

    Lipnikov, Konstantin; Veiga Da Beirao, L; Manzini, G

    2008-01-01

    We prove second-order convergence of the conservative variable and its flux in the high-order MFD method. The convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients. For the case of non-constant coefficients, we also develop a new family of high-order MFD methods. Theoretical result are confirmed through numerical experiments.

  2. Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations

    NASA Technical Reports Server (NTRS)

    Nordstrom, Jan; Carpenter, Mark H.

    1998-01-01

    Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.

  3. A Novel High Order Time Domain Vector Finite Element Method for the Simulation of Electromagnetic Devices

    SciTech Connect

    Rieben, R N

    2004-07-20

    The goal of this dissertation is twofold. The first part concerns the development of a numerical method for solving Maxwell's equations on unstructured hexahedral grids that employs both high order spatial and high order temporal discretizations. The second part involves the use of this method as a computational tool to perform high fidelity simulations of various electromagnetic devices such as optical transmission lines and photonic crystal structures to yield a level of accuracy that has previously been computationally cost prohibitive. This work is based on the initial research of Daniel White who developed a provably stable, charge and energy conserving method for solving Maxwell's equations in the time domain that is second order accurate in both space and time. The research presented here has involved the generalization of this procedure to higher order methods. High order methods are capable of yielding far more accurate numerical results for certain problems when compared to corresponding h-refined first order methods , and often times at a significant reduction in total computational cost. The first half of this dissertation presents the method as well as the necessary mathematics required for its derivation. The second half addresses the implementation of the method in a parallel computational environment, its validation using benchmark problems, and finally its use in large scale numerical simulations of electromagnetic transmission devices.

  4. Application of Novel High Order Time Domain Vector Finite Element Method to Photonic Band-Gap Waveguides

    SciTech Connect

    Rieben, R; White, D; Rodrigue, G

    2004-01-13

    In this paper we motivate the use of a novel high order time domain vector finite element method that is of arbitrary order accuracy in space and up to 5th order accurate in time; and in particular, we apply it to the case of photonic band-gap (PBG) structures. Such structures have been extensively studied in the literature with several practical applications; in particular, for the low loss transmission of electromagnetic energy around sharp 90 degree bends [1]. Typically, such structures are simulated via a numerical solution of Maxwell's equations either in the frequency domain or directly in the time domain over a computational grid. The majority of numerical simulations performed for such structures make use of the widely popular finite difference time domain (FDTD) method [2], where the time dependent electric and magnetic fields are discretized over a ''dual'' grid to second order accuracy in space and time. However, such methods do not generalize to unstructured, non-orthogonal grids or to higher order spatial discretization schemes. To simulate more complicated structures with curved boundaries, such as the structure of [3], a cell based finite element method with curvilinear elements is preferred over standard stair-stepped Cartesian meshes; and to more efficiently reduce the effects of numerical dispersion, a higher order method is highly desirable. In this paper, the high order basis functions of [5] are used in conjunction with the high order energy conserving symplectic time integration algorithms of [6] resulting in a high order, fully mimetic, mixed vector finite element method.

  5. Orbiting binary black hole evolutions with a multipatch high order finite-difference approach

    SciTech Connect

    Pazos, Enrique; Tiglio, Manuel; Duez, Matthew D.; Kidder, Lawrence E.; Teukolsky, Saul A.

    2009-07-15

    We present numerical simulations of orbiting black holes for around 12 cycles, using a high order multipatch approach. Unlike some other approaches, the computational speed scales almost perfectly for thousands of processors. Multipatch methods are an alternative to adaptive mesh refinement, with benefits of simplicity and better scaling for improving the resolution in the wave zone. The results presented here pave the way for multipatch evolutions of black hole-neutron star and neutron star-neutron star binaries, where high resolution grids are needed to resolve details of the matter flow.

  6. CoreSVM: a generalized high-order spectral volume method bearing Conservative Order RElease

    NASA Astrophysics Data System (ADS)

    Lamouroux, Raphael; Gressier, Jeremie; Joly, Laurent; Grondin, Gilles

    2014-11-01

    The spectral volume method (SVM) introduced by Wang in 2002 is based on a compact polynomial reconstruction where the interpolation's degree is driven by the partition of the spectral volumes. We propose a generalization of the SVM which releases the polynomial degree from this constraint and more importantly that allows to resort to any polynomial order inferior to the regular stencil order without changing the original spectral volume partition. Using one-dimensional advection and Burgers equation, we prove that the proposed extended method exhibits versatile high-order convergence together with conservativity properties. This new method is thus named the CoreSVM for Conservative Order-REleased SVM and we therefore explore its potential towards the numerical simulation of stiff problems. It is stressed that CoreSVM is indeed particularly suited to handle discontinuities, as the order-reduction serves to damp the numerical oscillations due to Runge's phenomenon. To ensure computational stability, local p-coarsening is used to obtain the highest adequate polynomial degree. It is advocated finally that, since the CoreSVM sets the polynomial order adaptation free from any stencil changes, these features do not come at the expense of any extra remeshing or data adaptation cost. Part of this research was funded by the French DGA.

  7. Application of High Order Acoustic Finite Elements to Transmission Losses and Enclosure Problems

    NASA Technical Reports Server (NTRS)

    Craggs, A.; Stevenson, G.

    1985-01-01

    A family of acoustic finite elements was developed based on C continuity (acoustic pressure being the nodal variable) and the no-flow condition. The family include triangular, quadrilateral and hexahedral isoparametric elements with linear quadratic and cubic variation in modelling and distortion. Of greatest use in problems with irregular boundaries are the cubic isoparametric elements: the 32 node hexahedral element for three-dimensional systems; and the twelve node quadrilateral and ten node triangular elements for two-dimensional/axisymmetric applications. These elements were applied to problems involving cavity resonances, transmission loss in silencers and the study of end effects, using a Floating Point Systems 164 attached array processor accessed through an Amdahl 5860 mainframe. The elements are presently being used to study the end effects associated with duct terminations within finite enclosures. The transmission losses with various silencers and sidebranches in ducts is also being studied using the same elements.

  8. Advanced modeling strategy for the analysis of heart valve leaflet tissue mechanics using high-order finite element method.

    PubMed

    Mohammadi, Hadi; Bahramian, Fereshteh; Wan, Wankei

    2009-11-01

    Modeling soft tissue using the finite element method is one of the most challenging areas in the field of biomechanical engineering. To date, many models have been developed to describe heart valve leaflet tissue mechanics, which are accurate to some extent. Nevertheless, there is no comprehensive method to modeling soft tissue mechanics, This is because (1) the degree of anisotropy in the heart valve leaflet changes layer by layer due to a variety of collagen fiber densities and orientations that cannot be taken into account in the model and also (2) a constitutive material model fully describing the mechanical properties of the leaflet structure is not available in the literature. In this framework, we develop a new high-order element using p-type finite element formulation to create anisotropic material properties similar to those of the heart valve leaflet tissue in only one single element. This element also takes the nonlinearity of the leaflet tissue into consideration using a bilinear material model. This new element is composed a two-dimensional finite element in the principal directions of leaflet tissue and a p-type finite element in the direction of thickness. The proposed element is easy to implement, much more efficient than standard elements available in commercial finite element packages. This study is one step towards the modeling of soft tissue mechanics using a meshless finite element approach to be applied in real-time haptic feedback of soft-tissue models in virtual reality simulation. PMID:19773193

  9. High order finite difference and multigrid methods for spatially evolving instability in a planar channel

    NASA Technical Reports Server (NTRS)

    Liu, C.; Liu, Z.

    1993-01-01

    The fourth-order finite-difference scheme with fully implicit time-marching presently used to computationally study the spatial instability of planar Poiseuille flow incorporates a novel treatment for outflow boundary conditions that renders the buffer area as short as one wavelength. A semicoarsening multigrid method accelerates convergence for the implicit scheme at each time step; a line-distributive relaxation is developed as a robust fast solver that is efficient for anisotropic grids. Computational cost is no greater than that of explicit schemes, and excellent agreement with linear theory is obtained.

  10. Nonlinear Comparison of High-Order and Optimized Finite-Difference Schemes

    NASA Technical Reports Server (NTRS)

    Hixon, R.

    1998-01-01

    The effect of reducing the formal order of accuracy of a finite-difference scheme in order to optimize its high-frequency performance is investigated using the I-D nonlinear unsteady inviscid Burgers'equation. It is found that the benefits of optimization do carry over into nonlinear applications. Both explicit and compact schemes are compared to Tam and Webb's explicit 7-point Dispersion Relation Preserving scheme as well as a Spectral-like compact scheme derived following Lele's work. Results are given for the absolute and L2 errors as a function of time.

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

    NASA Technical Reports Server (NTRS)

    Baker, A. J.

    1978-01-01

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

  12. Numerical pricing of options using high-order compact finite difference schemes

    NASA Astrophysics Data System (ADS)

    Tangman, D. Y.; Gopaul, A.; Bhuruth, M.

    2008-09-01

    We consider high-order compact (HOC) schemes for quasilinear parabolic partial differential equations to discretise the Black-Scholes PDE for the numerical pricing of European and American options. We show that for the heat equation with smooth initial conditions, the HOC schemes attain clear fourth-order convergence but fail if non-smooth payoff conditions are used. To restore the fourth-order convergence, we use a grid stretching that concentrates grid nodes at the strike price for European options. For an American option, an efficient procedure is also described to compute the option price, Greeks and the optimal exercise curve. Comparisons with a fourth-order non-compact scheme are also done. However, fourth-order convergence is not experienced with this strategy. To improve the convergence rate for American options, we discuss the use of a front-fixing transformation with the HOC scheme. We also show that the HOC scheme with grid stretching along the asset price dimension gives accurate numerical solutions for European options under stochastic volatility.

  13. 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.

  14. A priori grid quality estimation for high-order finite differencing

    NASA Astrophysics Data System (ADS)

    Fattah, Ryu; Angland, David; Zhang, Xin

    2016-06-01

    Structured grids using the finite differencing method contain two sources of grid-induced truncation errors. The first is dependent on the solution field. The second is related only to the metrics of the grid transformation. The accuracy of the grid transformation metrics is affected by the inverse metrics, which are spatial derivatives of the grid in the generalised coordinates. The truncation errors contained in the inverse metrics are generated by the spatial schemes. Fourier analysis shows that the dispersion errors, by spatial schemes, have similarities to the transfer function of spatial filters. This similarity is exploited to define a grid quality metric that can be used to identify areas in the mesh that are likely to generate significant grid-induced errors. An inviscid vortex convection benchmark case is used to quantify the correlation between the grid quality metric and the solution accuracy, for three common geometric features found in grids: abrupt changes in the grid metrics, skewness, and grid stretching. A strong correlation is obtained, provided that the grid transformation errors are the most significant sources of error.

  15. High-order conservative finite difference GLM-MHD schemes for cell-centered MHD

    NASA Astrophysics Data System (ADS)

    Mignone, Andrea; Tzeferacos, Petros; Bodo, Gianluigi

    2010-08-01

    We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. [J. Comput. Phys. 175 (2002) 645-673]. The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.

  16. Fully discrete energy stable high order finite difference methods for hyperbolic problems in deforming domains

    NASA Astrophysics Data System (ADS)

    Nikkar, Samira; Nordström, Jan

    2015-06-01

    A time-dependent coordinate transformation of a constant coefficient hyperbolic system of equations which results in a variable coefficient system of equations is considered. By applying the energy method, well-posed boundary conditions for the continuous problem are derived. Summation-by-Parts (SBP) operators for the space and time discretization, together with a weak imposition of boundary and initial conditions using Simultaneously Approximation Terms (SATs) lead to a provable fully-discrete energy-stable conservative finite difference scheme. We show how to construct a time-dependent SAT formulation that automatically imposes boundary conditions, when and where they are required. We also prove that a uniform flow field is preserved, i.e. the Numerical Geometric Conservation Law (NGCL) holds automatically by using SBP-SAT in time and space. The developed technique is illustrated by considering an application using the linearized Euler equations: the sound generated by moving boundaries. Numerical calculations corroborate the stability and accuracy of the new fully discrete approximations.

  17. Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver

    NASA Astrophysics Data System (ADS)

    Vincenti, H.; Vay, J.-L.

    2016-03-01

    Very high order or pseudo-spectral Maxwell solvers are the method of choice to reduce discretization effects (e.g. numerical dispersion) that are inherent to low order Finite-Difference Time-Domain (FDTD) schemes. However, due to their large stencils, these solvers are often subject to truncation errors in many electromagnetic simulations. These truncation errors come from non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the simulation results. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of the errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solvers and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.

  18. High-order mimetic finite elements for the hydrostatic primitive equations on a cubed-sphere grid using Hamiltonian methods

    NASA Astrophysics Data System (ADS)

    Eldred, Christopher; Dubos, Thomas; Kritsikis, Evaggelos

    2016-04-01

    There has been a great deal of work in the past decade on the development of mimetic and conservative numerical schemes for atmospheric dynamical cores using Hamiltonian methods, such as Dynamico (Dubos et. al 2015). This model conserves mass, potential vorticity and total energy; and posses properties such as a curl-free pressure gradient that does not produce spurious vorticity. Unfortunately, the underlying finite-difference discretization scheme used in Dynamico has been shown to be inconsistent on general grids. An alternative scheme based on mimetic finite elements has been developed for the rotating shallow water equations that solves these accuracy issues but retains the desirable mimetic and conservation properties. Preliminary results on the extension of this scheme to the hydrostatic primitive equations are shown. The compatible 2D finite elements spaces are extended to compatible 3D spaces using tensor products, in a way that preserves their properties. It is shown that use of the same prognostic variables as Dynamico combined with a Lorenz staggering leads to a relatively simple formulation that allows conservation of total energy along with high-order accuracy.

  19. 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.

  20. 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

  1. 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.

  2. Implicit Solution of the Four-field Extended-magnetohydroynamic Equations using High-order High-continuity Finite Elements

    SciTech Connect

    S.C. Jardin; J.A. Breslau

    2004-12-17

    Here we describe a technique for solving the four-field extended-magnetohydrodynamic (MHD) equations in two dimensions. The introduction of triangular high-order finite elements with continuous first derivatives (C{sup 1} continuity) leads to a compact representation compatible with direct inversion of the associated sparse matrices. The split semi-implicit method is introduced and used to integrate the equations in time, yielding unconditional stability for arbitrary time step. The method is applied to the cylindrical tilt mode problem with the result that a non-zero value of the collisionless ion skin depth will increase the growth rate of that mode. The effect of this parameter on the reconnection rate and geometry of a Harris equilibrium and on the Taylor reconnection problem is also demonstrated. This method forms the basis for a generalization to a full extended-MHD description of the plasma with six, eight, or more scalar fields.

  3. A High Order Mixed Vector Finite Element Method for Solving the Time Dependent Maxwell Equations on Unstructured Grids

    SciTech Connect

    Rieben, R N; Rodrigue, G H; White, D A

    2004-03-09

    We present a mixed vector finite element method for solving the time dependent coupled Ampere and Faraday laws of Maxwell's equations on unstructured hexahedral grids that employs high order discretization in both space and time. The method is of arbitrary order accuracy in space and up to 5th order accurate in time, making it well suited for electrically large problems where grid anisotropy and numerical dispersion have plagued other methods. In addition, the method correctly models both the jump discontinuities and the divergence-free properties of the electric and magnetic fields, is charge and energy conserving, conditionally stable, and free of spurious modes. Several computational experiments are performed to demonstrate the accuracy, efficiency and benefits of the method.

  4. 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.

  5. A high-order weighted essentially non-oscillatory (WENO) finite difference scheme for nonlinear degenerate parabolic equations

    NASA Astrophysics Data System (ADS)

    Abedian, Rooholah; Adibi, Hojatollah; Dehghan, Mehdi

    2013-08-01

    In this paper, we propose a new WENO finite difference procedure for nonlinear degenerate parabolic equations which may contain discontinuous solutions. Our scheme is based on the method of lines, with a high-order accurate conservative approximation to each of the diffusion terms based on an idea that has been recently presented by Liu et al. [Y. Liu, C.-W. Shu, M. Zhang, High order finite difference WENO schemes for non-linear degenerate parabolic equations, SIAM J. Sci. Comput. 33 (2011) 939-965]. Our scheme tries to circumvent the negative ideal weights that appear when applying the standard WENO idea, as is done in Liu et al. (2011) [13]. In one-dimensional case, first we obtain an optimum polynomial on a six-points stencil. This optimum polynomial is sixth-order accurate in regions of smoothness. Then, we consider this optimum polynomial as a symmetric and convex combination of four polynomials with ideal weights. Following the methodology of the classic WENO procedure, then we calculate the non-oscillatory weights with the ideal weights. Numerical examples are provided to demonstrate the resolution power and accuracy of the scheme. Finally, the new method is extended to multi-dimensional problems by dimension-by-dimension approach. More examples of multi-dimension problems are presented to show that our method remains non-oscillatory while giving good resolution of discontinuities. Finally, we would like to mention that this paper combines and extends the techniques proposed in [13] and Levy et al. (2000) [24].

  6. High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster

    SciTech Connect

    Komatitsch, Dimitri; Erlebacher, Gordon; Goeddeke, Dominik; Michea, David

    2010-10-01

    We implement a high-order finite-element application, which performs the numerical simulation of seismic wave propagation resulting for instance from earthquakes at the scale of a continent or from active seismic acquisition experiments in the oil industry, on a large cluster of NVIDIA Tesla graphics cards using the CUDA programming environment and non-blocking message passing based on MPI. Contrary to many finite-element implementations, ours is implemented successfully in single precision, maximizing the performance of current generation GPUs. We discuss the implementation and optimization of the code and compare it to an existing very optimized implementation in C language and MPI on a classical cluster of CPU nodes. We use mesh coloring to efficiently handle summation operations over degrees of freedom on an unstructured mesh, and non-blocking MPI messages in order to overlap the communications across the network and the data transfer to and from the device via PCIe with calculations on the GPU. We perform a number of numerical tests to validate the single-precision CUDA and MPI implementation and assess its accuracy. We then analyze performance measurements and depending on how the problem is mapped to the reference CPU cluster, we obtain a speedup of 20x or 12x.

  7. A Review of High-Order and Optimized Finite-Difference Methods for Simulating Linear Wave Phenomena

    NASA Technical Reports Server (NTRS)

    Zingg, David W.

    1996-01-01

    This paper presents a review of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, or elastic waves. The spatial operators reviewed include compact schemes, non-compact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods discussed include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fourth-order fully-discrete finite-difference methods are considered: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method studied, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. Recommendations are made with respect to the suitability of the methods for specific problems and practical aspects of their use, such as appropriate Courant numbers and grid densities. Avenues for future research are suggested.

  8. Multigrid methods and high order finite difference for flow in transition - Effects of isolated and distributed roughness elements

    NASA Technical Reports Server (NTRS)

    Liu, C.; Liu, Z.

    1993-01-01

    The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.

  9. Diffusion Synthetic Acceleration for High-Order Discontinuous Finite Element SN Transport Schemes and Application to Locally Refined Unstructured Meshes

    SciTech Connect

    Yaqi Wang; Jean C. Ragusa

    2011-10-01

    Diffusion synthetic acceleration (DSA) schemes compatible with adaptive mesh refinement (AMR) grids are derived for the SN transport equations discretized using high-order discontinuous finite elements. These schemes are directly obtained from the discretized transport equations by assuming a linear dependence in angle of the angular flux along with an exact Fick's law and, therefore, are categorized as partially consistent. These schemes are akin to the symmetric interior penalty technique applied to elliptic problems and are all based on a second-order discontinuous finite element discretization of a diffusion equation (as opposed to a mixed or P1 formulation). Therefore, they only have the scalar flux as unknowns. A Fourier analysis has been carried out to determine the convergence properties of the three proposed DSA schemes for various cell optical thicknesses and aspect ratios. Out of the three DSA schemes derived, the modified interior penalty (MIP) scheme is stable and effective for realistic problems, even with distorted elements, but loses effectiveness for some highly heterogeneous configurations. The MIP scheme is also symmetric positive definite and can be solved efficiently with a preconditioned conjugate gradient method. Its implementation in an AMR SN transport code has been performed for both source iteration and GMRes-based transport solves, with polynomial orders up to 4. Numerical results are provided and show good agreement with the Fourier analysis results. Results on AMR grids demonstrate that the cost of DSA can be kept low on locally refined meshes.

  10. A Numerical Study on Finite-Bandwidth Resonances of High-Order Axial Modes (HOAM) in a Gyrotron Cavity

    NASA Astrophysics Data System (ADS)

    Sabchevski, Svilen Petrov; Idehara, Toshitaka

    2015-07-01

    Many novel and prospective applications of the gyrotrons as sources of coherent radiation require a broadband and continuous frequency tunability. A promising and experimentally proven technique to achieve it is based on a successive excitation of a sequence of high-order axial modes (HOAM) in the cavity resonator. Therefore, the studies on HOAM are of both theoretical and practical importance and interest. In this paper, we present and discuss the methods and the results of a numerical investigation on the resonances of HOAM in a typical open gyrotron cavity. The simulations have been performed using the existing as well as novel computational modules of the problem-oriented software package GYROSIM (GYROtron SIMulation) for solution of both the homogeneous and the inhomogeneous Helmholtz equation with radiation boundary conditions, which governs the field amplitude along the axis of the resonant structure. The frequency response of the cavity is studied by analyzing several resonance curves (spectral domain analysis) obtained from the numerical solution of the boundary value problem for the inhomogeneous Helmholtz equation with a predefined source term (excitation) by the finite-difference method (FDM). The approach proposed here allows finite-bandwidth resonances of HOAM to be identified and represented on the dispersion diagram of the cavity mode as bands rather than as discrete points, in contrast to the frequently used physical models that neglect the finite width of these resonances. Developed numerical procedures for calculation of the field profiles for an arbitrary frequency and excitation will be embedded in the cold cavity and self-consistent codes of the GYROSIM package in order to study the beam-wave interaction and energy transfer in gyrotron cavities.

  11. 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.

  12. 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.

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

    SciTech Connect

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

    2007-11-19

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

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

    NASA Astrophysics Data System (ADS)

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

    2008-01-01

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

  15. Robust finite-time containment control for high-order multi-agent systems with matched uncertainties under directed communication graphs

    NASA Astrophysics Data System (ADS)

    Fu, Junjie; Wang, Jinzhi

    2016-06-01

    In this paper, we study the robust finite-time containment control problem for a class of high-order uncertain nonlinear multi-agent systems modelled as high-order integrator systems with bounded matched uncertainties. When relative state information between neighbouring agents is available, an observer-based distributed controller is proposed for each follower using the sliding mode control technique which solves the finite-time containment control problem under general directed communication graphs. When only relative output information is available, robust exact differentiators and high-order sliding-mode controllers are employed together with the distributed finite-time observers. It is shown that robust finite-time containment control can still be achieved in this situation. An application in the coordination of multiple non-holonomic mobile robots is used as an example to illustrate the effectiveness of the proposed control strategies.

  16. High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling

    PubMed Central

    Banks, H T; Birch, Malcolm J; Brewin, Mark P; Greenwald, Stephen E; Hu, Shuhua; Kenz, Zackary R; Kruse, Carola; Maischak, Matthias; Shaw, Simon; Whiteman, John R

    2014-01-01

    We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685–6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over for r ⩽100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin–Voigt and Maxwell–Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd. PMID:25834284

  17. High-order Finite-Element Seismic Wave Propagation Modeling with MPI on a large GPU Cluster

    NASA Astrophysics Data System (ADS)

    Göddeke, D.; Komatitsch, D.; Erlebacher, G.; Michéa, D.

    2011-12-01

    We develop a hybrid multi-GPU and CPU version of an algorithm to model seismic wave propagation based on the spectral-element method. We implement an open-source high-order finite-element application, called SPECFEM3D that performs the numerical simulation of seismic wave propagation resulting for instance from earthquakes at the scale of a continent or from active seismic acquisition experiments in the oil industry, on a large cluster of NVIDIA graphics cards using the CUDA programming environment and non-blocking message passing based on MPI. This allows users to handle large numerical grids and simulate a large number of time steps for each geophysical model under study. Contrary to many other numerical techniques, ours is implemented successfully in single precision, maximizing the performance of current generation GPUs. Our GPU code can handle models of the Earth containing both fluid and solid layers (which is the case for instance at the scale of the full Earth, whose outer core is fluid). We will discuss the implementation and optimization of the code and compare it to an existing very optimized implementation in C language and MPI on a classical cluster of CPU nodes. We remove dependencies between neighboring mesh elements, which cannot easily be handled in parallel, based upon a mesh coloring technique to create subsets of independent elements. Thus, we efficiently handle summation operations over degrees of freedom on an unstructured mesh. Non-blocking MPI messages allow overlap between communications across the network and the data transfer to and from the device via the PCI-Express bus with calculations on the GPU. We perform a number of numerical tests to validate the single-precision CUDA and MPI implementation and assess its accuracy. We then analyze performance measurements and depending on how the problem is mapped to the reference CPU cluster, we obtain a speedup of 20x or 12x. Thanks to the overlapping of communications and computation, we

  18. Utilizing Emerging Hardware for Multiphysics Simulation Through Implicit High-Order Finite Element Methods With Tensor Product Structure

    NASA Astrophysics Data System (ADS)

    Brown, J.; Ahmadia, A.; Knepley, M. G.; Smith, B.

    2011-12-01

    The cost of memory, especially memory bandwidth, is becoming increasingly expensive on modern high performance computing architectures including GPUs and multi-core systems. In contrast, floating point operations are relatively inexpensive when they can be vectorized (e.g. thread blocks on a GPU or vector registers on a CPU). This relative cost of memory to flops will continue to become even more pronounced due to fundamental issues of power utilization, therefore it is important to rethink algorithms to effectively utilize hardware. Commonly used methods for implicit solves with finite element methods involve assembly of a sparse matrix. Unfortunately, sparse matrix kernels have an arithmetic intensity (ratio of flops to bytes of memory movement) that is orders of magnitude less than that delivered by modern hardware, causing the floating point units to be massively under-utilized. The ``free flops'' can be effectively utilized by higher order methods which deliver improved accuracy for the same number of degrees of freedom. Effective use of high order methods require eschewing assembled data structures for matrix storage in exchange for unassembled representations. The resulting computation reduces to small dense tensor-product operations and indepedent ``physics'' kernels at each quadrature point, both of which are amenable to vectorization and capable of delivering a high fraction of peak performance. To reduce the effort required to implement new physics (e.g. constitutive relations and additional fields), retain code verifiability, and experiment with different vectorization strategies and solver algorithms, we express the continuum equations in Python and use automatic differentiation, symbolic methods, and code generation techniques to create vectorized kernels for residual evaluation, Jacobian storage, Jacobian application, and adjoints for each block of the system. The performance and effectiveness of these methods is demonstrated for free-surface Stokes

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

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

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

  20. Efficient high-order diffraction of extreme-ultraviolet light and soft x-rays by nanostructured volume gratings.

    PubMed

    Hambach, D; Schneider, G; Gullikson, E M

    2001-08-01

    We report what is believed to be the first demonstration that volume gratings diffract extreme-ultraviolet light (EUV) or soft x-rays into high orders approximately an order of magnitude more efficiently than predicted by classical thin-grating theory. At the 13-nm wavelength, copolymer grating structures with 200-nm period and aspect ratios of ~10:1 achieved diffraction efficiencies of 11.2%, 15.3%, 11.5%, and 9.1% in the orders m of 2, 3, 4, and 5, respectively. In addition, the measured transmission spectra are consistent with electrodynamic calculations by coupled-wave theory. High-order diffraction can now be employed for substantially improved diffractive EUV and x-ray optics, e.g., highly resolving diffractive lenses and large-aperture condensers. PMID:18049562

  1. 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

  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. 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.

  5. 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.

  6. A study of infrasound propagation based on high-order finite difference solutions of the Navier-Stokes equations.

    PubMed

    Marsden, O; Bogey, C; Bailly, C

    2014-03-01

    The feasibility of using numerical simulation of fluid dynamics equations for the detailed description of long-range infrasound propagation in the atmosphere is investigated. The two dimensional (2D) Navier Stokes equations are solved via high fidelity spatial finite differences and Runge-Kutta time integration, coupled with a shock-capturing filter procedure allowing large amplitudes to be studied. The accuracy of acoustic prediction over long distances with this approach is first assessed in the linear regime thanks to two test cases featuring an acoustic source placed above a reflective ground in a homogeneous and weakly inhomogeneous medium, solved for a range of grid resolutions. An atmospheric model which can account for realistic features affecting acoustic propagation is then described. A 2D study of the effect of source amplitude on signals recorded at ground level at varying distances from the source is carried out. Modifications both in terms of waveforms and arrival times are described. PMID:24606252

  7. 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.

  8. Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

    NASA Technical Reports Server (NTRS)

    Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul

    1993-01-01

    We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

  9. Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

    NASA Technical Reports Server (NTRS)

    Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul

    1994-01-01

    We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First a proper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

  10. Full Wave Analysis of RF Signal Attenuation in a Lossy Cave using a High Order Time Domain Vector Finite Element Method

    SciTech Connect

    Pingenot, J; Rieben, R; White, D

    2004-12-06

    We present a computational study of signal propagation and attenuation of a 200 MHz dipole antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The simulation is performed for a series of random meshes in order to generate statistical data for the propagation and attenuation properties of the cave environment. Results for the power spectral density and phase of the electric field vector components are presented and discussed.

  11. 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.

  12. A high-order WENO-Z finite difference based particle-source-in-cell method for computation of particle-laden flows with shocks

    SciTech Connect

    Jacobs, Gustaaf B. Don, W.-S.

    2009-03-20

    A high-order particle-source-in-cell (PSIC) algorithm is presented for the computation of the interaction between shocks, small scale structures, and liquid and/or solid particles in high-speed engineering applications. The improved high-order finite difference weighted essentially non-oscillatory (WENO-Z) method for solution of the hyperbolic conservation laws that govern the shocked carrier gas flow, lies at the heart of the algorithm. Finite sized particles are modeled as points and are traced in the Lagrangian frame. The physical coupling of particles in the Lagrangian frame and the gas in the Eulerian frame through momentum and energy exchange, is numerically treated through high-order interpolation and weighing. The centered high-order interpolation of the fluid properties to the particle location is shown to lead to numerical instability in shocked flow. An essentially non-oscillatory interpolation (ENO) scheme is devised for the coupling that improves stability. The ENO based algorithm is shown to be numerically stable and to accurately capture shocks, small flow features and particle dispersion. Both the carrier gas and the particles are updated in time without splitting with a third-order Runge-Kutta TVD method. One and two-dimensional computations of a shock moving into a particle cloud demonstrates the characteristics of the WENO-Z based PSIC method (PSIC/WENO-Z). The PSIC/WENO-Z computations are not only in excellent agreement with the numerical simulations with a third-order Rusanov based PSIC and physical experiments in [V. Boiko, V.P. Kiselev, S.P. Kiselev, A. Papyrin, S. Poplavsky, V. Fomin, Shock wave interaction with a cloud of particles, Shock Waves, 7 (1997) 275-285], but also show a significant improvement in the resolution of small scale structures. In two-dimensional simulations of the Mach 3 shock moving into forty thousand bronze particles arranged in the shape of a rectangle, the long time accuracy of the high-order method is demonstrated

  13. An efficient finite-difference method with high-order accuracy in both time and space domains for modelling scalar-wave propagation

    NASA Astrophysics Data System (ADS)

    Tan, Sirui; Huang, Lianjie

    2014-05-01

    For modelling large-scale 3-D scalar-wave propagation, the finite-difference (FD) method with high-order accuracy in space but second-order accuracy in time is widely used because of its relatively low requirements of computer memory. We develop a novel staggered-grid (SG) FD method with high-order accuracy not only in space, but also in time, for solving 2- and 3-D scalar-wave equations. We determine the coefficients of the FD operator in the joint time-space domain to achieve high-order accuracy in time while preserving high-order accuracy in space. Our new FD scheme is based on a stencil that contains a few more grid points than the standard stencil. It is 2M-th-order accurate in space and fourth-order accurate in time when using 2M grid points along each axis and wavefields at one time step as the standard SGFD method. We validate the accuracy and efficiency of our new FD scheme using dispersion analysis and numerical modelling of scalar-wave propagation in 2- and 3-D complex models with a wide range of velocity contrasts. For media with a velocity contrast up to five, our new FD scheme is approximately two times more computationally efficient than the standard SGFD scheme with almost the same computer-memory requirement as the latter. Further numerical experiments demonstrate that our new FD scheme loses its advantages over the standard SGFD scheme if the velocity contrast is 10. However, for most large-scale geophysical applications, the velocity contrasts often range approximately from 1 to 3. Our new method is thus particularly useful for large-scale 3-D scalar-wave modelling and full-waveform inversion.

  14. Full Wave Analysis of RF Signal Attenuation in a Lossy Rough Surface Cave using a High Order Time Domain Vector Finite Element Method

    SciTech Connect

    Pingenot, J; Rieben, R; White, D; Dudley, D

    2005-10-31

    We present a computational study of signal propagation and attenuation of a 200 MHz planar loop antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The numerical technique is first verified against theoretical results for a planar loop antenna in a smooth lossy cave. The simulation is then performed for a series of random rough surface meshes in order to generate statistical data for the propagation and attenuation properties of the antenna in a cave environment. Results for the mean and variance of the power spectral density of the electric field are presented and discussed.

  15. Simulation of two-phase liquid-vapor flows using a high-order compact finite-difference lattice Boltzmann method.

    PubMed

    Hejranfar, Kazem; Ezzatneshan, Eslam

    2015-11-01

    A high-order compact finite-difference lattice Boltzmann method (CFDLBM) is extended and applied to accurately simulate two-phase liquid-vapor flows with high density ratios. Herein, the He-Shan-Doolen-type lattice Boltzmann multiphase model is used and the spatial derivatives in the resulting equations are discretized by using the fourth-order compact finite-difference scheme and the temporal term is discretized with the fourth-order Runge-Kutta scheme to provide an accurate and efficient two-phase flow solver. A high-order spectral-type low-pass compact nonlinear filter is used to regularize the numerical solution and remove spurious waves generated by flow nonlinearities in smooth regions and at the same time to remove the numerical oscillations in the interfacial region between the two phases. Three discontinuity-detecting sensors for properly switching between a second-order and a higher-order filter are applied and assessed. It is shown that the filtering technique used can be conveniently adopted to reduce the spurious numerical effects and improve the numerical stability of the CFDLBM implemented. A sensitivity study is also conducted to evaluate the effects of grid size and the filtering procedure implemented on the accuracy and performance of the solution. The accuracy and efficiency of the proposed solution procedure based on the compact finite-difference LBM are examined by solving different two-phase systems. Five test cases considered herein for validating the results of the two-phase flows are an equilibrium state of a planar interface in a liquid-vapor system, a droplet suspended in the gaseous phase, a liquid droplet located between two parallel wettable surfaces, the coalescence of two droplets, and a phase separation in a liquid-vapor system at different conditions. Numerical results are also presented for the coexistence curve and the verification of the Laplace law. Results obtained are in good agreement with the analytical solutions and also

  16. Simulation of two-phase liquid-vapor flows using a high-order compact finite-difference lattice Boltzmann method

    NASA Astrophysics Data System (ADS)

    Hejranfar, Kazem; Ezzatneshan, Eslam

    2015-11-01

    A high-order compact finite-difference lattice Boltzmann method (CFDLBM) is extended and applied to accurately simulate two-phase liquid-vapor flows with high density ratios. Herein, the He-Shan-Doolen-type lattice Boltzmann multiphase model is used and the spatial derivatives in the resulting equations are discretized by using the fourth-order compact finite-difference scheme and the temporal term is discretized with the fourth-order Runge-Kutta scheme to provide an accurate and efficient two-phase flow solver. A high-order spectral-type low-pass compact nonlinear filter is used to regularize the numerical solution and remove spurious waves generated by flow nonlinearities in smooth regions and at the same time to remove the numerical oscillations in the interfacial region between the two phases. Three discontinuity-detecting sensors for properly switching between a second-order and a higher-order filter are applied and assessed. It is shown that the filtering technique used can be conveniently adopted to reduce the spurious numerical effects and improve the numerical stability of the CFDLBM implemented. A sensitivity study is also conducted to evaluate the effects of grid size and the filtering procedure implemented on the accuracy and performance of the solution. The accuracy and efficiency of the proposed solution procedure based on the compact finite-difference LBM are examined by solving different two-phase systems. Five test cases considered herein for validating the results of the two-phase flows are an equilibrium state of a planar interface in a liquid-vapor system, a droplet suspended in the gaseous phase, a liquid droplet located between two parallel wettable surfaces, the coalescence of two droplets, and a phase separation in a liquid-vapor system at different conditions. Numerical results are also presented for the coexistence curve and the verification of the Laplace law. Results obtained are in good agreement with the analytical solutions and also

  17. 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.

  18. 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

  19. 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

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

    NASA Astrophysics Data System (ADS)

    Byun, Jaeseung; Bodony, Daniel; Pantano, Carlos

    2014-11-01

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

  1. Generalized high order compact methods.

    SciTech Connect

    Spotz, William F.; Kominiarczuk, Jakub

    2010-09-01

    The fundamental ideas of the high order compact method are combined with the generalized finite difference method. The result is a finite difference method that works on unstructured, nonuniform grids, and is more accurate than one would classically expect from the number of grid points employed.

  2. 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.

  3. 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.

  4. 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.

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

    SciTech Connect

    Banks, J W; Hittinger, J A

    2009-11-24

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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences

    NASA Astrophysics Data System (ADS)

    Amore, Paolo; Boyd, John P.; Fernández, Francisco M.; Rösler, Boris

    2016-05-01

    We apply second order finite differences to calculate the lowest eigenvalues of the Helmholtz equation, for complicated non-tensor domains in the plane, using different grids which sample exactly the border of the domain. We show that the results obtained applying Richardson and Padé-Richardson extrapolations to a set of finite difference eigenvalues corresponding to different grids allow us to obtain extremely precise values. When possible we have assessed the precision of our extrapolations comparing them with the highly precise results obtained using the method of particular solutions. Our empirical findings suggest an asymptotic nature of the FD series. In all the cases studied, we are able to report numerical results which are more precise than those available in the literature.

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

    NASA Technical Reports Server (NTRS)

    Loyd, B.; Murman, E. M.

    1986-01-01

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

  3. 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.

  4. 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

  5. THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics

    NASA Astrophysics Data System (ADS)

    Radice, D.; Rezzolla, L.

    2012-11-01

    We present THC: a new high-order flux-vector-splitting code for Newtonian and special-relativistic hydrodynamics designed for direct numerical simulations of turbulent flows. Our code implements a variety of different reconstruction algorithms, such as the popular weighted essentially non oscillatory and monotonicity-preserving schemes, or the more specialised bandwidth-optimised WENO scheme that has been specifically designed for the study of compressible turbulence. We show the first systematic comparison of these schemes in Newtonian physics as well as for special-relativistic flows. In particular we will present the results obtained in simulations of grid-aligned and oblique shock waves and nonlinear, large-amplitude, smooth adiabatic waves. We will also discuss the results obtained in classical benchmarks such as the double-Mach shock reflection test in Newtonian physics or the linear and nonlinear development of the relativistic Kelvin-Helmholtz instability in two and three dimensions. Finally, we study the turbulent flow induced by the Kelvin-Helmholtz instability and we show that our code is able to obtain well-converged velocity spectra, from which we benchmark the effective resolution of the different schemes.

  6. A High-Order Multiscale Global Atmospheric Model

    NASA Astrophysics Data System (ADS)

    Nair, Ram

    2016-04-01

    The High-Order Method Modeling Environment (HOMME), developed at NCAR, is a petascale hydrostatic framework, which employs the cubed-sphere grid system and high-order continuous or discontinuous Galerkin (DG) methods. Recently, the HOMME framework is being extended to a non-hydrostatic dynamical core, named as the "High-Order Multiscale Atmospheric Model (HOMAM)." The spatial discretization is based on DG or high-order finite-volume methods. Orography is handled by the terrain-following height-based coordinate system. To alleviate the stringent CFL stability requirement resulting from the vertical aspects of the dynamics, an operator-splitting time integration scheme based on the horizontally explicit and vertically implicit (HEVI) philosophy is adopted for HOMAM. Preliminary results with the benchmark test cases proposed in the Dynamical Core Model Intercomparison project (DCMIP) test-suite will be presented in the seminar.

  7. 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

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

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

    NASA Astrophysics Data System (ADS)

    Rizzi, A.

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

  20. 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

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

    Energy Science and Technology Software Center (ESTSC)

    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. 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.

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

    NASA Technical Reports Server (NTRS)

    Gnoffo, Peter A.

    2006-01-01

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

  4. 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.

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

    SciTech Connect

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

    2015-12-15

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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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

  13. 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.

  14. High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

    NASA Astrophysics Data System (ADS)

    Shu, Chi-Wang

    2016-07-01

    For solving time-dependent convection-dominated partial differential equations (PDEs), which arise frequently in computational physics, high order numerical methods, including finite difference, finite volume, finite element and spectral methods, have been undergoing rapid developments over the past decades. In this article we give a brief survey of two selected classes of high order methods, namely the weighted essentially non-oscillatory (WENO) finite difference and finite volume schemes and discontinuous Galerkin (DG) finite element methods, emphasizing several of their recent developments: bound-preserving limiters for DG, finite volume and finite difference schemes, which address issues in robustness and accuracy; WENO limiters for DG methods, which address issues in non-oscillatory performance when there are strong shocks, and inverse Lax-Wendroff type boundary treatments for finite difference schemes, which address issues in solving complex geometry problems using Cartesian meshes.

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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).

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  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. 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.

  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. 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.

  12. 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

  13. 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.

  14. Pulsed high-order volume mode gyroklystron

    NASA Astrophysics Data System (ADS)

    Zaitsev, N. I.; Ilyakov, E. V.; Kuzikov, S. V.; Kulagin, I. S.; Lygin, V. K.; Moiseev, M. A.; Petelin, M. I.; Shevchenko, A. S.

    2005-10-01

    We present the results of studies of a gyroklystron with the TE53 output mode. A 30-dB gain is obtained at a frequency of 30 GHz for an output power of 5 MW, efficiency 25%, pulse duration 0.4 ms, and amplification bandwidth 40 MHz.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

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

    NASA Astrophysics Data System (ADS)

    Liu, Hongxu; Jiao, Xiangmin

    2016-06-01

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

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

    NASA Technical Reports Server (NTRS)

    Molvik, Gregory A.

    1987-01-01

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

  7. 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.

  8. 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.

  9. 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

  10. 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.

  11. 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

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. New high order schemes in BATS-R-US

    NASA Astrophysics Data System (ADS)

    Toth, G.; van der Holst, B.; Daldorff, L.; Chen, Y.; Gombosi, T. I.

    2013-12-01

    The University of Michigan global magnetohydrodynamics code BATS-R-US has long relied on the block-adaptive mesh refinement (AMR) to increase accuracy in regions of interest, and we used a second order accurate TVD scheme. While AMR can in principle produce arbitrarily accurate results, there are still practical limitations due to computational resources. To further improve the accuracy of the BATS-R-US code, recently, we have implemented a 4th order accurate finite volume scheme (McCorquodale and Colella, 2011}), the 5th order accurate Monotonicity Preserving scheme (MP5, Suresh and Huynh, 1997) and the 5th order accurate CWENO5 scheme (Capdeville, 2008). In the first implementation the high order accuracy is achieved in the uniform parts of the Cartesian grids, and we still use the second order TVD scheme at resolution changes. For spherical grids the new schemes are only second order accurate so far, but still much less diffusive than the TVD scheme. We show a few verification tests that demonstrate the order of accuracy as well as challenging space physics applications. The high order schemes are less robust than the TVD scheme, and it requires some tricks and effort to make the code work. When the high order scheme works, however, we find that in most cases it can obtain similar or better results than the TVD scheme on twice finer grids. For three dimensional time dependent simulations this means that the high order scheme is almost 10 times faster requires 8 times less storage than the second order method.

  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. 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.

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

    SciTech Connect

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

    1995-12-01

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

  20. 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.

  1. 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...

  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. On High-Order Radiation Boundary Conditions

    NASA Technical Reports Server (NTRS)

    Hagstrom, Thomas

    1995-01-01

    In this paper we develop the theory of high-order radiation boundary conditions for wave propagation problems. In particular, we study the convergence of sequences of time-local approximate conditions to the exact boundary condition, and subsequently estimate the error in the solutions obtained using these approximations. We show that for finite times the Pade approximants proposed by Engquist and Majda lead to exponential convergence if the solution is smooth, but that good long-time error estimates cannot hold for spatially local conditions. Applications in fluid dynamics are also discussed.

  4. 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

  5. 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.

  6. 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...

  7. 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.

  8. High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

    NASA Technical Reports Server (NTRS)

    Barth, Timothy (Editor); Deconinck, Herman (Editor)

    1999-01-01

    The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists

  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. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

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

    NASA Astrophysics Data System (ADS)

    Hu, Guanghui; Yi, Nianyu

    2016-05-01

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

  4. A Time-Accurate Upwind Unstructured Finite Volume Method for Compressible Flow with Cure of Pathological Behaviors

    NASA Technical Reports Server (NTRS)

    Loh, Ching Y.; Jorgenson, Philip C. E.

    2007-01-01

    A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.

  5. 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.

  6. 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.

  7. HODIF:High-Order Discretizations, Interpolations and

    SciTech Connect

    Kennedy, Christopher A.; Carpenter, Mark H.; Ray, Jaideen

    2006-06-20

    This software, a library, contains FORTRAN77 subroutines to calculate first and second derivatives up to 8th order, interpolations (1D and 2D) up to 10th order and filters up to 14th order. Only even orders are addressed and finite-difference stencils are implemented on a vertex-centered mesh. The primary aim of this library is to be used in block-structured adaptive mesh simulations where high order is desired. The interpolants in this library are essentially designed to do prolongations and restrictions between levels of rfinement - however, they assume that the refinement ratio is 2. The filters are provided to remove high wavenumber content from solutions in case Runge phenomenon occurs - a common occurrence in case of marginal resolution of the solution. Details of the derivation and use are to be found in "Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations and filters", by J. Ray, C.A. Kennedy, S. Lefantzi and H.N. Najm, Sandia Technical Report, SAND2005-7981. The software comes with a User's Guide and examples how to use it.

  8. HODIF:High-Order Discretizations, Interpolations and

    Energy Science and Technology Software Center (ESTSC)

    2006-06-20

    This software, a library, contains FORTRAN77 subroutines to calculate first and second derivatives up to 8th order, interpolations (1D and 2D) up to 10th order and filters up to 14th order. Only even orders are addressed and finite-difference stencils are implemented on a vertex-centered mesh. The primary aim of this library is to be used in block-structured adaptive mesh simulations where high order is desired. The interpolants in this library are essentially designed to domore » prolongations and restrictions between levels of rfinement - however, they assume that the refinement ratio is 2. The filters are provided to remove high wavenumber content from solutions in case Runge phenomenon occurs - a common occurrence in case of marginal resolution of the solution. Details of the derivation and use are to be found in "Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations and filters", by J. Ray, C.A. Kennedy, S. Lefantzi and H.N. Najm, Sandia Technical Report, SAND2005-7981. The software comes with a User's Guide and examples how to use it.« less

  9. Surface Remeshing with Robust High-Order Reconstruction

    SciTech Connect

    Ray, Navamita; Delaney, Tristan; Einstein, Daniel R.; Jiao, Xiangmin

    2014-03-26

    Remeshing is an important problem in variety of applications, such as finite element methods and geometry processing. Surface remeshing poses some unique challenges, as it must deliver not only good mesh quality but also good geometric accuracy. For applications such as finite elements with high-order elements (quadratic or cubic elements), the geometry must be preserved to high-order (third-order or higher) accuracy, since low-order accuracy may undermine the convergence of numerical computations. The problem is particularly challenging if the CAD model is not available for the underlying geometry, and is even more so if the surface meshes contain some inverted elements. We describe remeshing strategies that can simultaneously produce high-quality triangular meshes, untangling mildly folded triangles and preserve the geometry to high-order of accuracy. Our approach extends our earlier works on high-order surface reconstruction and mesh optimization by enhancing its robustness with a geometric limiter for under-resolved geometries. We also integrate high-order surface reconstruction with surface mesh adaptation techniques, which alter the number of triangles and nodes. We demonstrate the utilization of our method to meshes for high-order finite elements, biomedical image-based surface meshes, and complex interface meshes in fluid simulations.

  10. Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang

    2004-01-01

    This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier