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

NASA Technical Reports Server (NTRS)

Yefet, Amir; Petropoulos, Peter G.

1999-01-01

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

Energy stable and high-order-accurate finite difference methods on staggered grids

NASA Astrophysics Data System (ADS)

O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan

2017-10-01

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

Accurate Finite Difference Algorithms

NASA Technical Reports Server (NTRS)

Goodrich, John W.

1996-01-01

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

Effects of finite volume on the K L – K S mass difference

DOE PAGES

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

2015-06-24

Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the Kmore » L – K S mass difference ΔM K 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

A robust method of computing finite difference coefficients based on Vandermonde matrix

NASA Astrophysics Data System (ADS)

Zhang, Yijie; Gao, Jinghuai; Peng, Jigen; Han, Weimin

2018-05-01

When the finite difference (FD) method is employed to simulate the wave propagation, high-order FD method is preferred in order to achieve better accuracy. However, if the order of FD scheme is high enough, the coefficient matrix of the formula for calculating finite difference coefficients is close to be singular. In this case, when the FD coefficients are computed by matrix inverse operator of MATLAB, inaccuracy can be produced. In order to overcome this problem, we have suggested an algorithm based on Vandermonde matrix in this paper. After specified mathematical transformation, the coefficient matrix is transformed into a Vandermonde matrix. Then the FD coefficients of high-order FD method can be computed by the algorithm of Vandermonde matrix, which prevents the inverse of the singular matrix. The dispersion analysis and numerical results of a homogeneous elastic model and a geophysical model of oil and gas reservoir demonstrate that the algorithm based on Vandermonde matrix has better accuracy compared with matrix inverse operator of MATLAB.

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.

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wiley, J.C.

The author describes a general `hp` finite element method with adaptive grids. The code was based on the work of Oden, et al. The term `hp` refers to the method of spatial refinement (h), in conjunction with the order of polynomials used as a part of the finite element discretization (p). This finite element code seems to handle well the different mesh grid sizes occuring between abuted grids with different resolutions.

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Greene, William H.

1989-01-01

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

Navier-Stokes Solutions for Spin-Up from Rest in a Cylindrical Container

DTIC Science & Technology

1979-09-01

CONDITIONS The calculations employ a finite - difference analog of the unsteady axisyimetric Navier-Stokes equations formulated in cylindrical coordinates...derivatives are approximated by second- order accurate one-sided difference formulae involving three time levels. * The following finite - difference ...equation are identical in form to Equations (13). The finite - difference representations for the ?-equation are: "(i)[aJ~lk " /i’,J-l2k] T (14a) •g I

Application of finite element approach to transonic flow problems

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C., Jr.

1976-01-01

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions, and blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, nonrectangular elements, and discontinuous approximation of shock waves are also discussed.

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

NASA Technical Reports Server (NTRS)

Steger, J. L.; Caradonna, F. X.

1980-01-01

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

A new multigrid formulation for high order finite difference methods on summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Weinerfelt, Per; Nordström, Jan

2018-04-01

Multigrid schemes for high order finite difference methods on summation-by-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserve the summation-by-parts property on each grid level is considered. Clear improvements of the convergence rate for relevant model problems are achieved.

A simple finite-difference scheme for handling topography with the first-order wave equation

NASA Astrophysics Data System (ADS)

Mulder, W. A.; Huiskes, M. J.

2017-07-01

One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the second-order formulation of the wave equation that only involves the pressure. Here, a similar method is considered for the first-order formulation in terms of pressure and particle velocity, using a staggered finite-difference discretization both in space and in time. In one space dimension, the boundary conditions consist in imposing antisymmetry for the pressure and symmetry for particle velocity components. For the pressure, this means that the solution values as well as all even derivatives up to a certain order are zero on the boundary. For the particle velocity, all odd derivatives are zero. In 2D, the 1-D assumption is used along each coordinate direction, with antisymmetry for the pressure along the coordinate and symmetry for the particle velocity component parallel to that coordinate direction. Since the symmetry or antisymmetry should hold along the direction normal to the boundary rather than along the coordinate directions, this generates an additional numerical error on top of the time stepping errors and the errors due to the interior spatial discretization. Numerical experiments in 2D and 3D nevertheless produce acceptable results.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Numerical Methods for Analysis of Charged Vacancy Diffusion in Dielectric Solids

DTIC Science & Technology

2006-12-01

theory for charged vacancy diffusion in elastic dielectric materials is formulated and implemented numerically in a finite difference code. The...one of the co-authors on neutral vacancy kinetics (Grinfeld and Hazzledine, 1997). The theory is implemented numerically in a finite difference code...accuracy of order ( )2x∆ , using a finite difference approximation (Hoffman, 1992) for the second spatial derivative of φ : ( )21 1 0ˆ2 /i i i i Rxφ

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

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

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

Finite element dynamic analysis on CDC STAR-100 computer

NASA Technical Reports Server (NTRS)

Noor, A. K.; Lambiotte, J. J., Jr.

1978-01-01

Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

NASA Technical Reports Server (NTRS)

Li, Yong; Moorthi, S.; Bates, J. Ray; Suarez, Max J.

1994-01-01

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Swarnava; Suryanarayana, Phanish, E-mail: phanish.suryanarayana@ce.gatech.edu

2016-02-15

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a generalized framework for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we propose a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In this framework, evaluation of both the electronic ground-state and forces on the nuclei are amenable to computations that scale linearly with the number of atoms. We develop a parallel implementation of this formulation using the finite-difference discretization.more » We demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson's mixing. We validate the accuracy of the results by comparing the energies and forces with plane-wave methods for selected examples, including the vacancy formation energy in Aluminum. Overall, the suitability of the proposed formulation for scalable high performance computing makes it an attractive choice for large-scale OF-DFT calculations consisting of thousands of atoms.« less

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique

NASA Technical Reports Server (NTRS)

Nordmann, R.; Weiser, P.

1989-01-01

The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.

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.

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

NASA Technical Reports Server (NTRS)

Skollermo, G.

1979-01-01

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Electron-phonon coupling from finite differences

NASA Astrophysics Data System (ADS)

Monserrat, Bartomeu

2018-02-01

The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction.

Accuracy of finite-difference modeling of seismic waves : Simulation versus laboratory measurements

NASA Astrophysics Data System (ADS)

Arntsen, B.

2017-12-01

The finite-difference technique for numerical modeling of seismic waves is still important and for some areas extensively used.For exploration purposes is finite-difference simulation at the core of both traditional imaging techniques such as reverse-time migration and more elaborate Full-Waveform Inversion techniques.The accuracy and fidelity of finite-difference simulation of seismic waves are hard to quantify and meaningfully error analysis is really onlyeasily available for simplistic media. A possible alternative to theoretical error analysis is provided by comparing finite-difference simulated data with laboratory data created using a scale model. The advantage of this approach is the accurate knowledge of the model, within measurement precision, and the location of sources and receivers.We use a model made of PVC immersed in water and containing horizontal and tilted interfaces together with several spherical objects to generateultrasonic pressure reflection measurements. The physical dimensions of the model is of the order of a meter, which after scaling represents a model with dimensions of the order of 10 kilometer and frequencies in the range of one to thirty hertz.We find that for plane horizontal interfaces the laboratory data can be reproduced by the finite-difference scheme with relatively small error, but for steeply tilted interfaces the error increases. For spherical interfaces the discrepancy between laboratory data and simulated data is sometimes much more severe, to the extent that it is not possible to simulate reflections from parts of highly curved bodies. The results are important in view of the fact that finite-difference modeling is often at the core of imaging and inversion algorithms tackling complicatedgeological areas with highly curved interfaces.

Experiments with explicit filtering for LES using a finite-difference method

NASA Technical Reports Server (NTRS)

Lund, T. S.; Kaltenbach, H. J.

1995-01-01

The equations for large-eddy simulation (LES) are derived formally by applying a spatial filter to the Navier-Stokes equations. The filter width as well as the details of the filter shape are free parameters in LES, and these can be used both to control the effective resolution of the simulation and to establish the relative importance of different portions of the resolved spectrum. An analogous, but less well justified, approach to filtering is more or less universally used in conjunction with LES using finite-difference methods. In this approach, the finite support provided by the computational mesh as well as the wavenumber-dependent truncation errors associated with the finite-difference operators are assumed to define the filter operation. This approach has the advantage that it is also 'automatic' in the sense that no explicit filtering: operations need to be performed. While it is certainly convenient to avoid the explicit filtering operation, there are some practical considerations associated with finite-difference methods that favor the use of an explicit filter. Foremost among these considerations is the issue of truncation error. All finite-difference approximations have an associated truncation error that increases with increasing wavenumber. These errors can be quite severe for the smallest resolved scales, and these errors will interfere with the dynamics of the small eddies if no corrective action is taken. Years of experience at CTR with a second-order finite-difference scheme for high Reynolds number LES has repeatedly indicated that truncation errors must be minimized in order to obtain acceptable simulation results. While the potential advantages of explicit filtering are rather clear, there is a significant cost associated with its implementation. In particular, explicit filtering reduces the effective resolution of the simulation compared with that afforded by the mesh. The resolution requirements for LES are usually set by the need to capture most of the energy-containing eddies, and if explicit filtering is used, the mesh must be enlarged so that these motions are passed by the filter. Given the high cost of explicit filtering, the following interesting question arises. Since the mesh must be expanded in order to perform the explicit filter, might it be better to take advantage of the increased resolution and simply perform an unfiltered simulation on the larger mesh? The cost of the two approaches is roughly the same, but the philosophy is rather different. In the filtered simulation, resolution is sacrificed in order to minimize the various forms of numerical error. In the unfiltered simulation, the errors are left intact, but they are concentrated at very small scales that could be dynamically unimportant from a LES perspective. Very little is known about this tradeoff and the objective of this work is to study this relationship in high Reynolds number channel flow simulations using a second-order finite-difference method.

A compact finite element method for elastic bodies

NASA Technical Reports Server (NTRS)

Rose, M. E.

1984-01-01

A nonconforming finite method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose is examined. A condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization.

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, Sirui, E-mail: siruitan@hotmail.com; Huang, Lianjie, E-mail: ljh@lanl.gov

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within amore » given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.« less

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

2004-01-01

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or 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 addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of accuracy increases, the partitioning for 3D requires the introduction of a large number of parameters, whose optimization to achieve convergence becomes increasingly more difficult. Also, the number of interior facets required to subdivide non-planar faces, and the additional increase in the number of quadrature points for each facet, increases the computational cost greatly.

High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition

NASA Astrophysics Data System (ADS)

Zhong, Xiaolin

1998-08-01

Direct numerical simulation (DNS) has become a powerful tool in studying fundamental phenomena of laminar-turbulent transition of high-speed boundary layers. Previous DNS studies of supersonic and hypersonic boundary layer transition have been limited to perfect-gas flow over flat-plate boundary layers without shock waves. For hypersonic boundary layers over realistic blunt bodies, DNS studies of transition need to consider the effects of bow shocks, entropy layers, surface curvature, and finite-rate chemistry. It is necessary that numerical methods for such studies are robust and high-order accurate both in resolving wide ranges of flow time and length scales and in resolving the interaction between the bow shocks and flow disturbance waves. This paper presents a new high-order shock-fitting finite-difference method for the DNS of the stability and transition of hypersonic boundary layers over blunt bodies with strong bow shocks and with (or without) thermo-chemical nonequilibrium. The proposed method includes a set of new upwind high-order finite-difference schemes which are stable and are less dissipative than a straightforward upwind scheme using an upwind-bias grid stencil, a high-order shock-fitting formulation, and third-order semi-implicit Runge-Kutta schemes for temporal discretization of stiff reacting flow equations. The accuracy and stability of the new schemes are validated by numerical experiments of the linear wave equation and nonlinear Navier-Stokes equations. The algorithm is then applied to the DNS of the receptivity of hypersonic boundary layers over a parabolic leading edge to freestream acoustic disturbances.

Existence of entire solutions of some non-linear differential-difference equations.

PubMed

Chen, Minfeng; Gao, Zongsheng; Du, Yunfei

2017-01-01

In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation [Formula: see text], where [Formula: see text], [Formula: see text] are two non-constant polynomials, [Formula: see text], m , n are positive integers and satisfy [Formula: see text] except for [Formula: see text], [Formula: see text].

Evaluating the role of higher order nonlinearity in water of finite and shallow depth with a direct numerical simulation method of Euler equations

NASA Astrophysics Data System (ADS)

Fernandez, L.; Toffoli, A.; Monbaliu, J.

2012-04-01

In deep water, the dynamics of surface gravity waves is dominated by the instability of wave packets to side band perturbations. This mechanism, which is a nonlinear third order in wave steepness effect, can lead to a particularly strong focusing of wave energy, which in turn results in the formation of waves of very large amplitude also known as freak or rogue waves [1]. In finite water depth, however, the interaction between waves and the ocean floor induces a mean current. This subtracts energy from wave instability and causes it to cease for relative water depth , where k is the wavenumber and h the water depth [2]. Yet, this contradicts field observations of extreme waves such as the infamous 26-m "New Year" wave that have mainly been recorded in regions of relatively shallow water . In this respect, recent studies [3] seem to suggest that higher order nonlinearity in water of finite depth may sustain instability. In order to assess the role of higher order nonlinearity in water of finite and shallow depth, here we use a Higher Order Spectral Method [4] to simulate the evolution of surface gravity waves according to the Euler equations of motion. This method is based on an expansion of the vertical velocity about the surface elevation under the assumption of weak nonlinearity and has a great advantage of allowing the activation or deactivation of different orders of nonlinearity. The model is constructed to deal with an arbitrary order of nonlinearity and water depths so that finite and shallow water regimes can be analyzed. Several wave configurations are considered with oblique and collinear with the primary waves disturbances and different water depths. The analysis confirms that nonlinearity higher than third order play a substantial role in the destabilization of a primary wave train and subsequent growth of side band perturbations.

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Fisher, Travis C.

2013-01-01

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

Slat Noise Predictions Using Higher-Order Finite-Difference Methods on Overset Grids

NASA Technical Reports Server (NTRS)

Housman, Jeffrey A.; Kiris, Cetin

2016-01-01

Computational aeroacoustic simulations using the structured overset grid approach and higher-order finite difference methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are presented for slat noise predictions. The simulations are part of a collaborative study comparing noise generation mechanisms between a conventional slat and a Krueger leading edge flap. Simulation results are compared with experimental data acquired during an aeroacoustic test in the NASA Langley Quiet Flow Facility. Details of the structured overset grid, numerical discretization, and turbulence model are provided.

The Finite-Surface Method for incompressible flow: a step beyond staggered grid

NASA Astrophysics Data System (ADS)

Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

2017-11-01

We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method: 2-D aspects

NASA Astrophysics Data System (ADS)

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

2014-06-01

The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative terms and quadrature. The Euler equations used here are in a flux form based on the hydrostatic pressure vertical coordinate, which are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate is implemented in this model. We verified the model by conducting widely used standard benchmark tests: the inertia-gravity wave, rising thermal bubble, density current wave, and linear hydrostatic mountain wave. The results from those tests demonstrate that the horizontally spectral element vertically finite difference model is accurate and robust. By using the 2-D slice model, we effectively show that the combined spatial discretization method of the spectral element and finite difference method in the horizontal and vertical directions, respectively, offers a viable method for the development of a NH dynamical core.

Numerical simulation using vorticity-vector potential formulation

NASA Technical Reports Server (NTRS)

Tokunaga, Hiroshi

1993-01-01

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Dynamical Quasicondensation of Hard-Core Bosons at Finite Momenta: A Non-equilibrium Condensation Effect

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Vidmar, L.; Ronzheimer, J. P.; Hodgman, S.; Schreiber, M.; Braun, S.; Langer, S.; Bloch, I.; Schneider, U.

2016-05-01

Long-range order in quantum many-body systems is usually associated with equilibrium situations. Here, we experimentally investigate the quasicondensation of strongly interacting bosons at finite momenta in a far-from-equilibrium case. We prepare an inhomogeneous initial state consisting of one-dimensional Mott insulators in the center of otherwise empty one-dimensional chains in an optical lattice with a lattice constant d. After suddenly quenching the trapping potential to zero, we observe the onset of coherence in spontaneously forming quasicondensates in the lattice. Remarkably, the emerging phase order differs from the ground-state order and is characterized by peaks at finite momenta +/-(π / 2)(ℏ / d) in the momentum distribution function. Supported by the DFG via FOR 801.

Boundary Closures for Fourth-order Energy Stable Weighted Essentially Non-Oscillatory Finite Difference Schemes

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.; Yamaleev, Nail K.; Frankel, Steven H.

2009-01-01

A general strategy exists for constructing Energy Stable Weighted Essentially Non Oscillatory (ESWENO) finite difference schemes up to eighth-order on periodic domains. These ESWENO schemes satisfy an energy norm stability proof for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, boundary closures are developed for the fourth-order ESWENO scheme that maintain wherever possible the WENO stencil biasing properties, while satisfying the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L2 norm. Second-order, and third-order boundary closures are developed that achieve stability in diagonal and block norms, respectively. The global accuracy for the second-order closures is three, and for the third-order closures is four. A novel set of non-uniform flux interpolation points is necessary near the boundaries to simultaneously achieve 1) accuracy, 2) the SBP convention, and 3) WENO stencil biasing mechanics.

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.

Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Webb, Jay C.

1994-01-01

In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The effectiveness of the correction factor in providing improvements to the computed solution is demonstrated in this paper.

Deformation of two-phase aggregates using standard numerical methods

NASA Astrophysics Data System (ADS)

Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.

2013-04-01

Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a Lagrangian marker-in-cell technique to represent the deforming fluid. Thanks to it Eulerian nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the Lagrangian finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to Lagrangian finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the Eulerian mesh.

High-order finite difference formulations for the incompressible Navier-Stokes equations on the CM-5

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tafti, D.

1995-12-01

The paper describes the features and implementation of a general purpose high-order accurate finite difference computer program for direct and large-eddy simulations of turbulence on the CM-5 in the data parallel mode. Benchmarking studies for a direct simulation of turbulent channel flow are discussed. Performance of up to 8.8 GFLOPS is obtained for the high-order formulations on 512 processing nodes of the CM-5. The execution time for a simulation with 24 million nodes in a domain with two periodic directions is in the range of 0.2 {mu}secs/time-step/degree of freedom on 512 processing nodes of the CM-5.

Optimization of finite difference forward modeling for elastic waves based on optimum combined window functions

NASA Astrophysics Data System (ADS)

Jian, Wang; Xiaohong, Meng; Hong, Liu; Wanqiu, Zheng; Yaning, Liu; Sheng, Gui; Zhiyang, Wang

2017-03-01

Full waveform inversion and reverse time migration are active research areas for seismic exploration. Forward modeling in the time domain determines the precision of the results, and numerical solutions of finite difference have been widely adopted as an important mathematical tool for forward modeling. In this article, the optimum combined of window functions was designed based on the finite difference operator using a truncated approximation of the spatial convolution series in pseudo-spectrum space, to normalize the outcomes of existing window functions for different orders. The proposed combined window functions not only inherit the characteristics of the various window functions, to provide better truncation results, but also control the truncation error of the finite difference operator manually and visually by adjusting the combinations and analyzing the characteristics of the main and side lobes of the amplitude response. Error level and elastic forward modeling under the proposed combined system were compared with outcomes from conventional window functions and modified binomial windows. Numerical dispersion is significantly suppressed, which is compared with modified binomial window function finite-difference and conventional finite-difference. Numerical simulation verifies the reliability of the proposed method.

FLUX-CORRECTED TRANSPORT TECHNIQUE FOR OPEN CHANNEL FLOW. (R825200)

EPA Science Inventory

In modeling flow in open channels, the traditional finite difference/finite volume schemes become inefficient and warrant special numerical treatment in the presence of shocks and discontinuities. The numerical oscillations that arise by making use of a second- and higher-order s...

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.

A time-space domain stereo finite difference method for 3D scalar wave propagation

NASA Astrophysics Data System (ADS)

Chen, Yushu; Yang, Guangwen; Ma, Xiao; He, Conghui; Song, Guojie

2016-11-01

The time-space domain finite difference methods reduce numerical dispersion effectively by minimizing the error in the joint time-space domain. However, their interpolating coefficients are related with the Courant numbers, leading to significantly extra time costs for loading the coefficients consecutively according to velocity in heterogeneous models. In the present study, we develop a time-space domain stereo finite difference (TSSFD) method for 3D scalar wave equation. The method propagates both the displacements and their gradients simultaneously to keep more information of the wavefields, and minimizes the maximum phase velocity error directly using constant interpolation coefficients for different Courant numbers. We obtain the optimal constant coefficients by combining the truncated Taylor series approximation and the time-space domain optimization, and adjust the coefficients to improve the stability condition. Subsequent investigation shows that the TSSFD can suppress numerical dispersion effectively with high computational efficiency. The maximum phase velocity error of the TSSFD is just 3.09% even with only 2 sampling points per minimum wavelength when the Courant number is 0.4. Numerical experiments show that to generate wavefields with no visible numerical dispersion, the computational efficiency of the TSSFD is 576.9%, 193.5%, 699.0%, and 191.6% of those of the 4th-order and 8th-order Lax-Wendroff correction (LWC) method, the 4th-order staggered grid method (SG), and the 8th-order optimal finite difference method (OFD), respectively. Meanwhile, the TSSFD is compatible to the unsplit convolutional perfectly matched layer (CPML) boundary condition for absorbing artificial boundaries. The efficiency and capability to handle complex velocity models make it an attractive tool in imaging methods such as acoustic reverse time migration (RTM).

Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

DOE PAGES

Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; ...

2015-09-15

Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinearmore » normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.« less

Vertical discretization with finite elements for a global hydrostatic model on the cubed sphere

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong; Park, Ja-Rin

2017-06-01

A formulation of Galerkin finite element with basis-spline functions on a hybrid sigma-pressure coordinate is presented to discretize the vertical terms of global Eulerian hydrostatic equations employed in a numerical weather prediction system, which is horizontally discretized with high-order spectral elements on a cubed sphere grid. This replaces the vertical discretization of conventional central finite difference that is first-order accurate in non-uniform grids and causes numerical instability in advection-dominant flows. Therefore, a model remains in the framework of Galerkin finite elements for both the horizontal and vertical spatial terms. The basis-spline functions, obtained from the de-Boor algorithm, are employed to derive both the vertical derivative and integral operators, since Eulerian advection terms are involved. These operators are used to discretize the vertical terms of the prognostic and diagnostic equations. To verify the vertical discretization schemes and compare their performance, various two- and three-dimensional idealized cases and a hindcast case with full physics are performed in terms of accuracy and stability. It was shown that the vertical finite element with the cubic basis-spline function is more accurate and stable than that of the vertical finite difference, as indicated by faster residual convergence, fewer statistical errors, and reduction in computational mode. This leads to the general conclusion that the overall performance of a global hydrostatic model might be significantly improved with the vertical finite element.

High-order flux correction/finite difference schemes for strand grids

NASA Astrophysics Data System (ADS)

Katz, Aaron; Work, Dalon

2015-02-01

A novel high-order method combining unstructured flux correction along body surfaces and high-order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids. The flux correction algorithm is applied in each unstructured layer of the strand grid, and the layers are then coupled together via a source term containing derivatives in the strand direction. Strand-direction derivatives are approximated to high-order via summation-by-parts operators for first derivatives and second derivatives with variable coefficients. We show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme. The resulting scheme possesses third-order design accuracy, but often exhibits fourth-order accuracy when higher-order derivatives are employed in the strand direction, especially for highly viscous flows. We prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms. Results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second-order algorithms.

FDTD simulation of EM wave propagation in 3-D media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, T.; Tripp, A.C.

1996-01-01

A finite-difference, time-domain solution to Maxwell`s equations has been developed for simulating electromagnetic wave propagation in 3-D media. The algorithm allows arbitrary electrical conductivity and permittivity variations within a model. The staggered grid technique of Yee is used to sample the fields. A new optimized second-order difference scheme is designed to approximate the spatial derivatives. Like the conventional fourth-order difference scheme, the optimized second-order scheme needs four discrete values to calculate a single derivative. However, the optimized scheme is accurate over a wider wavenumber range. Compared to the fourth-order scheme, the optimized scheme imposes stricter limitations on the time stepmore » sizes but allows coarser grids. The net effect is that the optimized scheme is more efficient in terms of computation time and memory requirement than the fourth-order scheme. The temporal derivatives are approximated by second-order central differences throughout. The Liao transmitting boundary conditions are used to truncate an open problem. A reflection coefficient analysis shows that this transmitting boundary condition works very well. However, it is subject to instability. A method that can be easily implemented is proposed to stabilize the boundary condition. The finite-difference solution is compared to closed-form solutions for conducting and nonconducting whole spaces and to an integral-equation solution for a 3-D body in a homogeneous half-space. In all cases, the finite-difference solutions are in good agreement with the other solutions. Finally, the use of the algorithm is demonstrated with a 3-D model. Numerical results show that both the magnetic field response and electric field response can be useful for shallow-depth and small-scale investigations.« less

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

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.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gyrya, V.; Lipnikov, K.

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, K.; Petersson, N. A.; Rodgers, A.

Acoustic waveform modeling is a computationally intensive task and full three-dimensional simulations are often impractical for some geophysical applications such as long-range wave propagation and high-frequency sound simulation. In this study, we develop a two-dimensional high-order accurate finite-difference code for acoustic wave modeling. We solve the linearized Euler equations by discretizing them with the sixth order accurate finite difference stencils away from the boundary and the third order summation-by-parts (SBP) closure near the boundary. Non-planar topographic boundary is resolved by formulating the governing equation in curvilinear coordinates following the interface. We verify the implementation of the algorithm by numerical examplesmore » and demonstrate the capability of the proposed method for practical acoustic wave propagation problems in the atmosphere.« less

Transition to Quantum Turbulence and the Propagation of Vortex Loops at Finite Temperatures

NASA Astrophysics Data System (ADS)

Yamamoto, Shinji; Adachi, Hiroyuki; Tsubota, Makoto

2011-02-01

We performed numerical simulation of the transition to quantum turbulence and the propagation of vortex loops at finite temperatures in order to understand the experiments using vibrating wires in superfluid 4He by Yano et al. We injected vortex rings to a finite volume in order to simulate emission of vortices from the wire. When the injected vortices are dilute, they should decay by mutual friction. When they are dense, however, vortex tangle are generated through vortex reconnections and emit large vortex loops. The large vortex loops can travel a long distance before disappearing, which is much different from the dilute case. The numerical results are consistent with the experimental results.

Finite-difference model for 3-D flow in bays and estuaries

USGS Publications Warehouse

Smith, Peter E.; Larock, Bruce E.; ,

1993-01-01

This paper describes a semi-implicit finite-difference model for the numerical solution of three-dimensional flow in bays and estuaries. The model treats the gravity wave and vertical diffusion terms in the governing equations implicitly, and other terms explicitly. The model achieves essentially second-order accurate and stable solutions in strongly nonlinear problems by using a three-time-level leapfrog-trapezoidal scheme for the time integration.

Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iaroshenko, Oleksandr; Gyrya, Vitaliy; Manzini, Gianmarco

2016-09-01

In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a flux variable from edges to vertices. We showed that for a non-degenerate element this transformation is locally equivalent, i.e. there is a one-to-one map between the new and the old DoF. Globally, on the other hand, this transformation leads to a reduction of the total number of degrees of freedom (by up to 40%) and additional continuity of the discrete flux.

A detailed analysis of inviscid flux splitting algorithms for real gases with equilibrium or finite-rate chemistry

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun; Liou, Meng-Sing; Van Leer, Bram

1989-01-01

The extension of the known flux-vector and flux-difference splittings to real gases via rigorous mathematical procedures is demonstrated. Formulations of both equilibrium and finite-rate chemistry for real-gas flows are described, with emphasis on derivations of finite-rate chemistry. Split-flux formulas from other authors are examined. A second-order upwind-based TVD scheme is adopted to eliminate oscillations and to obtain a sharp representation of discontinuities.

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S.; Rosen, I. G.

1988-01-01

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Documentation of the Fourth Order Band Model

NASA Technical Reports Server (NTRS)

Kalnay-Rivas, E.; Hoitsma, D.

1979-01-01

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given.

Computational aspects of sensitivity calculations in linear transient structural analysis. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Greene, William H.

1990-01-01

A study was performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal of the study was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semi-analytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. In several cases this fixed mode approach resulted in very poor approximations of the stress sensitivities. Almost all of the original modes were required for an accurate sensitivity and for small numbers of modes, the accuracy was extremely poor. To overcome this poor accuracy, two semi-analytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in accurate values of the stress sensitivities with a small number of modes and much lower computational costs than if the vibration modes were recalculated and then used in an overall finite difference method.

Dispersion analysis of the Pn -Pn-1DG mixed finite element pair for atmospheric modelling

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2018-02-01

Mixed finite element methods provide a generalisation of staggered grid finite difference methods with a framework to extend the method to high orders. The ability to generate a high order method is appealing for applications on the kind of quasi-uniform grids that are popular for atmospheric modelling, so that the method retains an acceptable level of accuracy even around special points in the grid. The dispersion properties of such schemes are important to study as they provide insight into the numerical adjustment to imbalance that is an important component in atmospheric modelling. This paper extends the recent analysis of the P2 - P1DG pair, that is a quadratic continuous and linear discontinuous finite element pair, to higher polynomial orders and also spectral element type pairs. In common with the previously studied element pair, and also with other schemes such as the spectral element and discontinuous Galerkin methods, increasing the polynomial order is found to provide a more accurate dispersion relation for the well resolved part of the spectrum but at the cost of a number of unphysical spectral gaps. The effects of these spectral gaps are investigated and shown to have a varying impact depending upon the width of the gap. Finally, the tensor product nature of the finite element spaces is exploited to extend the dispersion analysis into two-dimensions.

A fast Cauchy-Riemann solver. [differential equation solution for boundary conditions by finite difference approximation

NASA Technical Reports Server (NTRS)

Ghil, M.; Balgovind, R.

1979-01-01

The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.

High-order asynchrony-tolerant finite difference schemes for partial differential equations

NASA Astrophysics Data System (ADS)

Aditya, Konduri; Donzis, Diego A.

2017-12-01

Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Sudden change of geometric quantum discord in finite temperature reservoirs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Ming-Liang, E-mail: mingliang0301@163.com; Sun, Jian

2015-03-15

We investigate sudden change (SC) behaviors of the distance-based measures of geometric quantum discords (GQDs) for two non-interacting qubits subject to the two-sided and the one-sided thermal reservoirs. We found that the GQDs defined by different distances exhibit different SCs, and thus the SCs are the combined result of the chosen discord measure and the property of a state. We also found that the thermal reservoir may generate states having different orderings related to different GQDs. These inherent differences of the GQDs reveal that they are incompatible in characterizing quantum correlations both quantitatively and qualitatively. - Highlights: • Comparable studymore » of different distance-based geometric quantum discords. • Evolution of the geometric quantum discords in finite temperature reservoirs. • Different geometric quantum discords exhibit distinct sudden changes. • Nonunique states ordering imposed by different geometric quantum discords.« less

Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles

2011-01-01

Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.

A comparison of matrix methods for calculating eigenvalues in acoustically lined ducts

NASA Technical Reports Server (NTRS)

Watson, W.; Lansing, D. L.

1976-01-01

Three approximate methods - finite differences, weighted residuals, and finite elements - were used to solve the eigenvalue problem which arises in finding the acoustic modes and propagation constants in an absorptively lined two-dimensional duct without airflow. The matrix equations derived for each of these methods were solved for the eigenvalues corresponding to various values of wall impedance. Two matrix orders, 20 x 20 and 40 x 40, were used. The cases considered included values of wall admittance for which exact eigenvalues were known and for which several nearly equal roots were present. Ten of the lower order eigenvalues obtained from the three approximate methods were compared with solutions calculated from the exact characteristic equation in order to make an assessment of the relative accuracy and reliability of the three methods. The best results were given by the finite element method using a cubic polynomial. Excellent accuracy was consistently obtained, even for nearly equal eigenvalues, by using a 20 x 20 order matrix.

The arbitrary order mixed mimetic finite difference method for the diffusion equation

DOE PAGES

Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco

2016-05-01

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less

High order multi-grid methods to solve the Poisson equation

NASA Technical Reports Server (NTRS)

Schaffer, S.

1981-01-01

High order multigrid methods based on finite difference discretization of the model problem are examined. The following methods are described: (1) a fixed high order FMG-FAS multigrid algorithm; (2) the high order methods; and (3) results are presented on four problems using each method with the same underlying fixed FMG-FAS algorithm.

A study of the response of nonlinear springs

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Knott, T. W.; Johnson, E. R.

1991-01-01

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

A family of four stages embedded explicit six-step methods with eliminated phase-lag and its derivatives for the numerical solution of the second order problems

NASA Astrophysics Data System (ADS)

Simos, T. E.

2017-11-01

A family of four stages high algebraic order embedded explicit six-step methods, for the numerical solution of second order initial or boundary-value problems with periodical and/or oscillating solutions, are studied in this paper. The free parameters of the new proposed methods are calculated solving the linear system of equations which is produced by requesting the vanishing of the phase-lag of the methods and the vanishing of the phase-lag's derivatives of the schemes. For the new obtained methods we investigate: • Its local truncation error (LTE) of the methods.• The asymptotic form of the LTE obtained using as model problem the radial Schrödinger equation.• The comparison of the asymptotic forms of LTEs for several methods of the same family. This comparison leads to conclusions on the efficiency of each method of the family.• The stability and the interval of periodicity of the obtained methods of the new family of embedded finite difference pairs.• The applications of the new obtained family of embedded finite difference pairs to the numerical solution of several second order problems like the radial Schrödinger equation, astronomical problems etc. The above applications lead to conclusion on the efficiency of the methods of the new family of embedded finite difference pairs.

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

Polarization effects on spectra of spherical core/shell nanostructures: Perturbation theory against finite difference approach

NASA Astrophysics Data System (ADS)

Ibral, Asmaa; Zouitine, Asmaa; Assaid, El Mahdi; El Achouby, Hicham; Feddi, El Mustapha; Dujardin, Francis

2015-02-01

Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image-charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap.

Time dependent wave envelope finite difference analysis of sound propagation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1984-01-01

A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.

Optimization Based Efficiencies in First Order Reliability Analysis

NASA Technical Reports Server (NTRS)

Peck, Jeffrey A.; Mahadevan, Sankaran

2003-01-01

This paper develops a method for updating the gradient vector of the limit state function in reliability analysis using Broyden's rank one updating technique. In problems that use commercial code as a black box, the gradient calculations are usually done using a finite difference approach, which becomes very expensive for large system models. The proposed method replaces the finite difference gradient calculations in a standard first order reliability method (FORM) with Broyden's Quasi-Newton technique. The resulting algorithm of Broyden updates within a FORM framework (BFORM) is used to run several example problems, and the results compared to standard FORM results. It is found that BFORM typically requires fewer functional evaluations that FORM to converge to the same answer.

An improved rotated staggered-grid finite-difference method with fourth-order temporal accuracy for elastic-wave modeling in anisotropic media

DOE PAGES

Gao, Kai; Huang, Lianjie

2017-08-31

The rotated staggered-grid (RSG) finite-difference method is a powerful tool for elastic-wave modeling in 2D anisotropic media where the symmetry axes of anisotropy are not aligned with the coordinate axes. We develop an improved RSG scheme with fourth-order temporal accuracy to reduce the numerical dispersion associated with prolonged wave propagation or a large temporal step size. The high-order temporal accuracy is achieved by including high-order temporal derivatives, which can be converted to high-order spatial derivatives to reduce computational cost. Dispersion analysis and numerical tests show that our method exhibits very low temporal dispersion even with a large temporal step sizemore » for elastic-wave modeling in complex anisotropic media. Using the same temporal step size, our method is more accurate than the conventional RSG scheme. In conclusion, our improved RSG scheme is therefore suitable for prolonged modeling of elastic-wave propagation in 2D anisotropic media.« less

An improved rotated staggered-grid finite-difference method with fourth-order temporal accuracy for elastic-wave modeling in anisotropic media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Kai; Huang, Lianjie

The rotated staggered-grid (RSG) finite-difference method is a powerful tool for elastic-wave modeling in 2D anisotropic media where the symmetry axes of anisotropy are not aligned with the coordinate axes. We develop an improved RSG scheme with fourth-order temporal accuracy to reduce the numerical dispersion associated with prolonged wave propagation or a large temporal step size. The high-order temporal accuracy is achieved by including high-order temporal derivatives, which can be converted to high-order spatial derivatives to reduce computational cost. Dispersion analysis and numerical tests show that our method exhibits very low temporal dispersion even with a large temporal step sizemore » for elastic-wave modeling in complex anisotropic media. Using the same temporal step size, our method is more accurate than the conventional RSG scheme. In conclusion, our improved RSG scheme is therefore suitable for prolonged modeling of elastic-wave propagation in 2D anisotropic media.« less

High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation

NASA Astrophysics Data System (ADS)

Anderson, R.; Dobrev, V.; Kolev, Tz.; Kuzmin, D.; Quezada de Luna, M.; Rieben, R.; Tomov, V.

2017-04-01

In this work we present a FCT-like Maximum-Principle Preserving (MPP) method to solve the transport equation. We use high-order polynomial spaces; in particular, we consider up to 5th order spaces in two and three dimensions and 23rd order spaces in one dimension. The method combines the concepts of positive basis functions for discontinuous Galerkin finite element spatial discretization, locally defined solution bounds, element-based flux correction, and non-linear local mass redistribution. We consider a simple 1D problem with non-smooth initial data to explain and understand the behavior of different parts of the method. Convergence tests in space indicate that high-order accuracy is achieved. Numerical results from several benchmarks in two and three dimensions are also reported.

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bailey, Harry E.; Beam, Richard M.

1991-01-01

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

Finite difference schemes for long-time integration

NASA Technical Reports Server (NTRS)

Haras, Zigo; Taasan, Shlomo

1993-01-01

Finite difference schemes for the evaluation of first and second derivatives are presented. These second order compact schemes were designed for long-time integration of evolution equations by solving a quadratic constrained minimization problem. The quadratic cost function measures the global truncation error while taking into account the initial data. The resulting schemes are applicable for integration times fourfold, or more, longer than similar previously studied schemes. A similar approach was used to obtain improved integration schemes.

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations.

Efficient calculation of higher-order optical waveguide dispersion.

PubMed

Mores, J A; Malheiros-Silveira, G N; Fragnito, H L; Hernández-Figueroa, H E

2010-09-13

An efficient numerical strategy to compute the higher-order dispersion parameters of optical waveguides is presented. For the first time to our knowledge, a systematic study of the errors involved in the higher-order dispersions' numerical calculation process is made, showing that the present strategy can accurately model those parameters. Such strategy combines a full-vectorial finite element modal solver and a proper finite difference differentiation algorithm. Its performance has been carefully assessed through the analysis of several key geometries. In addition, the optimization of those higher-order dispersion parameters can also be carried out by coupling to the present scheme a genetic algorithm, as shown here through the design of a photonic crystal fiber suitable for parametric amplification applications.

A mixed pseudospectral/finite difference method for the axisymmetric flow in a heated, rotating spherical shell. [for experimental atmospheric simulation

NASA Technical Reports Server (NTRS)

Macaraeg, M. G.

1986-01-01

For a Spacelab flight, a model experiment of the earth's atmospheric circulation has been proposed. This experiment is known as the Atmospheric General Circulation Experiment (AGCE). In the experiment concentric spheres will rotate as a solid body, while a dielectric fluid is confined in a portion of the gap between the spheres. A zero gravity environment will be required in the context of the simulation of the gravitational body force on the atmosphere. The present study is concerned with the development of pseudospectral/finite difference (PS/FD) model and its subsequent application to physical cases relevant to the AGCE. The model is based on a hybrid scheme involving a pseudospectral latitudinal formulation, and finite difference radial and time discretization. The advantages of the use of the hybrid PS/FD method compared to a pure second-order accurate finite difference (FD) method are discussed, taking into account the higher accuracy and efficiency of the PS/FD method.

Surface and finite size effect on fluctuations dynamics in nanoparticles with long-range order

NASA Astrophysics Data System (ADS)

Morozovska, A. N.; Eliseev, E. A.

2010-02-01

The influence of surface and finite size on the dynamics of the order parameter fluctuations and critical phenomena in the three-dimensional (3D)-confined systems with long-range order was not considered theoretically. In this paper, we study the influence of surface and finite size on the dynamics of the order parameter fluctuations in the particles of arbitrary shape. We consider concrete examples of the spherical and cylindrical ferroic nanoparticles within Landau-Ginzburg-Devonshire phenomenological approach. Allowing for the strong surface energy contribution in micro and nanoparticles, the analytical expressions derived for the Ornstein-Zernike correlator of the long-range order parameter spatial-temporal fluctuations, dynamic generalized susceptibility, relaxation times, and correlation radii discrete spectra are different from those known for bulk systems. Obtained analytical expressions for the correlation function of the order parameter spatial-temporal fluctuations in micro and nanosized systems can be useful for the quantitative analysis of the dynamical structural factors determined from magnetic resonance diffraction and scattering spectra. Besides the practical importance of the correlation function for the analysis of the experimental data, derived expressions for the fluctuations strength determine the fundamental limits of phenomenological theories applicability for 3D-confined systems.

Shear-flexible finite-element models of laminated composite plates and shells

NASA Technical Reports Server (NTRS)

Noor, A. K.; Mathers, M. D.

1975-01-01

Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.

Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

Viscoelastic Finite Difference Modeling Using Graphics Processing Units

NASA Astrophysics Data System (ADS)

Fabien-Ouellet, G.; Gloaguen, E.; Giroux, B.

2014-12-01

Full waveform seismic modeling requires a huge amount of computing power that still challenges today's technology. This limits the applicability of powerful processing approaches in seismic exploration like full-waveform inversion. This paper explores the use of Graphics Processing Units (GPU) to compute a time based finite-difference solution to the viscoelastic wave equation. The aim is to investigate whether the adoption of the GPU technology is susceptible to reduce significantly the computing time of simulations. The code presented herein is based on the freely accessible software of Bohlen (2002) in 2D provided under a General Public License (GNU) licence. This implementation is based on a second order centred differences scheme to approximate time differences and staggered grid schemes with centred difference of order 2, 4, 6, 8, and 12 for spatial derivatives. The code is fully parallel and is written using the Message Passing Interface (MPI), and it thus supports simulations of vast seismic models on a cluster of CPUs. To port the code from Bohlen (2002) on GPUs, the OpenCl framework was chosen for its ability to work on both CPUs and GPUs and its adoption by most of GPU manufacturers. In our implementation, OpenCL works in conjunction with MPI, which allows computations on a cluster of GPU for large-scale model simulations. We tested our code for model sizes between 1002 and 60002 elements. Comparison shows a decrease in computation time of more than two orders of magnitude between the GPU implementation run on a AMD Radeon HD 7950 and the CPU implementation run on a 2.26 GHz Intel Xeon Quad-Core. The speed-up varies depending on the order of the finite difference approximation and generally increases for higher orders. Increasing speed-ups are also obtained for increasing model size, which can be explained by kernel overheads and delays introduced by memory transfers to and from the GPU through the PCI-E bus. Those tests indicate that the GPU memory size and the slow memory transfers are the limiting factors of our GPU implementation. Those results show the benefits of using GPUs instead of CPUs for time based finite-difference seismic simulations. The reductions in computation time and in hardware costs are significant and open the door for new approaches in seismic inversion.

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

DOE PAGES

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

2015-11-22

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. 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 themore » 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 discretization 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 solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes

NASA Astrophysics Data System (ADS)

Austin, Travis M.; Brezina, Marian; Jamroz, Ben; Jhurani, Chetan; Manteuffel, Thomas A.; Ruge, John

2012-05-01

High-order finite elements often have a higher accuracy per degree of freedom than the classical low-order finite elements. However, in the context of implicit time-stepping methods, high-order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element matrix. There are many cases where simulations are limited by the memory required to store the matrix and/or the algorithmic components of the linear solver. We are particularly interested in preconditioned Krylov methods for linear systems generated by discretization of elliptic partial differential equations with high-order finite elements. Using a preconditioner like Algebraic Multigrid can be costly in terms of memory due to the need to store matrix information at the various levels. We present a novel method for defining a preconditioner for systems generated by high-order finite elements that is based on a much sparser system than the original high-order finite element system. We investigate the performance for non-uniform meshes on a cube and a cubed sphere mesh, showing that the sparser preconditioner is more efficient and uses significantly less memory. Finally, we explore new methods to construct the sparse preconditioner and examine their effectiveness for non-uniform meshes. We compare results to a direct use of Algebraic Multigrid as a preconditioner and to a two-level additive Schwarz method.

Solution of an eigenvalue problem for the Laplace operator on a spherical surface. M.S. Thesis - Maryland Univ.

NASA Technical Reports Server (NTRS)

Walden, H.

1974-01-01

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

Double absorbing boundaries for finite-difference time-domain electromagnetics

DOE Office of Scientific and Technical Information (OSTI.GOV)

LaGrone, John, E-mail: jlagrone@smu.edu; Hagstrom, Thomas, E-mail: thagstrom@smu.edu

We describe the implementation of optimal local radiation boundary condition sequences for second order finite difference approximations to Maxwell's equations and the scalar wave equation using the double absorbing boundary formulation. Numerical experiments are presented which demonstrate that the design accuracy of the boundary conditions is achieved and, for comparable effort, exceeds that of a convolution perfectly matched layer with reasonably chosen parameters. An advantage of the proposed approach is that parameters can be chosen using an accurate a priori error bound.

Finite difference time domain (FDTD) modeling of implanted deep brain stimulation electrodes and brain tissue.

PubMed

Gabran, S R I; Saad, J H; Salama, M M A; Mansour, R R

2009-01-01

This paper demonstrates the electromagnetic modeling and simulation of an implanted Medtronic deep brain stimulation (DBS) electrode using finite difference time domain (FDTD). The model is developed using Empire XCcel and represents the electrode surrounded with brain tissue assuming homogenous and isotropic medium. The model is created to study the parameters influencing the electric field distribution within the tissue in order to provide reference and benchmarking data for DBS and intra-cortical electrode development.

A weak Galerkin generalized multiscale finite element method

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2016-03-31

In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.

A weak Galerkin generalized multiscale finite element method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Wang, Junping; Ye, Xiu

In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.

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 three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

A Technique of Treating Negative Weights in WENO Schemes

NASA Technical Reports Server (NTRS)

Shi, Jing; Hu, Changqing; Shu, Chi-Wang

2000-01-01

High order accurate weighted essentially non-oscillatory (WENO) schemes have recently been developed for finite difference and finite volume methods both in structural and in unstructured meshes. A key idea in WENO scheme is a linear combination of lower order fluxes or reconstructions to obtain a high order approximation. The combination coefficients, also called linear weights, are determined by local geometry of the mesh and order of accuracy and may become negative. WENO procedures cannot be applied directly to obtain a stable scheme if negative linear weights are present. Previous strategy for handling this difficulty is by either regrouping of stencils or reducing the order of accuracy to get rid of the negative linear weights. In this paper we present a simple and effective technique for handling negative linear weights without a need to get rid of them.

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.

Reynolds number effects on mixing due to topological chaos.

PubMed

Smith, Spencer A; Warrier, Sangeeta

2016-03-01

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To help clarify this dependency, we numerically simulate the effects of a batch stirring device on a 2D incompressible Newtonian fluid in the laminar regime. In particular, we calculate the finite time Lyapunov exponent (FTLE) field for three different stirring protocols, one topologically complex (pseudo-Anosov) and two simple (finite-order), over a range of viscosities. After extracting appropriate measures indicative of both the amount of mixing and the area of effective mixing from the FTLE field, we see a clearly defined Reynolds number range in which the relative efficacy of the pseudo-Anosov protocol over the finite-order protocols justifies the application of topological chaos. More unexpectedly, we see that while the measures of effective mixing area increase with increasing Reynolds number for the finite-order protocols, they actually exhibit non-monotonic behavior for the pseudo-Anosov protocol.

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

A finite difference solution for the propagation of sound in near sonic flows

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Lester, H. C.

1983-01-01

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

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.

A method for modeling finite-core vortices in wake-flow calculations

NASA Technical Reports Server (NTRS)

Stremel, P. M.

1984-01-01

A numerical method for computing nonplanar vortex wakes represented by finite-core vortices is presented. The approach solves for the velocity on an Eulerian grid, using standard finite-difference techniques; the vortex wake is tracked by Lagrangian methods. In this method, the distribution of continuous vorticity in the wake is replaced by a group of discrete vortices. An axially symmetric distribution of vorticity about the center of each discrete vortex is used to represent the finite-core model. Two distributions of vorticity, or core models, are investigated: a finite distribution of vorticity represented by a third-order polynomial, and a continuous distribution of vorticity throughout the wake. The method provides for a vortex-core model that is insensitive to the mesh spacing. Results for a simplified case are presented. Computed results for the roll-up of a vortex wake generated by wings with different spanwise load distributions are presented; contour plots of the flow-field velocities are included; and comparisons are made of the computed flow-field velocities with experimentally measured velocities.

High-order centered difference methods with sharp shock resolution

NASA Technical Reports Server (NTRS)

Gustafsson, Bertil; Olsson, Pelle

1994-01-01

In this paper we consider high-order centered finite difference approximations of hyperbolic conservation laws. We propose different ways of adding artificial viscosity to obtain sharp shock resolution. For the Riemann problem we give simple explicit formulas for obtaining stationary one and two-point shocks. This can be done for any order of accuracy. It is shown that the addition of artificial viscosity is equivalent to ensuring the Lax k-shock condition. We also show numerical experiments that verify the theoretical results.

Accurate finite difference methods for time-harmonic wave propagation

NASA Technical Reports Server (NTRS)

Harari, Isaac; Turkel, Eli

1994-01-01

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

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.

Performance of finite order distribution-generated universal portfolios

NASA Astrophysics Data System (ADS)

Pang, Sook Theng; Liew, How Hui; Chang, Yun Fah

2017-04-01

A Constant Rebalanced Portfolio (CRP) is an investment strategy which reinvests by redistributing wealth equally among a set of stocks. The empirical performance of the distribution-generated universal portfolio strategies are analysed experimentally concerning 10 higher volume stocks from different categories in Kuala Lumpur Stock Exchange. The time interval of study is from January 2000 to December 2015, which includes the credit crisis from September 2008 to March 2009. The performance of the finite-order universal portfolio strategies has been shown to be better than Constant Rebalanced Portfolio with some selected parameters of proposed universal portfolios.

Computation of rapidly varied unsteady, free-surface flow

USGS Publications Warehouse

Basco, D.R.

1987-01-01

Many unsteady flows in hydraulics occur with relatively large gradients in free surface profiles. The assumption of hydrostatic pressure distribution with depth is no longer valid. These are rapidly-varied unsteady flows (RVF) of classical hydraulics and also encompass short wave propagation of coastal hydraulics. The purpose of this report is to present an introductory review of the Boussinnesq-type differential equations that describe these flows and to discuss methods for their numerical integration. On variable slopes and for large scale (finite-amplitude) disturbances, three independent derivational methods all gave differences in the motion equation for higher order terms. The importance of these higher-order terms for riverine applications must be determined by numerical experiments. Care must be taken in selection of the appropriate finite-difference scheme to minimize truncation error effects and the possibility of diverging (double mode) numerical solutions. It is recommended that practical hydraulics cases be established and tested numerically to demonstrate the order of differences in solution with those obtained from the long wave equations of St. Venant. (USGS)

Discretizing singular point sources in hyperbolic wave propagation problems

DOE PAGES

Petersson, N. Anders; O'Reilly, Ossian; Sjogreen, Bjorn; ...

2016-06-01

Here, we develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as themore » number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.« less

Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements

NASA Astrophysics Data System (ADS)

Lohmann, Christoph; Kuzmin, Dmitri; Shadid, John N.; Mabuza, Sibusiso

2017-09-01

This work extends the flux-corrected transport (FCT) methodology to arbitrary order continuous finite element discretizations of scalar conservation laws on simplex meshes. Using Bernstein polynomials as local basis functions, we constrain the total variation of the numerical solution by imposing local discrete maximum principles on the Bézier net. The design of accuracy-preserving FCT schemes for high order Bernstein-Bézier finite elements requires the development of new algorithms and/or generalization of limiting techniques tailored for linear and multilinear Lagrange elements. In this paper, we propose (i) a new discrete upwinding strategy leading to local extremum bounded low order approximations with compact stencils, (ii) high order variational stabilization based on the difference between two gradient approximations, and (iii) new localized limiting techniques for antidiffusive element contributions. The optional use of a smoothness indicator, based on a second derivative test, makes it possible to potentially avoid unnecessary limiting at smooth extrema and achieve optimal convergence rates for problems with smooth solutions. The accuracy of the proposed schemes is assessed in numerical studies for the linear transport equation in 1D and 2D.

An implicit spatial and high-order temporal finite difference scheme for 2D acoustic modelling

NASA Astrophysics Data System (ADS)

Wang, Enjiang; Liu, Yang

2018-01-01

The finite difference (FD) method exhibits great superiority over other numerical methods due to its easy implementation and small computational requirement. We propose an effective FD method, characterised by implicit spatial and high-order temporal schemes, to reduce both the temporal and spatial dispersions simultaneously. For the temporal derivative, apart from the conventional second-order FD approximation, a special rhombus FD scheme is included to reach high-order accuracy in time. Compared with the Lax-Wendroff FD scheme, this scheme can achieve nearly the same temporal accuracy but requires less floating-point operation times and thus less computational cost when the same operator length is adopted. For the spatial derivatives, we adopt the implicit FD scheme to improve the spatial accuracy. Apart from the existing Taylor series expansion-based FD coefficients, we derive the least square optimisation based implicit spatial FD coefficients. Dispersion analysis and modelling examples demonstrate that, our proposed method can effectively decrease both the temporal and spatial dispersions, thus can provide more accurate wavefields.

Methods for compressible fluid simulation on GPUs using high-order finite differences

NASA Astrophysics Data System (ADS)

Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit J.; Käpylä, Petri J.; Anjum, Omer

2017-08-01

We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this makes them an attractive platform for fluid simulation. However, high-order stencil computation is memory-intensive with respect to both main memory and the caches of the GPU. We present two approaches for simulating compressible fluids using 55-point and 19-point stencils. We seek to reduce the requirements for memory bandwidth and cache size in our methods by using cache blocking and decomposing a latency-bound kernel into several bandwidth-bound kernels. Our fastest implementation is bandwidth-bound and integrates 343 million grid points per second on a Tesla K40t GPU, achieving a 3 . 6 × speedup over a comparable hydrodynamics solver benchmarked on two Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is latency-bound and achieves the rate of 168 million updates per second.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Motamarri, P.; Nowak, M.R.; Leiter, K.

2013-11-15

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposedmore » solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources, and good scalability of the present implementation up to 192 processors.« less

Position-dependent mass, finite-gap systems, and supersymmetry

NASA Astrophysics Data System (ADS)

Bravo, Rafael; Plyushchay, Mikhail S.

2016-05-01

The ordering problem in quantum systems with position-dependent mass (PDM) is treated by inclusion of the classically fictitious similarity transformation into the kinetic term. This provides a generation of supersymmetry with the first-order supercharges from the kinetic term alone, while inclusion of the potential term allows us also to generate nonlinear supersymmetry with higher-order supercharges. A broad class of finite-gap systems with PDM is obtained by different reduction procedures, and general results on supersymmetry generation are applied to them. We show that elliptic finite-gap systems of Lamé and Darboux-Treibich-Verdier types can be obtained by reduction to Seiffert's spherical spiral and Bernoulli lemniscate in the presence of Calogero-like or harmonic oscillator potentials, or by angular momentum reduction of a free motion on some AdS2 -related surfaces in the presence of Aharonov-Bohm flux. The limiting cases include the Higgs and Mathews-Lakshmanan oscillator models as well as a reflectionless model with PDM exploited recently in the discussion of cosmological inflationary scenarios.

Chiral phase transition at finite chemical potential in 2 +1 -flavor soft-wall anti-de Sitter space QCD

NASA Astrophysics Data System (ADS)

Bartz, Sean P.; Jacobson, Theodore

2018-04-01

The phase transition from hadronic matter to chirally symmetric quark-gluon plasma is expected to be a rapid crossover at zero quark chemical potential (μ ), becoming first order at some finite value of μ , indicating the presence of a critical point. Using a three-flavor soft-wall model of anti-de Sitter/QCD, we investigate the effect of varying the light and strange quark masses on the order of the chiral phase transition. At zero quark chemical potential, we reproduce the Columbia Plot, which summarizes the results of lattice QCD and other holographic models. We then extend this holographic model to examine the effects of finite quark chemical potential. We find that the the chemical potential does not affect the critical line that separates first-order from rapid crossover transitions. This excludes the possibility of a critical point in this model, suggesting that a different setup is necessary to reproduce all the features of the QCD phase diagram.

Demonstration Of Ultra HI-FI (UHF) Methods

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2004-01-01

Computational aero-acoustics (CAA) requires efficient, high-resolution simulation tools. Most current techniques utilize finite-difference approaches because high order accuracy is considered too difficult or expensive to achieve with finite volume or finite element methods. However, a novel finite volume approach (Ultra HI-FI or UHF) which utilizes Hermite fluxes is presented which can achieve both arbitrary accuracy and fidelity in space and time. The technique can be applied to unstructured grids with some loss of fidelity or with multi-block structured grids for maximum efficiency and resolution. In either paradigm, it is possible to resolve ultra-short waves (less than 2 PPW). This is demonstrated here by solving the 4th CAA workshop Category 1 Problem 1.

Guidelines and Recommendations on the Use of Higher Order Finite Elements for Bending Analysis of Plates

NASA Astrophysics Data System (ADS)

Carrera, E.; Miglioretti, F.; Petrolo, M.

2011-11-01

This paper compares and evaluates various plate finite elements to analyse the static response of thick and thin plates subjected to different loading and boundary conditions. Plate elements are based on different assumptions for the displacement distribution along the thickness direction. Classical (Kirchhoff and Reissner-Mindlin), refined (Reddy and Kant), and other higher-order displacement fields are implemented up to fourth-order expansion. The Unified Formulation UF by the first author is used to derive finite element matrices in terms of fundamental nuclei which consist of 3×3 arrays. The MITC4 shear-locking free type formulation is used for the FE approximation. Accuracy of a given plate element is established in terms of the error vs. thickness-to-length parameter. A significant number of finite elements for plates are implemented and compared using displacement and stress variables for various plate problems. Reduced models that are able to detect the 3D solution are built and a Best Plate Diagram (BPD) is introduced to give guidelines for the construction of plate theories based on a given accuracy and number of terms. It is concluded that the UF is a valuable tool to establish, for a given plate problem, the most accurate FE able to furnish results within a certain accuracy range. This allows us to obtain guidelines and recommendations in building refined elements in the bending analysis of plates for various geometries, loadings, and boundary conditions.

Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory

NASA Technical Reports Server (NTRS)

Putcha, N. S.; Reddy, J. N.

1986-01-01

A mixed shear flexible finite element, with relaxed continuity, is developed for the geometrically linear and nonlinear analysis of layered anisotropic plates. The element formulation is based on a refined higher order theory which satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate and requires no shear correction coefficients. The mixed finite element developed herein consists of eleven degrees of freedom per node which include three displacements, two rotations and six moment resultants. The element is evaluated for its accuracy in the analysis of the stability and vibration of anisotropic rectangular plates with different lamination schemes and boundary conditions. The mixed finite element described here for the higher order theory gives very accurate results for buckling loads and natural frequencies.

Microscopic and macroscopic instabilities in finitely strained porous elastomers

NASA Astrophysics Data System (ADS)

Michel, J. C.; Lopez-Pamies, O.; Ponte Castañeda, P.; Triantafyllidis, N.

2007-05-01

The present work is an in-depth study of the connections between microstructural instabilities and their macroscopic manifestations—as captured through the effective properties—in finitely strained porous elastomers. The powerful second-order homogenization (SOH) technique initially developed for random media, is used for the first time here to study the onset of failure in periodic porous elastomers and the results are compared to more accurate finite element method (FEM) calculations. The influence of different microgeometries (random and periodic), initial porosity, matrix constitutive law and macroscopic load orientation on the microscopic buckling (for periodic microgeometries) and macroscopic loss of ellipticity (for all microgeometries) is investigated in detail. In addition to the above-described stability-based onset-of-failure mechanisms, constraints on the principal solution are also addressed, thus giving a complete picture of the different possible failure mechanisms present in finitely strained porous elastomers.

Second-order accurate nonoscillatory schemes for scalar conservation laws

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

1989-01-01

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

High-resolution schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Harten, A.

1982-01-01

A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurae scheme to an appropriately modified flux function. The so derived second order accurate schemes achieve high resolution while preserving the robustness of the original nonoscillatory first order accurate scheme.

Numerical investigation of sixth order Boussinesq equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.; Vucheva, V.

2017-10-01

We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.

Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Q.; Sprague, M. A.; Jonkman, J.

2014-01-01

This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context ofmore » LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.« less

A higher-order theory for geometrically nonlinear analysis of composite laminates

NASA Technical Reports Server (NTRS)

Reddy, J. N.; Liu, C. F.

1987-01-01

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

A time-spectral approach to numerical weather prediction

NASA Astrophysics Data System (ADS)

Scheffel, Jan; Lindvall, Kristoffer; Yik, Hiu Fai

2018-05-01

Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.

The aggregated unfitted finite element method for elliptic problems

NASA Astrophysics Data System (ADS)

Badia, Santiago; Verdugo, Francesc; Martín, Alberto F.

2018-07-01

Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hinders the practical usage of unfitted methods for realistic large scale applications. In this work, we present a technique that addresses such conditioning problems by constructing enhanced finite element spaces based on a cell aggregation technique. The presented method, called aggregated unfitted finite element method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming Lagrangian finite element spaces. The mathematical analysis of the new method states that the condition number of the resulting linear system matrix scales as in standard finite elements for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal finite element convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments.

Quantum Quenches in a Spinor Condensate

NASA Astrophysics Data System (ADS)

Lamacraft, Austen

2007-04-01

We discuss the ordering of a spin-1 condensate when quenched from its paramagnetic phase to its ferromagnetic phase by reducing the magnetic field. We first elucidate the nature of the equilibrium quantum phase transition. Quenching rapidly through this transition reveals XY ordering either at a specific wave vector, or the “light-cone” correlations familiar from relativistic theories, depending on the end point of the quench. For a quench proceeding at a finite rate the ordering scale is governed by the Kibble-Zurek mechanism. The creation of vortices through growth of the magnetization fluctuations is also discussed. The long-time dynamics again depends on the end point, conserving the order parameter in a zero field, but not at a finite field, with differing exponents for the coarsening of magnetic order. The results are discussed in the light of a recent experiment by Sadler et al.

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.

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.

Finite volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Rössler, Thomas

2015-11-01

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark flow technique.

Measures with locally finite support and spectrum.

PubMed

Meyer, Yves F

2016-03-22

The goal of this paper is the construction of measures μ on R(n)enjoying three conflicting but fortunately compatible properties: (i) μ is a sum of weighted Dirac masses on a locally finite set, (ii) the Fourier transform μ f μ is also a sum of weighted Dirac masses on a locally finite set, and (iii) μ is not a generalized Dirac comb. We give surprisingly simple examples of such measures. These unexpected patterns strongly differ from quasicrystals, they provide us with unusual Poisson's formulas, and they might give us an unconventional insight into aperiodic order.

Measures with locally finite support and spectrum

PubMed Central

Meyer, Yves F.

2016-01-01

The goal of this paper is the construction of measures μ on Rn enjoying three conflicting but fortunately compatible properties: (i) μ is a sum of weighted Dirac masses on a locally finite set, (ii) the Fourier transform μ^ of μ is also a sum of weighted Dirac masses on a locally finite set, and (iii) μ is not a generalized Dirac comb. We give surprisingly simple examples of such measures. These unexpected patterns strongly differ from quasicrystals, they provide us with unusual Poisson's formulas, and they might give us an unconventional insight into aperiodic order. PMID:26929358

Finite-temperature mechanical instability in disordered lattices.

PubMed

Zhang, Leyou; Mao, Xiaoming

2016-02-01

Mechanical instability takes different forms in various ordered and disordered systems and little is known about how thermal fluctuations affect different classes of mechanical instabilities. We develop an analytic theory involving renormalization of rigidity and coherent potential approximation that can be used to understand finite-temperature mechanical stabilities in various disordered systems. We use this theory to study two disordered lattices: a randomly diluted triangular lattice and a randomly braced square lattice. These two lattices belong to two different universality classes as they approach mechanical instability at T=0. We show that thermal fluctuations stabilize both lattices. In particular, the triangular lattice displays a critical regime in which the shear modulus scales as G∼T(1/2), whereas the square lattice shows G∼T(2/3). We discuss generic scaling laws for finite-T mechanical instabilities and relate them to experimental systems.

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brinkman, D., E-mail: Daniel.Brinkman@asu.edu; School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287; Heitzinger, C., E-mail: Clemens.Heitzinger@asu.edu

2014-01-15

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

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

NASA Astrophysics Data System (ADS)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.

Four-level conservative finite-difference schemes for Boussinesq paradigm equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.

2013-10-01

In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.

Distributed Finite-Time Cooperative Control of Multiple High-Order Nonholonomic Mobile Robots.

PubMed

Du, Haibo; Wen, Guanghui; Cheng, Yingying; He, Yigang; Jia, Ruting

2017-12-01

The consensus problem of multiple nonholonomic mobile robots in the form of high-order chained structure is considered in this paper. Based on the model features and the finite-time control technique, a finite-time cooperative controller is explicitly constructed which guarantees that the states consensus is achieved in a finite time. As an application of the proposed results, finite-time formation control of multiple wheeled mobile robots is studied and a finite-time formation control algorithm is proposed. To show effectiveness of the proposed approach, a simulation example is given.

Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

DOE PAGES

Petersson, N. Anders; Sjogreen, Bjorn

2015-07-20

We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-fieldmore » technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.« less

A novel unsplit perfectly matched layer for the second-order acoustic wave equation.

PubMed

Ma, Youneng; Yu, Jinhua; Wang, Yuanyuan

2014-08-01

When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach. Copyright © 2014 Elsevier B.V. All rights reserved.

Possible higher order phase transition in large-N gauge theory at finite temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nishimura, Hiromichi

2017-08-07

We analyze the phase structure of SU(¥) gauge theory at finite temperature using matrix models. Our basic assumption is that the effective potential is dominated by double-trace terms for the Polyakov loops. As a function of the temperature, a background field for the Polyakov loop, and a quartic coupling, it exhibits a universal structure: in the large portion of the parameter space, there is a continuous phase transition analogous to the third-order phase transition of Gross,Witten and Wadia, but the order of phase transition can be higher than third. We show that different confining potentials give rise to drastically differentmore » behavior of the eigenvalue density and the free energy. Therefore lattice simulations at large N could probe the order of phase transition and test our results. Critical« less

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

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

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

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

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

NASA Astrophysics Data System (ADS)

Yang, Zailin; Wang, Yao; Hei, Baoping

2013-12-01

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of onedimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.

Boundary conditions in Chebyshev and Legendre methods

NASA Technical Reports Server (NTRS)

Canuto, C.

1984-01-01

Two different ways of treating non-Dirichlet boundary conditions in Chebyshev and Legendre collocation methods are discussed for second order differential problems. An error analysis is provided. The effect of preconditioning the corresponding spectral operators by finite difference matrices is also investigated.

Flow Applications of the Least Squares Finite Element Method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1998-01-01

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Dynamic earthquake rupture simulations on nonplanar faults embedded in 3D geometrically complex, heterogeneous elastic solids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duru, Kenneth, E-mail: kduru@stanford.edu; Dunham, Eric M.; Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA

Dynamic propagation of shear ruptures on a frictional interface in an elastic solid is a useful idealization of natural earthquakes. The conditions relating discontinuities in particle velocities across fault zones and tractions acting on the fault are often expressed as nonlinear friction laws. The corresponding initial boundary value problems are both numerically and computationally challenging. In addition, seismic waves generated by earthquake ruptures must be propagated for many wavelengths away from the fault. Therefore, reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods. We present a high order accurate finite difference method for: a)more » enforcing nonlinear friction laws, in a consistent and provably stable manner, suitable for efficient explicit time integration; b) dynamic propagation of earthquake ruptures along nonplanar faults; and c) accurate propagation of seismic waves in heterogeneous media with free surface topography. We solve the first order form of the 3D elastic wave equation on a boundary-conforming curvilinear mesh, in terms of particle velocities and stresses that are collocated in space and time, using summation-by-parts (SBP) finite difference operators in space. Boundary and interface conditions are imposed weakly using penalties. By deriving semi-discrete energy estimates analogous to the continuous energy estimates we prove numerical stability. The finite difference stencils used in this paper are sixth order accurate in the interior and third order accurate close to the boundaries. However, the method is applicable to any spatial operator with a diagonal norm satisfying the SBP property. Time stepping is performed with a 4th order accurate explicit low storage Runge–Kutta scheme, thus yielding a globally fourth order accurate method in both space and time. We show numerical simulations on band limited self-similar fractal faults revealing the complexity of rupture dynamics on rough faults.« less

Dynamic earthquake rupture simulations on nonplanar faults embedded in 3D geometrically complex, heterogeneous elastic solids

NASA Astrophysics Data System (ADS)

Duru, Kenneth; Dunham, Eric M.

2016-01-01

Dynamic propagation of shear ruptures on a frictional interface in an elastic solid is a useful idealization of natural earthquakes. The conditions relating discontinuities in particle velocities across fault zones and tractions acting on the fault are often expressed as nonlinear friction laws. The corresponding initial boundary value problems are both numerically and computationally challenging. In addition, seismic waves generated by earthquake ruptures must be propagated for many wavelengths away from the fault. Therefore, reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods. We present a high order accurate finite difference method for: a) enforcing nonlinear friction laws, in a consistent and provably stable manner, suitable for efficient explicit time integration; b) dynamic propagation of earthquake ruptures along nonplanar faults; and c) accurate propagation of seismic waves in heterogeneous media with free surface topography. We solve the first order form of the 3D elastic wave equation on a boundary-conforming curvilinear mesh, in terms of particle velocities and stresses that are collocated in space and time, using summation-by-parts (SBP) finite difference operators in space. Boundary and interface conditions are imposed weakly using penalties. By deriving semi-discrete energy estimates analogous to the continuous energy estimates we prove numerical stability. The finite difference stencils used in this paper are sixth order accurate in the interior and third order accurate close to the boundaries. However, the method is applicable to any spatial operator with a diagonal norm satisfying the SBP property. Time stepping is performed with a 4th order accurate explicit low storage Runge-Kutta scheme, thus yielding a globally fourth order accurate method in both space and time. We show numerical simulations on band limited self-similar fractal faults revealing the complexity of rupture dynamics on rough faults.

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

NASA Astrophysics Data System (ADS)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

Improved finite-difference computation of the van der Waals force: One-dimensional case

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pinto, Fabrizio

2009-10-15

We present an improved demonstration of the calculation of Casimir forces in one-dimensional systems based on the recently proposed numerical imaginary frequency Green's function computation approach. The dispersion force on two thick lossy dielectric slabs separated by an empty gap and placed within a perfectly conducting cavity is obtained from the Green's function of the modified Helmholtz equation by means of an ordinary finite-difference method. In order to demonstrate the possibility to develop algorithms to explore complex geometries in two and three dimensions to higher order in the mesh spacing, we generalize existing classical electromagnetism algebraic methods to generate themore » difference equations for dielectric boundaries not coinciding with any grid points. Diagnostic tests are presented to monitor the accuracy of our implementation of the method and follow-up applications in higher dimensions are introduced.« less

Frequency domain finite-element and spectral-element acoustic wave modeling using absorbing boundaries and perfectly matched layer

NASA Astrophysics Data System (ADS)

Rahimi Dalkhani, Amin; Javaherian, Abdolrahim; Mahdavi Basir, Hadi

2018-04-01

Wave propagation modeling as a vital tool in seismology can be done via several different numerical methods among them are finite-difference, finite-element, and spectral-element methods (FDM, FEM and SEM). Some advanced applications in seismic exploration benefit the frequency domain modeling. Regarding flexibility in complex geological models and dealing with the free surface boundary condition, we studied the frequency domain acoustic wave equation using FEM and SEM. The results demonstrated that the frequency domain FEM and SEM have a good accuracy and numerical efficiency with the second order interpolation polynomials. Furthermore, we developed the second order Clayton and Engquist absorbing boundary condition (CE-ABC2) and compared it with the perfectly matched layer (PML) for the frequency domain FEM and SEM. In spite of PML method, CE-ABC2 does not add any additional computational cost to the modeling except assembling boundary matrices. As a result, considering CE-ABC2 is more efficient than PML for the frequency domain acoustic wave propagation modeling especially when computational cost is high and high-level absorbing performance is unnecessary.

Reynolds number effects on mixing due to topological chaos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Spencer A.; Warrier, Sangeeta

2016-03-15

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To help clarify this dependency, we numerically simulate the effects of a batch stirring device on a 2D incompressible Newtonian fluid in the laminar regime. In particular, we calculate the finite time Lyapunov exponent (FTLE) field for threemore » different stirring protocols, one topologically complex (pseudo-Anosov) and two simple (finite-order), over a range of viscosities. After extracting appropriate measures indicative of both the amount of mixing and the area of effective mixing from the FTLE field, we see a clearly defined Reynolds number range in which the relative efficacy of the pseudo-Anosov protocol over the finite-order protocols justifies the application of topological chaos. More unexpectedly, we see that while the measures of effective mixing area increase with increasing Reynolds number for the finite-order protocols, they actually exhibit non-monotonic behavior for the pseudo-Anosov protocol.« less

Total Variation Diminishing (TVD) schemes of uniform accuracy

NASA Technical Reports Server (NTRS)

Hartwich, PETER-M.; Hsu, Chung-Hao; Liu, C. H.

1988-01-01

Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.

A finite difference scheme for the equilibrium equations of elastic bodies

NASA Technical Reports Server (NTRS)

Phillips, T. N.; Rose, M. E.

1984-01-01

A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques.

Rupture Dynamics Simulation for Non-Planar fault by a Curved Grid Finite Difference Method

NASA Astrophysics Data System (ADS)

Zhang, Z.; Zhu, G.; Chen, X.

2011-12-01

We first implement the non-staggered finite difference method to solve the dynamic rupture problem, with split-node, for non-planar fault. Split-node method for dynamic simulation has been used widely, because of that it's more precise to represent the fault plane than other methods, for example, thick fault, stress glut and so on. The finite difference method is also a popular numeric method to solve kinematic and dynamic problem in seismology. However, previous works focus most of theirs eyes on the staggered-grid method, because of its simplicity and computational efficiency. However this method has its own disadvantage comparing to non-staggered finite difference method at some fact for example describing the boundary condition, especially the irregular boundary, or non-planar fault. Zhang and Chen (2006) proposed the MacCormack high order non-staggered finite difference method based on curved grids to precisely solve irregular boundary problem. Based upon on this non-staggered grid method, we make success of simulating the spontaneous rupture problem. The fault plane is a kind of boundary condition, which could be irregular of course. So it's convinced that we could simulate rupture process in the case of any kind of bending fault plane. We will prove this method is valid in the case of Cartesian coordinate first. In the case of bending fault, the curvilinear grids will be used.

A two-dimensional, finite-difference model of the oxidation of a uranium carbide fuel pellet

NASA Astrophysics Data System (ADS)

Shepherd, James; Fairweather, Michael; Hanson, Bruce C.; Heggs, Peter J.

2015-12-01

The oxidation of spent uranium carbide fuel, a candidate fuel for Generation IV nuclear reactors, is an important process in its potential reprocessing cycle. However, the oxidation of uranium carbide in air is highly exothermic. A model has therefore been developed to predict the temperature rise, as well as other useful information such as reaction completion times, under different reaction conditions in order to help in deriving safe oxidation conditions. Finite difference-methods are used to model the heat and mass transfer processes occurring during the reaction in two dimensions and are coupled to kinetics found in the literature.

Flux vector splitting of the inviscid equations with application to finite difference methods

NASA Technical Reports Server (NTRS)

Steger, J. L.; Warming, R. F.

1979-01-01

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Finite element methods for the biomechanics of soft hydrated tissues: nonlinear analysis and adaptive control of meshes.

PubMed

Spilker, R L; de Almeida, E S; Donzelli, P S

1992-01-01

This chapter addresses computationally demanding numerical formulations in the biomechanics of soft tissues. The theory of mixtures can be used to represent soft hydrated tissues in the human musculoskeletal system as a two-phase continuum consisting of an incompressible solid phase (collagen and proteoglycan) and an incompressible fluid phase (interstitial water). We first consider the finite deformation of soft hydrated tissues in which the solid phase is represented as hyperelastic. A finite element formulation of the governing nonlinear biphasic equations is presented based on a mixed-penalty approach and derived using the weighted residual method. Fluid and solid phase deformation, velocity, and pressure are interpolated within each element, and the pressure variables within each element are eliminated at the element level. A system of nonlinear, first-order differential equations in the fluid and solid phase deformation and velocity is obtained. In order to solve these equations, the contributions of the hyperelastic solid phase are incrementally linearized, a finite difference rule is introduced for temporal discretization, and an iterative scheme is adopted to achieve equilibrium at the end of each time increment. We demonstrate the accuracy and adequacy of the procedure using a six-node, isoparametric axisymmetric element, and we present an example problem for which independent numerical solution is available. Next, we present an automated, adaptive environment for the simulation of soft tissue continua in which the finite element analysis is coupled with automatic mesh generation, error indicators, and projection methods. Mesh generation and updating, including both refinement and coarsening, for the two-dimensional examples examined in this study are performed using the finite quadtree approach. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. To allow the finite difference algorithm to proceed in time using an updated mesh, solution values must be transferred to the new nodal locations. This rezoning is accomplished using a projected field for the primary variables. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using a linear, two-dimensional, axisymmetric problem corresponding to the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients and to produce solutions in good agreement with independent, converged, numerical solutions.

Stabilization of a finite slice in miscible displacement in homogeneous porous media

NASA Astrophysics Data System (ADS)

Pramanik, Satyajit; Mishra, Manoranjan

2016-11-01

We numerically studied the miscible displacement of a finite slice of variable viscosity and density. The stability of the finite slice depends on different flow parameters, such as displacement velocity U, mobility ratio R , and the density contrast. Series of numerical simulations corresponding to different ordered pair (R, U) in the parameter space, and a given density contrast reveal six different instability regions. We have shown that independent of the width of the slice, there always exists a region of stable displacement, and below a critical value of the slice width, this stable region increases with decreasing slice width. Further we observe that the viscous fingering (buoyancy-induced instability) at the upper interface induces buoyancy-induced instability (viscous fingering) at the lower interface. Besides the fundamental fluid dynamics understanding, our results can be helpful to model CO2 sequestration and chromatographic separation.

Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures

NASA Astrophysics Data System (ADS)

Pötz, Walter

2017-11-01

A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

Simulation of hot spots formation and evolution in HMX

NASA Astrophysics Data System (ADS)

Wang, Cheng; Yang, Tonghui

2017-06-01

In order to study the formation and evolution of hot spots under shock loading, HMX explosives were selected as the object of study for the two-dimensional finite difference numerical simulation. A fifth order finite difference weighted essentially non-oscillatory (WENO) scheme and a third order TVD Runge-Kutta method are utilized for the spatial discretization and the time advance, respectively. The governing equations are based on the fluid elasto-plastic control equations. The Mie-Gruneisen equation of state and the ideal gas equation of state are selected to use in the state equation of the solid explosives and gas material. In order to simplify the calculation of the model, the reaction can be considered to complete in one step. The calculated area is [ 3.0 ×10-5 m ] × [ 3.0 ×10-5 m ] . The radius is 0.6 ×10-5 m, and the internal gas is not involved in the reaction. The calculation area is divided into 300×300 grids and 10 grids are selected from the bottom of each column to give the particle velocity u as the initial condition. In the selected grid, different initial velocity 100m/s and 200m/s are loaded respectively to study the influence of hot spot formation and evolution in different impact intensity.

Two variants of minimum discarded fill ordering

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Azevedo, E.F.; Forsyth, P.A.; Tang, Wei-Pai

1991-01-01

It is well known that the ordering of the unknowns can have a significant effect on the convergence of Preconditioned Conjugate Gradient (PCG) methods. There has been considerable experimental work on the effects of ordering for regular finite difference problems. In many cases, good results have been obtained with preconditioners based on diagonal, spiral or natural row orderings. However, for finite element problems having unstructured grids or grids generated by a local refinement approach, it is difficult to define many of the orderings for more regular problems. A recently proposed Minimum Discarded Fill (MDF) ordering technique is effective in findingmore » high quality Incomplete LU (ILU) preconditioners, especially for problems arising from unstructured finite element grids. Testing indicates this algorithm can identify a rather complicated physical structure in an anisotropic problem and orders the unknowns in the preferred'' direction. The MDF technique may be viewed as the numerical analogue of the minimum deficiency algorithm in sparse matrix technology. At any stage of the partial elimination, the MDF technique chooses the next pivot node so as to minimize the amount of discarded fill. In this work, two efficient variants of the MDF technique are explored to produce cost-effective high-order ILU preconditioners. The Threshold MDF orderings combine MDF ideas with drop tolerance techniques to identify the sparsity pattern in the ILU preconditioners. These techniques identify an ordering that encourages fast decay of the entries in the ILU factorization. The Minimum Update Matrix (MUM) ordering technique is a simplification of the MDF ordering and is closely related to the minimum degree algorithm. The MUM ordering is especially for large problems arising from Navier-Stokes problems. Some interesting pictures of the orderings are presented using a visualization tool. 22 refs., 4 figs., 7 tabs.« less

Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

PubMed Central

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

[Application of finite element method in spinal biomechanics].

PubMed

Liu, Qiang; Zhang, Jun; Sun, Shu-Chun; Wang, Fei

2017-02-25

The finite element model is one of the most important methods in study of modern spinal biomechanics, according to the needs to simulate the various states of the spine, calculate the stress force and strain distribution of the different groups in the state, and explore its principle of mechanics, mechanism of injury, and treatment effectiveness. In addition, in the study of the pathological state of the spine, the finite element is mainly used in the understanding the mechanism of lesion location, evaluating the effects of different therapeutic tool, assisting and completing the selection and improvement of therapeutic tool, in order to provide a theoretical basis for the rehabilitation of spinal lesions. Finite element method can be more provide the service for the patients suffering from spinal correction, operation and individual implant design. Among the design and performance evaluation of the implant need to pay attention to the individual difference and perfect the evaluation system. At present, how to establish a model which is more close to the real situation has been the focus and difficulty of the study of human body's finite element.Although finite element method can better simulate complex working condition, it is necessary to improve the authenticity of the model and the sharing of the group by using many kinds of methods, such as image science, statistics, kinematics and so on. Copyright© 2017 by the China Journal of Orthopaedics and Traumatology Press.

a Bounded Finite-Difference Discretization of a Two-Dimensional Diffusion Equation with Logistic Nonlinear Reaction

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

In the present manuscript, we introduce a finite-difference scheme to approximate solutions of the two-dimensional version of Fisher's equation from population dynamics, which is a model for which the existence of traveling-wave fronts bounded within (0,1) is a well-known fact. The method presented here is a nonstandard technique which, in the linear regime, approximates the solutions of the original model with a consistency of second order in space and first order in time. The theory of M-matrices is employed here in order to elucidate conditions under which the method is able to preserve the positivity and the boundedness of solutions. In fact, our main result establishes relatively flexible conditions under which the preservation of the positivity and the boundedness of new approximations is guaranteed. Some simulations of the propagation of a traveling-wave solution confirm the analytical results derived in this work; moreover, the experiments evince a good agreement between the numerical result and the analytical solutions.

Finite Element Analysis of Folded Airbag in Frontal Impact of Adapted Vehicles for Disabled Drivers

NASA Astrophysics Data System (ADS)

Masiá, J.; Eixerés, B.; Dols, J. F.; Esquerdo, T. V.

2009-11-01

The car control adaptations are used in vehicles in order to facilitate the driving to persons with physical handicaps. This does not have to suppose a decrease of the passive safety that is required to the vehicles. In order to analyze this relation there will be characterized the different control adaptations that are in use together with the different devices of passive safety that can be mounted in the vehicles in diverse cases of impact in order to generate models of simulation. The methodology used to generate this simulation consists of the first phase in which there develops the three-dimensional model of the driving place. For it, there has been used a commercial software of three-dimensional design. Once realized this one divides, the model is imported to the finite elements software in which meshing is generated. Finally, dynamic simulation software is used to assign the most important characteristics like material properties, contact interfaces, gas expansion models, airbag fold types, etc.

The MUSIC algorithm for impedance tomography of small inclusions from discrete data

NASA Astrophysics Data System (ADS)

Lechleiter, A.

2015-09-01

We consider a point-electrode model for electrical impedance tomography and show that current-to-voltage measurements from finitely many electrodes are sufficient to characterize the positions of a finite number of point-like inclusions. More precisely, we consider an asymptotic expansion with respect to the size of the small inclusions of the relative Neumann-to-Dirichlet operator in the framework of the point electrode model. This operator is naturally finite-dimensional and models difference measurements by finitely many small electrodes of the electric potential with and without the small inclusions. Moreover, its leading-order term explicitly characterizes the centers of the small inclusions if the (finite) number of point electrodes is large enough. This characterization is based on finite-dimensional test vectors and leads naturally to a MUSIC algorithm for imaging the inclusion centers. We show both the feasibility and limitations of this imaging technique via two-dimensional numerical experiments, considering in particular the influence of the number of point electrodes on the algorithm’s images.

Computation of ground motion amplification in Kolkata megacity (India) using finite-difference method for seismic microzonation

NASA Astrophysics Data System (ADS)

Shiuly, Amit; Kumar, Vinay; Narayan, Jay

2014-06-01

This paper presents the ground motion amplification scenario along with fundamental frequency (F 0) of sedimentary deposit for the seismic microzonation of Kolkata City, situated on the world's largest delta island with very soft soil deposit. A 4th order accurate SH-wave viscoelastic finite-difference algorithm is used for computation of response of 1D model for each borehole location. Different maps, such as for F 0, amplification at F 0, average spectral amplification (ASA) in the different frequency bandwidth of earthquake engineering interest are developed for a variety of end-users communities. The obtained ASA of the order of 3-6 at most of the borehole locations in a frequency range of 0.25-10.0 Hz reveals that Kolkata City may suffer severe damage even during a moderate earthquake. Further, unexpected severe damage to collapse of multi-storey buildings may occur in localities near Hoogly River and Salt Lake area due to double resonance effects during distant large earthquakes.

Evaluation of the use of a singularity element in finite element analysis of center-cracked plates

NASA Technical Reports Server (NTRS)

Mendelson, A.; Gross, B.; Srawley, J., E.

1972-01-01

Two different methods are applied to the analyses of finite width linear elastic plates with central cracks. Both methods give displacements as a primary part of the solution. One method makes use of Fourier transforms. The second method employs a coarse mesh of triangular second-order finite elements in conjunction with a single singularity element subjected to appropriate additional constraints. The displacements obtained by these two methods are in very good agreement. The results suggest considerable potential for the use of a cracked element for related crack problems, particularly in connection with the extension to nonlinear material behavior.

Pre- and postprocessing techniques for determining goodness of computational meshes

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Westermann, T.; Bass, J. M.

1993-01-01

Research in error estimation, mesh conditioning, and solution enhancement for finite element, finite difference, and finite volume methods has been incorporated into AUDITOR, a modern, user-friendly code, which operates on 2D and 3D unstructured neutral files to improve the accuracy and reliability of computational results. Residual error estimation capabilities provide local and global estimates of solution error in the energy norm. Higher order results for derived quantities may be extracted from initial solutions. Within the X-MOTIF graphical user interface, extensive visualization capabilities support critical evaluation of results in linear elasticity, steady state heat transfer, and both compressible and incompressible fluid dynamics.

Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials

NASA Astrophysics Data System (ADS)

Britt, S.; Tsynkov, S.; Turkel, E.

2018-02-01

We solve the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time. This is accomplished using an implicit finite difference (FD) scheme for the wave equation and solving an elliptic (modified Helmholtz) equation at each time step with fourth order spatial accuracy by the method of difference potentials (MDP). High-order MDP utilizes compact FD schemes on regular structured grids to efficiently solve problems on nonconforming domains while maintaining the design convergence rate of the underlying FD scheme. Asymptotically, the computational complexity of high-order MDP scales the same as that for FD.

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2000-01-01

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. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Green's function enriched Poisson solver for electrostatics in many-particle systems

NASA Astrophysics Data System (ADS)

Sutmann, Godehard

2016-06-01

A highly accurate method is presented for the construction of the charge density for the solution of the Poisson equation in particle simulations. The method is based on an operator adjusted source term which can be shown to produce exact results up to numerical precision in the case of a large support of the charge distribution, therefore compensating the discretization error of finite difference schemes. This is achieved by balancing an exact representation of the known Green's function of regularized electrostatic problem with a discretized representation of the Laplace operator. It is shown that the exact calculation of the potential is possible independent of the order of the finite difference scheme but the computational efficiency for higher order methods is found to be superior due to a faster convergence to the exact result as a function of the charge support.

Finite time control for MIMO nonlinear system based on higher-order sliding mode.

PubMed

Liu, Xiangjie; Han, Yaozhen

2014-11-01

Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Higher and lowest order mixed finite element approximation of subsurface flow problems with solutions of low regularity

NASA Astrophysics Data System (ADS)

Bause, Markus

2008-02-01

In this work we study mixed finite element approximations of Richards' equation for simulating variably saturated subsurface flow and simultaneous reactive solute transport. Whereas higher order schemes have proved their ability to approximate reliably reactive solute transport (cf., e.g. [Bause M, Knabner P. Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping. Comput Visual Sci 7;2004:61-78]), the Raviart- Thomas mixed finite element method ( RT0) with a first order accurate flux approximation is popular for computing the underlying water flow field (cf. [Bause M, Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27;2004:565-581, Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26;2003:373-394, Starke G. Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J Sci Comput 21;2000:1869-1885, Younes A, Mosé R, Ackerer P, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comp Phys 149;1999:148-167, Woodward CS, Dawson CN. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37;2000:701-724]). This combination might be non-optimal. Higher order techniques could increase the accuracy of the flow field calculation and thereby improve the prediction of the solute transport. Here, we analyse the application of the Brezzi- Douglas- Marini element ( BDM1) with a second order accurate flux approximation to elliptic, parabolic and degenerate problems whose solutions lack the regularity that is assumed in optimal order error analyses. For the flow field calculation a superiority of the BDM1 approach to the RT0 one is observed, which however is less significant for the accompanying solute transport.

Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

PubMed

Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

2018-02-01

In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Higher order cumulants in colorless partonic plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cherif, S.; Laboratoire de Physique et de Mathématiques Appliquées; Ahmed, M. A. A.

2016-06-10

Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume T{sub 0}(V), a new approach based on the finite-size cumulant expansion of the order parameter and the ℒ{sub m,n}-Method is used. We have shown that both cumulants of higher order and their ratios, associated to themore » thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.« less

Vectorial finite elements for solving the radiative transfer equation

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Le Corre, S.; Digonnet, H.; Favennec, Y.

2018-06-01

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

Recent Development of Multigrid Algorithms for Mixed and Noncomforming Methods for Second Order Elliptical Problems

NASA Technical Reports Server (NTRS)

Chen, Zhangxin; Ewing, Richard E.

1996-01-01

Multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements are considered. The construction of several coarse-to-fine intergrid transfer operators for nonconforming multigrid algorithms is discussed. The equivalence between the nonconforming and mixed finite element methods with and without projection of the coefficient of the differential problems into finite element spaces is described.

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.

On the effects of grid ill-conditioning in three dimensional finite element vector potential magnetostatic field computations

NASA Technical Reports Server (NTRS)

Wang, R.; Demerdash, N. A.

1990-01-01

The effects of finite element grid geometries and associated ill-conditioning were studied in single medium and multi-media (air-iron) three dimensional magnetostatic field computation problems. The sensitivities of these 3D field computations to finite element grid geometries were investigated. It was found that in single medium applications the unconstrained magnetic vector potential curl-curl formulation in conjunction with first order finite elements produce global results which are almost totally insensitive to grid geometries. However, it was found that in multi-media (air-iron) applications first order finite element results are sensitive to grid geometries and consequent elemental shape ill-conditioning. These sensitivities were almost totally eliminated by means of the use of second order finite elements in the field computation algorithms. Practical examples are given in this paper to demonstrate these aspects mentioned above.

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Lower- and higher-order aberrations predicted by an optomechanical model of arcuate keratotomy for astigmatism.

PubMed

Navarro, Rafael; Palos, Fernando; Lanchares, Elena; Calvo, Begoña; Cristóbal, José A

2009-01-01

To develop a realistic model of the optomechanical behavior of the cornea after curved relaxing incisions to simulate the induced astigmatic change and predict the optical aberrations produced by the incisions. ICMA Consejo Superior de Investigaciones Científicas and Universidad de Zaragoza, Zaragoza, Spain. A 3-dimensional finite element model of the anterior hemisphere of the ocular surface was used. The corneal tissue was modeled as a quasi-incompressible, anisotropic hyperelastic constitutive behavior strongly dependent on the physiological collagen fibril distribution. Similar behaviors were assigned to the limbus and sclera. With this model, some corneal incisions were computer simulated after the Lindstrom nomogram. The resulting geometry of the biomechanical simulation was analyzed in the optical zone, and finite ray tracing was performed to compute refractive power and higher-order aberrations (HOAs). The finite-element simulation provided new geometry of the corneal surfaces, from which elevation topographies were obtained. The surgically induced astigmatism (SIA) of the simulated incisions according to the Lindstrom nomogram was computed by finite ray tracing. However, paraxial computations would yield slightly different results (undercorrection of astigmatism). In addition, arcuate incisions would induce significant amounts of HOAs. Finite-element models, together with finite ray-tracing computations, yielded realistic simulations of the biomechanical and optical changes induced by relaxing incisions. The model reproduced the SIA indicated by the Lindstrom nomogram for the simulated incisions and predicted a significant increase in optical aberrations induced by arcuate keratotomy.

Three-phase compositional modeling of CO2 injection by higher-order finite element methods with CPA equation of state for aqueous phase

NASA Astrophysics Data System (ADS)

Moortgat, Joachim; Li, Zhidong; Firoozabadi, Abbas

2012-12-01

Most simulators for subsurface flow of water, gas, and oil phases use empirical correlations, such as Henry's law, for the CO2 composition in the aqueous phase, and equations of state (EOS) that do not represent the polar interactions between CO2and water. Widely used simulators are also based on lowest-order finite difference methods and suffer from numerical dispersion and grid sensitivity. They may not capture the viscous and gravitational fingering that can negatively affect hydrocarbon (HC) recovery, or aid carbon sequestration in aquifers. We present a three-phase compositional model based on higher-order finite element methods and incorporate rigorous and efficient three-phase-split computations for either three HC phases or water-oil-gas systems. For HC phases, we use the Peng-Robinson EOS. We allow solubility of CO2in water and adopt a new cubic-plus-association (CPA) EOS, which accounts for cross association between H2O and CO2 molecules, and association between H2O molecules. The CPA-EOS is highly accurate over a broad range of pressures and temperatures. The main novelty of this work is the formulation of a reservoir simulator with new EOS-based unique three-phase-split computations, which satisfy both the equalities of fugacities in all three phases and the global minimum of Gibbs free energy. We provide five examples that demonstrate twice the convergence rate of our method compared with a finite difference approach, and compare with experimental data and other simulators. The examples consider gravitational fingering during CO2sequestration in aquifers, viscous fingering in water-alternating-gas injection, and full compositional modeling of three HC phases.

A new weak Galerkin finite element method for elliptic interface problems

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu; ...

2016-08-26

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

A new weak Galerkin finite element method for elliptic interface problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Wang, Junping; Ye, Xiu

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

Earthquake Rupture Dynamics using Adaptive Mesh Refinement and High-Order Accurate Numerical Methods

NASA Astrophysics Data System (ADS)

Kozdon, J. E.; Wilcox, L.

2013-12-01

Our goal is to develop scalable and adaptive (spatial and temporal) numerical methods for coupled, multiphysics problems using high-order accurate numerical methods. To do so, we are developing an opensource, parallel library known as bfam (available at http://bfam.in). The first application to be developed on top of bfam is an earthquake rupture dynamics solver using high-order discontinuous Galerkin methods and summation-by-parts finite difference methods. In earthquake rupture dynamics, wave propagation in the Earth's crust is coupled to frictional sliding on fault interfaces. This coupling is two-way, required the simultaneous simulation of both processes. The use of laboratory-measured friction parameters requires near-fault resolution that is 4-5 orders of magnitude higher than that needed to resolve the frequencies of interest in the volume. This, along with earlier simulations using a low-order, finite volume based adaptive mesh refinement framework, suggest that adaptive mesh refinement is ideally suited for this problem. The use of high-order methods is motivated by the high level of resolution required off the fault in earlier the low-order finite volume simulations; we believe this need for resolution is a result of the excessive numerical dissipation of low-order methods. In bfam spatial adaptivity is handled using the p4est library and temporal adaptivity will be accomplished through local time stepping. In this presentation we will present the guiding principles behind the library as well as verification of code against the Southern California Earthquake Center dynamic rupture code validation test problems.

Improving finite element results in modeling heart valve mechanics.

PubMed

Earl, Emily; Mohammadi, Hadi

2018-06-01

Finite element analysis is a well-established computational tool which can be used for the analysis of soft tissue mechanics. Due to the structural complexity of the leaflet tissue of the heart valve, the currently available finite element models do not adequately represent the leaflet tissue. A method of addressing this issue is to implement computationally expensive finite element models, characterized by precise constitutive models including high-order and high-density mesh techniques. In this study, we introduce a novel numerical technique that enhances the results obtained from coarse mesh finite element models to provide accuracy comparable to that of fine mesh finite element models while maintaining a relatively low computational cost. Introduced in this study is a method by which the computational expense required to solve linear and nonlinear constitutive models, commonly used in heart valve mechanics simulations, is reduced while continuing to account for large and infinitesimal deformations. This continuum model is developed based on the least square algorithm procedure coupled with the finite difference method adhering to the assumption that the components of the strain tensor are available at all nodes of the finite element mesh model. The suggested numerical technique is easy to implement, practically efficient, and requires less computational time compared to currently available commercial finite element packages such as ANSYS and/or ABAQUS.

Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements

NASA Technical Reports Server (NTRS)

Gould, Dana C.

2000-01-01

This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.

Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prochnow, Bo; O'Reilly, Ossian; Dunham, Eric M.

In this paper, we develop a high-order finite difference scheme for axisymmetric wave propagation in a cylindrical conduit filled with a viscous fluid. The scheme is provably stable, and overcomes the difficulty of the polar coordinate singularity in the radial component of the diffusion operator. The finite difference approximation satisfies the principle of summation-by-parts (SBP), which is used to establish stability using the energy method. To treat the coordinate singularity without losing the SBP property of the scheme, a staggered grid is introduced and quadrature rules with weights set to zero at the endpoints are considered. Finally, the accuracy ofmore » the scheme is studied both for a model problem with periodic boundary conditions at the ends of the conduit and its practical utility is demonstrated by modeling acoustic-gravity waves in a magmatic conduit.« less

Symmetry breaking and the geometry of reduced density matrices

NASA Astrophysics Data System (ADS)

Zauner, V.; Draxler, D.; Vanderstraeten, L.; Haegeman, J.; Verstraete, F.

2016-11-01

The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. We demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all possible many body wavefunctions. The surfaces of these convex bodies exhibit non-analyticities, which signal the emergence of symmetry breaking and of an associated order parameter and also show different characteristics for different types of phase transitions. We illustrate this with three paradigmatic examples of many body systems exhibiting symmetry breaking: the quantum Ising model, the classical q-state Potts model in two-dimensions at finite temperature and the ideal Bose gas in three-dimensions at finite temperature. This state based viewpoint on phase transitions provides a unique novel tool for studying exotic many body phenomena in quantum and classical systems.

A novel equivalent definition of Caputo fractional derivative without singular kernel and superconvergent analysis

NASA Astrophysics Data System (ADS)

Liu, Zhengguang; Li, Xiaoli

2018-05-01

In this article, we present a new second-order finite difference discrete scheme for a fractal mobile/immobile transport model based on equivalent transformative Caputo formulation. The new transformative formulation takes the singular kernel away to make the integral calculation more efficient. Furthermore, this definition is also effective where α is a positive integer. Besides, the T-Caputo derivative also helps us to increase the convergence rate of the discretization of the α-order(0 < α < 1) Caputo derivative from O(τ2-α) to O(τ3-α), where τ is the time step. For numerical analysis, a Crank-Nicolson finite difference scheme to solve the fractal mobile/immobile transport model is introduced and analyzed. The unconditional stability and a priori estimates of the scheme are given rigorously. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

2-D to 3-D global/local finite element analysis of cross-ply composite laminates

NASA Technical Reports Server (NTRS)

Thompson, D. Muheim; Griffin, O. Hayden, Jr.

1990-01-01

An example of two-dimensional to three-dimensional global/local finite element analysis of a laminated composite plate with a hole is presented. The 'zoom' technique of global/local analysis is used, where displacements of the global/local interface from the two-dimensional global model are applied to the edges of the three-dimensional local model. Three different hole diameters, one, three, and six inches, are considered in order to compare the effect of hole size on the three-dimensional stress state around the hole. In addition, three different stacking sequences are analyzed for the six inch hole case in order to study the effect of stacking sequence. The existence of a 'critical' hole size, where the interlaminar stresses are maximum, is indicated. Dispersion of plies at the same angle, as opposed to clustering, is found to reduce the magnitude of some interlaminar stress components and increase others.

Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid

DOE PAGES

Prochnow, Bo; O'Reilly, Ossian; Dunham, Eric M.; ...

2017-03-16

In this paper, we develop a high-order finite difference scheme for axisymmetric wave propagation in a cylindrical conduit filled with a viscous fluid. The scheme is provably stable, and overcomes the difficulty of the polar coordinate singularity in the radial component of the diffusion operator. The finite difference approximation satisfies the principle of summation-by-parts (SBP), which is used to establish stability using the energy method. To treat the coordinate singularity without losing the SBP property of the scheme, a staggered grid is introduced and quadrature rules with weights set to zero at the endpoints are considered. Finally, the accuracy ofmore » the scheme is studied both for a model problem with periodic boundary conditions at the ends of the conduit and its practical utility is demonstrated by modeling acoustic-gravity waves in a magmatic conduit.« less

Gradient corrections to the exchange-correlation free energy

DOE PAGES

Sjostrom, Travis; Daligault, Jerome

2014-10-07

We develop the first-order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite-temperature density functional calculations. Based on this, we propose and implement a simple temperature-dependent extension for functionals beyond the local density approximation. These finite-temperature functionals show improvement over zero-temperature functionals, as compared to path-integral Monte Carlo calculations for deuterium equations of state, and perform without computational cost increase compared to zero-temperature functionals and so should be used for finite-temperature calculations. Furthermore, while the present functionals are valid at all temperatures including zero, non-negligible difference with zero-temperature functionals begins at temperatures abovemore » 10 000 K.« less

A 3D finite element ALE method using an approximate Riemann solution

DOE PAGES

Chiravalle, V. P.; Morgan, N. R.

2016-08-09

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

A 3D finite element ALE method using an approximate Riemann solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiravalle, V. P.; Morgan, N. R.

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

Seismic modeling with radial basis function-generated finite differences (RBF-FD) – a simplified treatment of interfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martin, Bradley, E-mail: brma7253@colorado.edu; Fornberg, Bengt, E-mail: Fornberg@colorado.edu

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy formore » the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.« less

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.

Seismic modeling with radial basis function-generated finite differences (RBF-FD) - a simplified treatment of interfaces

NASA Astrophysics Data System (ADS)

Martin, Bradley; Fornberg, Bengt

2017-04-01

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy for the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.

Un-collided-flux preconditioning for the first order transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rigley, M.; Koebbe, J.; Drumm, C.

2013-07-01

Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods. These codes include a least squares finite element method and a discontinuous finite element method. The performance of each code is shown on problems in one and two dimensions. The un-collided-flux preconditioner shows good speedup on each of the given methods. The un-collided-flux preconditioner has been used on the second-order equation, and here we extend those results to the first order equation. (authors)

Robust finite-time chaos synchronization of uncertain permanent magnet synchronous motors.

PubMed

Chen, Qiang; Ren, Xuemei; Na, Jing

2015-09-01

In this paper, a robust finite-time chaos synchronization scheme is proposed for two uncertain third-order permanent magnet synchronous motors (PMSMs). The whole synchronization error system is divided into two cascaded subsystems: a first-order subsystem and a second-order subsystem. For the first subsystem, we design a finite-time controller based on the finite-time Lyapunov stability theory. Then, according to the backstepping idea and the adding a power integrator technique, a second finite-time controller is constructed recursively for the second subsystem. No exogenous forces are required in the controllers design but only the direct-axis (d-axis) and the quadrature-axis (q-axis) stator voltages are used as manipulated variables. Comparative simulations are provided to show the effectiveness and superior performance of the proposed method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes

NASA Astrophysics Data System (ADS)

Don, Wai-Sun; Borges, Rafael

2013-10-01

In the reconstruction step of (2r-1) order weighted essentially non-oscillatory conservative finite difference schemes (WENO) for solving hyperbolic conservation laws, nonlinear weights αk and ωk, such as the WENO-JS weights by Jiang et al. and the WENO-Z weights by Borges et al., are designed to recover the formal (2r-1) order (optimal order) of the upwinded central finite difference scheme when the solution is sufficiently smooth. The smoothness of the solution is determined by the lower order local smoothness indicators βk in each substencil. These nonlinear weight formulations share two important free parameters in common: the power p, which controls the amount of numerical dissipation, and the sensitivity ε, which is added to βk to avoid a division by zero in the denominator of αk. However, ε also plays a role affecting the order of accuracy of WENO schemes, especially in the presence of critical points. It was recently shown that, for any design order (2r-1), ε should be of Ω(Δx2) (Ω(Δxm) means that ε⩾CΔxm for some C independent of Δx, as Δx→0) for the WENO-JS scheme to achieve the optimal order, regardless of critical points. In this paper, we derive an alternative proof of the sufficient condition using special properties of βk. Moreover, it is unknown if the WENO-Z scheme should obey the same condition on ε. Here, using same special properties of βk, we prove that in fact the optimal order of the WENO-Z scheme can be guaranteed with a much weaker condition ε=Ω(Δxm), where m(r,p)⩾2 is the optimal sensitivity order, regardless of critical points. Both theoretical results are confirmed numerically on smooth functions with arbitrary order of critical points. This is a highly desirable feature, as illustrated with the Lax problem and the Mach 3 shock-density wave interaction of one dimensional Euler equations, for a smaller ε allows a better essentially non-oscillatory shock capturing as it does not over-dominate over the size of βk. We also show that numerical oscillations can be further attenuated by increasing the power parameter 2⩽p⩽r-1, at the cost of increased numerical dissipation. Compact formulas of βk for WENO schemes are also presented.

A New Discretization Method of Order Four for the Numerical Solution of One-Space Dimensional Second-Order Quasi-Linear Hyperbolic Equation

ERIC Educational Resources Information Center

Mohanty, R. K.; Arora, Urvashi

2002-01-01

Three level-implicit finite difference methods of order four are discussed for the numerical solution of the mildly quasi-linear second-order hyperbolic equation A(x, t, u)u[subscript xx] + 2B(x, t, u)u[subscript xt] + C(x, t, u)u[subscript tt] = f(x, t, u, u[subscript x], u[subscript t]), 0 less than x less than 1, t greater than 0 subject to…

Single Polygon Counting on Cayley Tree of Order 3

NASA Astrophysics Data System (ADS)

Pah, Chin Hee

2010-07-01

We showed that one form of generalized Catalan numbers is the solution to the problem of finding different connected component with finite vertices containing a fixed root for the semi-infinite Cayley tree of order 3. We give the formula for the full graph, Cayley tree of order 3 which is derived from the generalized Catalan numbers. Using ratios of Gamma functions, two upper bounds are given for problem defined on semi-infinite Cayley tree of order 3 as well as the full graph.

Propagation and stability of wavelike solutions of finite difference equations with variable coefficients

NASA Technical Reports Server (NTRS)

Giles, M. B.; Thompkins, W. T., Jr.

1985-01-01

The propagation and dissipation of wavelike solutions to finite difference equations is analyzed on the basis of an asymptotic approach in which a wave solution is expressed as a product of a complex amplitude and an oscillatory phase function whose frequency and wavenumber may also be complex. An asymptotic expansion leads to a local dispersion relation for wavenumber and frequency; the first-order terms produce an equation for the amplitude in which the local group velocity appears as the convection velocity of the amplitude. Equations for the motion of wavepackets and their interaction at boundaries are derived, and a global stability analysis is carried out.

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

NASA Technical Reports Server (NTRS)

Bridgeman, J. O.; Steger, J. L.; Caradonna, F. X.

1982-01-01

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1975-10-01

The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P$sub 1$) in up to three- dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First- order perturbation analysis capability is available at the macroscopic cross section level. (auth)

Numerical solution of transport equation for applications in environmental hydraulics and hydrology

NASA Astrophysics Data System (ADS)

Rashidul Islam, M.; Hanif Chaudhry, M.

1997-04-01

The advective term in the one-dimensional transport equation, when numerically discretized, produces artificial diffusion. To minimize such artificial diffusion, which vanishes only for Courant number equal to unity, transport owing to advection has been modeled separately. The numerical solution of the advection equation for a Gaussian initial distribution is well established; however, large oscillations are observed when applied to an initial distribution with sleep gradients, such as trapezoidal distribution of a constituent or propagation of mass from a continuous input. In this study, the application of seven finite-difference schemes and one polynomial interpolation scheme is investigated to solve the transport equation for both Gaussian and non-Gaussian (trapezoidal) initial distributions. The results obtained from the numerical schemes are compared with the exact solutions. A constant advective velocity is assumed throughout the transport process. For a Gaussian distribution initial condition, all eight schemes give excellent results, except the Lax scheme which is diffusive. In application to the trapezoidal initial distribution, explicit finite-difference schemes prove to be superior to implicit finite-difference schemes because the latter produce large numerical oscillations near the steep gradients. The Warming-Kutler-Lomax (WKL) explicit scheme is found to be better among this group. The Hermite polynomial interpolation scheme yields the best result for a trapezoidal distribution among all eight schemes investigated. The second-order accurate schemes are sufficiently accurate for most practical problems, but the solution of unusual problems (concentration with steep gradient) requires the application of higher-order (e.g. third- and fourth-order) accurate schemes.

Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation

NASA Astrophysics Data System (ADS)

Popescu, Mihaela; Shyy, Wei; Garbey, Marc

2005-12-01

In developing suitable numerical techniques for computational aero-acoustics, the dispersion-relation-preserving (DRP) scheme by Tam and co-workers and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. In the present study, finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications. Linear and nonlinear wave equations, with and without viscous dissipation, have been adopted as the test problems. Highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes offers substantially better solutions in regions of high gradient or discontinuity.

Validation of drift and diffusion coefficients from experimental data

NASA Astrophysics Data System (ADS)

Riera, R.; Anteneodo, C.

2010-04-01

Many fluctuation phenomena, in physics and other fields, can be modeled by Fokker-Planck or stochastic differential equations whose coefficients, associated with drift and diffusion components, may be estimated directly from the observed time series. Its correct characterization is crucial to determine the system quantifiers. However, due to the finite sampling rates of real data, the empirical estimates may significantly differ from their true functional forms. In the literature, low-order corrections, or even no corrections, have been applied to the finite-time estimates. A frequent outcome consists of linear drift and quadratic diffusion coefficients. For this case, exact corrections have been recently found, from Itô-Taylor expansions. Nevertheless, model validation constitutes a necessary step before determining and applying the appropriate corrections. Here, we exploit the consequences of the exact theoretical results obtained for the linear-quadratic model. In particular, we discuss whether the observed finite-time estimates are actually a manifestation of that model. The relevance of this analysis is put into evidence by its application to two contrasting real data examples in which finite-time linear drift and quadratic diffusion coefficients are observed. In one case the linear-quadratic model is readily rejected while in the other, although the model constitutes a very good approximation, low-order corrections are inappropriate. These examples give warning signs about the proper interpretation of finite-time analysis even in more general diffusion processes.

Melting of Domain Wall in Charge Ordered Dirac Electron of Organic Conductor α-(BEDT-TTF)2I3

NASA Astrophysics Data System (ADS)

Ohki, Daigo; Matsuno, Genki; Omori, Yukiko; Kobayashi, Akito

2018-05-01

The origin of charge order melting is identified by using the real space dependent mean-field theory in the extended Hubbard model describing an organic Dirac electron system α-(BEDT-TTF)2I3. In this model, the width of a domain wall which arises between different types of the charge ordered phase exhibits a divergent increase with decreasing the strength of electron-electron correlations. By analyzing the finite-size effect carefully, it is shown that the divergence coincides with a topological transition where a pair of Dirac cones merges in keeping with a finite gap. It is also clarified that the gap opening point and the topological transition point are different, which leads to the existence of an exotic massive Dirac electron phase with melted-type domain wall and gapless edge states. The present result also indicated that multiple metastable states are emerged in massive Dirac Electron phase. In the trivial charge ordered phase, the gapless domain-wall bound state takes place instead of the gapless edge states, accompanying with a form change of the domain wall from melted-type into hyperbolic-tangent-type.

Summary Report of Working Group 2: Computation

NASA Astrophysics Data System (ADS)

Stoltz, P. H.; Tsung, R. S.

2009-01-01

The working group on computation addressed three physics areas: (i) plasma-based accelerators (laser-driven and beam-driven), (ii) high gradient structure-based accelerators, and (iii) electron beam sources and transport [1]. Highlights of the talks in these areas included new models of breakdown on the microscopic scale, new three-dimensional multipacting calculations with both finite difference and finite element codes, and detailed comparisons of new electron gun models with standard models such as PARMELA. The group also addressed two areas of advances in computation: (i) new algorithms, including simulation in a Lorentz-boosted frame that can reduce computation time orders of magnitude, and (ii) new hardware architectures, like graphics processing units and Cell processors that promise dramatic increases in computing power. Highlights of the talks in these areas included results from the first large-scale parallel finite element particle-in-cell code (PIC), many order-of-magnitude speedup of, and details of porting the VPIC code to the Roadrunner supercomputer. The working group featured two plenary talks, one by Brian Albright of Los Alamos National Laboratory on the performance of the VPIC code on the Roadrunner supercomputer, and one by David Bruhwiler of Tech-X Corporation on recent advances in computation for advanced accelerators. Highlights of the talk by Albright included the first one trillion particle simulations, a sustained performance of 0.3 petaflops, and an eight times speedup of science calculations, including back-scatter in laser-plasma interaction. Highlights of the talk by Bruhwiler included simulations of 10 GeV accelerator laser wakefield stages including external injection, new developments in electromagnetic simulations of electron guns using finite difference and finite element approaches.

Summary Report of Working Group 2: Computation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stoltz, P. H.; Tsung, R. S.

2009-01-22

The working group on computation addressed three physics areas: (i) plasma-based accelerators (laser-driven and beam-driven), (ii) high gradient structure-based accelerators, and (iii) electron beam sources and transport [1]. Highlights of the talks in these areas included new models of breakdown on the microscopic scale, new three-dimensional multipacting calculations with both finite difference and finite element codes, and detailed comparisons of new electron gun models with standard models such as PARMELA. The group also addressed two areas of advances in computation: (i) new algorithms, including simulation in a Lorentz-boosted frame that can reduce computation time orders of magnitude, and (ii) newmore » hardware architectures, like graphics processing units and Cell processors that promise dramatic increases in computing power. Highlights of the talks in these areas included results from the first large-scale parallel finite element particle-in-cell code (PIC), many order-of-magnitude speedup of, and details of porting the VPIC code to the Roadrunner supercomputer. The working group featured two plenary talks, one by Brian Albright of Los Alamos National Laboratory on the performance of the VPIC code on the Roadrunner supercomputer, and one by David Bruhwiler of Tech-X Corporation on recent advances in computation for advanced accelerators. Highlights of the talk by Albright included the first one trillion particle simulations, a sustained performance of 0.3 petaflops, and an eight times speedup of science calculations, including back-scatter in laser-plasma interaction. Highlights of the talk by Bruhwiler included simulations of 10 GeV accelerator laser wakefield stages including external injection, new developments in electromagnetic simulations of electron guns using finite difference and finite element approaches.« less

Finite-time containment control of perturbed multi-agent systems based on sliding-mode control

NASA Astrophysics Data System (ADS)

Yu, Di; Ji, Xiang Yang

2018-01-01

Aimed at faster convergence rate, this paper investigates finite-time containment control problem for second-order multi-agent systems with norm-bounded non-linear perturbation. When topology between the followers are strongly connected, the nonsingular fast terminal sliding-mode error is defined, corresponding discontinuous control protocol is designed and the appropriate value range of control parameter is obtained by applying finite-time stability analysis, so that the followers converge to and move along the desired trajectories within the convex hull formed by the leaders in finite time. Furthermore, on the basis of the sliding-mode error defined, the corresponding distributed continuous control protocols are investigated with fast exponential reaching law and double exponential reaching law, so as to make the followers move to the small neighbourhoods of their desired locations and keep within the dynamic convex hull formed by the leaders in finite time to achieve practical finite-time containment control. Meanwhile, we develop the faster control scheme according to comparison of the convergence rate of these two different reaching laws. Simulation examples are given to verify the correctness of theoretical results.

Inhomogeneous Radiation Boundary Conditions Simulating Incoming Acoustic Waves for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Fang, Jun; Kurbatskii, Konstantin A.

1996-01-01

A set of nonhomogeneous radiation and outflow conditions which automatically generate prescribed incoming acoustic or vorticity waves and, at the same time, are transparent to outgoing sound waves produced internally in a finite computation domain is proposed. This type of boundary condition is needed for the numerical solution of many exterior aeroacoustics problems. In computational aeroacoustics, the computation scheme must be as nondispersive ans nondissipative as possible. It must also support waves with wave speeds which are nearly the same as those of the original linearized Euler equations. To meet these requirements, a high-order/large-stencil scheme is necessary The proposed nonhomogeneous radiation and outflow boundary conditions are designed primarily for use in conjunction with such high-order/large-stencil finite difference schemes.

Finite Moment Tensors of Southern California Earthquakes

NASA Astrophysics Data System (ADS)

Jordan, T. H.; Chen, P.; Zhao, L.

2003-12-01

We have developed procedures for inverting broadband waveforms for the finite moment tensors (FMTs) of regional earthquakes. The FMT is defined in terms of second-order polynomial moments of the source space-time function and provides the lowest order representation of a finite fault rupture; it removes the fault-plane ambiguity of the centroid moment tensor (CMT) and yields several additional parameters of seismological interest: the characteristic length L{c}, width W{c}, and duration T{c} of the faulting, as well as the directivity vector {v}{d} of the fault slip. To formulate the inverse problem, we follow and extend the methods of McGuire et al. [2001, 2002], who have successfully recovered the second-order moments of large earthquakes using low-frequency teleseismic data. We express the Fourier spectra of a synthetic point-source waveform in its exponential (Rytov) form and represent the observed waveform relative to the synthetic in terms two frequency-dependent differential times, a phase delay δ τ {p}(ω ) and an amplitude-reduction time δ τ {q}(ω ), which we measure using Gee and Jordan's [1992] isolation-filter technique. We numerically calculate the FMT partial derivatives in terms of second-order spatiotemporal gradients, which allows us to use 3D finite-difference seismograms as our isolation filters. We have applied our methodology to a set of small to medium-sized earthquakes in Southern California. The errors in anelastic structure introduced perturbations larger than the signal level caused by finite source effect. We have therefore employed a joint inversion technique that recovers the CMT parameters of the aftershocks, as well as the CMT and FMT parameters of the mainshock, under the assumption that the source finiteness of the aftershocks can be ignored. The joint system of equations relating the δ τ {p} and δ τ {q} data to the source parameters of the mainshock-aftershock cluster is denuisanced for path anomalies in both observables; this projection operation effectively corrects the mainshock data for path-related amplitude anomalies in a way similar to, but more flexible than, empirical Green function (EGF) techniques.

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

NASA Technical Reports Server (NTRS)

Bates, J. R.; Semazzi, F. H. M.; Higgins, R. W.; Barros, Saulo R. M.

1990-01-01

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

Numerical analysis for finite-range multitype stochastic contact financial market dynamic systems

NASA Astrophysics Data System (ADS)

Yang, Ge; Wang, Jun; Fang, Wen

2015-04-01

In an attempt to reproduce and study the dynamics of financial markets, a random agent-based financial price model is developed and investigated by the finite-range multitype contact dynamic system, in which the interaction and dispersal of different types of investment attitudes in a stock market are imitated by viruses spreading. With different parameters of birth rates and finite-range, the normalized return series are simulated by Monte Carlo simulation method and numerical studied by power-law distribution analysis and autocorrelation analysis. To better understand the nonlinear dynamics of the return series, a q-order autocorrelation function and a multi-autocorrelation function are also defined in this work. The comparisons of statistical behaviors of return series from the agent-based model and the daily historical market returns of Shanghai Composite Index and Shenzhen Component Index indicate that the proposed model is a reasonable qualitative explanation for the price formation process of stock market systems.

Empirical performance of the multivariate normal universal portfolio

NASA Astrophysics Data System (ADS)

Tan, Choon Peng; Pang, Sook Theng

2013-09-01

Universal portfolios generated by the multivariate normal distribution are studied with emphasis on the case where variables are dependent, namely, the covariance matrix is not diagonal. The moving-order multivariate normal universal portfolio requires very long implementation time and large computer memory in its implementation. With the objective of reducing memory and implementation time, the finite-order universal portfolio is introduced. Some stock-price data sets are selected from the local stock exchange and the finite-order universal portfolio is run on the data sets, for small finite order. Empirically, it is shown that the portfolio can outperform the moving-order Dirichlet universal portfolio of Cover and Ordentlich[2] for certain parameters in the selected data sets.

Accuracy Improvement in Magnetic Field Modeling for an Axisymmetric Electromagnet

NASA Technical Reports Server (NTRS)

Ilin, Andrew V.; Chang-Diaz, Franklin R.; Gurieva, Yana L.; Il,in, Valery P.

2000-01-01

This paper examines the accuracy and calculation speed for the magnetic field computation in an axisymmetric electromagnet. Different numerical techniques, based on an adaptive nonuniform grid, high order finite difference approximations, and semi-analitical calculation of boundary conditions are considered. These techniques are being applied to the modeling of the Variable Specific Impulse Magnetoplasma Rocket. For high-accuracy calculations, a fourth-order scheme offers dramatic advantages over a second order scheme. For complex physical configurations of interest in plasma propulsion, a second-order scheme with nonuniform mesh gives the best results. Also, the relative advantages of various methods are described when the speed of computation is an important consideration.

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1990-01-01

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

An Efficient Finite Element Framework to Assess Flexibility Performances of SMA Self-Expandable Carotid Artery Stents

PubMed Central

Ferraro, Mauro; Auricchio, Ferdinando; Boatti, Elisa; Scalet, Giulia; Conti, Michele; Morganti, Simone; Reali, Alessandro

2015-01-01

Computer-based simulations are nowadays widely exploited for the prediction of the mechanical behavior of different biomedical devices. In this aspect, structural finite element analyses (FEA) are currently the preferred computational tool to evaluate the stent response under bending. This work aims at developing a computational framework based on linear and higher order FEA to evaluate the flexibility of self-expandable carotid artery stents. In particular, numerical simulations involving large deformations and inelastic shape memory alloy constitutive modeling are performed, and the results suggest that the employment of higher order FEA allows accurately representing the computational domain and getting a better approximation of the solution with a widely-reduced number of degrees of freedom with respect to linear FEA. Moreover, when buckling phenomena occur, higher order FEA presents a superior capability of reproducing the nonlinear local effects related to buckling phenomena. PMID:26184329

A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Salinas, P.; Pavlidis, D.; Xie, Z.; Osman, H.; Pain, C. C.; Jackson, M. D.

2018-01-01

We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.

Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect

NASA Astrophysics Data System (ADS)

Novitski, Roman; Scheuer, Jacob; Steinberg, Ben Z.

2013-02-01

We present two unconditionally stable finite-difference time-domain (FDTD) methods for modeling the Sagnac effect in rotating optical microsensors. The methods are based on the implicit Crank-Nicolson scheme, adapted to hold in the rotating system reference frame—the rotating Crank-Nicolson (RCN) methods. The first method (RCN-2) is second order accurate in space whereas the second method (RCN-4) is fourth order accurate. Both methods are second order accurate in time. We show that the RCN-4 scheme is more accurate and has better dispersion isotropy. The numerical results show good correspondence with the expression for the classical Sagnac resonant frequency splitting when using group refractive indices of the resonant modes of a microresonator. Also we show that the numerical results are consistent with the perturbation theory for the rotating degenerate microcavities. We apply our method to simulate the effect of rotation on an entire Coupled Resonator Optical Waveguide (CROW) consisting of a set of coupled microresonators. Preliminary results validate the formation of a rotation-induced gap at the center of a transfer function of a CROW.

High Order Finite Difference Methods with Subcell Resolution for 2D Detonation Waves

NASA Technical Reports Server (NTRS)

Wang, W.; Shu, C. W.; Yee, H. C.; Sjogreen, B.

2012-01-01

In simulating hyperbolic conservation laws in conjunction with an inhomogeneous stiff source term, if the solution is discontinuous, spurious numerical results may be produced due to different time scales of the transport part and the source term. This numerical issue often arises in combustion and high speed chemical reacting flows.

Revision of the documentation for a model for calculating effects of liquid waste disposal in deep saline aquifers

USGS Publications Warehouse

INTERA Environmental Consultants, Inc.

1979-01-01

The major limitation of the model arises using second-order correct (central-difference) finite-difference approximation in space. To avoid numerical oscillations in the solution, the user must restrict grid block and time step sizes depending upon the magnitude of the dispersivity.

High-Order Thermal Radiative Transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woods, Douglas Nelson; Cleveland, Mathew Allen; Wollaeger, Ryan Thomas

2017-09-18

The objective of this research is to asses the sensitivity of the linearized thermal radiation transport equations to finite element order on unstructured meshes and to investigate the sensitivity of the nonlinear TRT equations due to evaluating the opacities and heat capacity at nodal temperatures in 2-D using high-order finite elements.

A spectral-finite difference solution of the Navier-Stokes equations in three dimensions

NASA Astrophysics Data System (ADS)

Alfonsi, Giancarlo; Passoni, Giuseppe; Pancaldo, Lea; Zampaglione, Domenico

1998-07-01

A new computational code for the numerical integration of the three-dimensional Navier-Stokes equations in their non-dimensional velocity-pressure formulation is presented. The system of non-linear partial differential equations governing the time-dependent flow of a viscous incompressible fluid in a channel is managed by means of a mixed spectral-finite difference method, in which different numerical techniques are applied: Fourier decomposition is used along the homogeneous directions, second-order Crank-Nicolson algorithms are employed for the spatial derivatives in the direction orthogonal to the solid walls and a fourth-order Runge-Kutta procedure is implemented for both the calculation of the convective term and the time advancement. The pressure problem, cast in the Helmholtz form, is solved with the use of a cyclic reduction procedure. No-slip boundary conditions are used at the walls of the channel and cyclic conditions are imposed at the other boundaries of the computing domain.Results are provided for different values of the Reynolds number at several time steps of integration and are compared with results obtained by other authors.

Calculating the Malliavin derivative of some stochastic mechanics problems

PubMed Central

Hauseux, Paul; Hale, Jack S.

2017-01-01

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. PMID:29261776

The morphological state space revisited: what do phylogenetic patterns in homoplasy tell us about the number of possible character states?

PubMed Central

Hoyal Cuthill, Jennifer F.

2015-01-01

Biological variety and major evolutionary transitions suggest that the space of possible morphologies may have varied among lineages and through time. However, most models of phylogenetic character evolution assume that the potential state space is finite. Here, I explore what the morphological state space might be like, by analysing trends in homoplasy (repeated derivation of the same character state). Analyses of ten published character matrices are compared against computer simulations with different state space models: infinite states, finite states, ordered states and an ‘inertial' model, simulating phylogenetic constraints. Of these, only the infinite states model results in evolution without homoplasy, a prediction which is not generally met by real phylogenies. Many authors have interpreted the ubiquity of homoplasy as evidence that the number of evolutionary alternatives is finite. However, homoplasy is also predicted by phylogenetic constraints on the morphological distance that can be traversed between ancestor and descendent. Phylogenetic rarefaction (sub-sampling) shows that finite and inertial state spaces do produce contrasting trends in the distribution of homoplasy. Two clades show trends characteristic of phylogenetic inertia, with decreasing homoplasy (increasing consistency index) as we sub-sample more distantly related taxa. One clade shows increasing homoplasy, suggesting exhaustion of finite states. Different clades may, therefore, show different patterns of character evolution. However, when parsimony uninformative characters are excluded (which may occur without documentation in cladistic studies), it may no longer be possible to distinguish inertial and finite state spaces. Interestingly, inertial models predict that homoplasy should be clustered among comparatively close relatives (parallel evolution), whereas finite state models do not. If morphological evolution is often inertial in nature, then homoplasy (false homology) may primarily occur between close relatives, perhaps being replaced by functional analogy at higher taxonomic scales. PMID:26640650

Numerical time-domain electromagnetics based on finite-difference and convolution

NASA Astrophysics Data System (ADS)

Lin, Yuanqu

Time-domain methods posses a number of advantages over their frequency-domain counterparts for the solution of wideband, nonlinear, and time varying electromagnetic scattering and radiation phenomenon. Time domain integral equation (TDIE)-based methods, which incorporate the beneficial properties of integral equation method, are thus well suited for solving broadband scattering problems for homogeneous scatterers. Widespread adoption of TDIE solvers has been retarded relative to other techniques by their inefficiency, inaccuracy and instability. Moreover, two-dimensional (2D) problems are especially problematic, because 2D Green's functions have infinite temporal support, exacerbating these difficulties. This thesis proposes a finite difference delay modeling (FDDM) scheme for the solution of the integral equations of 2D transient electromagnetic scattering problems. The method discretizes the integral equations temporally using first- and second-order finite differences to map Laplace-domain equations into the Z domain before transforming to the discrete time domain. The resulting procedure is unconditionally stable because of the nature of the Laplace- to Z-domain mapping. The first FDDM method developed in this thesis uses second-order Lagrange basis functions with Galerkin's method for spatial discretization. The second application of the FDDM method discretizes the space using a locally-corrected Nystrom method, which accelerates the precomputation phase and achieves high order accuracy. The Fast Fourier Transform (FFT) is applied to accelerate the marching-on-time process in both methods. While FDDM methods demonstrate impressive accuracy and stability in solving wideband scattering problems for homogeneous scatterers, they still have limitations in analyzing interactions between several inhomogenous scatterers. Therefore, this thesis devises a multi-region finite-difference time-domain (MR-FDTD) scheme based on domain-optimal Green's functions for solving sparsely-populated problems. The scheme uses a discrete Green's function (DGF) on the FDTD lattice to truncate the local subregions, and thus reduces reflection error on the local boundary. A continuous Green's function (CGF) is implemented to pass the influence of external fields into each FDTD region which mitigates the numerical dispersion and anisotropy of standard FDTD. Numerical results will illustrate the accuracy and stability of the proposed techniques.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Noise Reduction Design of the Volute for a Centrifugal Compressor

NASA Astrophysics Data System (ADS)

Song, Zhen; Wen, Huabing; Hong, Liangxing; Jin, Yudong

2017-08-01

In order to effectively control the aerodynamic noise of a compressor, this paper takes into consideration a marine exhaust turbocharger compressor as a research object. According to the different design concept of volute section, tongue and exit cone, six different volute models were established. The finite volume method is used to calculate the flow field, whiles the finite element method is used for the acoustic calculation. Comparison and analysis of different structure designs from three aspects: noise level, isentropic efficiency and Static pressure recovery coefficient. The results showed that under the concept of volute section model 1 yielded the best result, under the concept of tongue analysis model 3 yielded the best result and finally under exit cone analysis model 6 yielded the best results.

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063

Finite-nuclear-size contribution to the g factor of a bound electron: Higher-order effects

NASA Astrophysics Data System (ADS)

Karshenboim, Savely G.; Ivanov, Vladimir G.

2018-02-01

A precision comparison of theory and experiments on the g factor of an electron bound in a hydrogenlike ion with a spinless nucleus requires a detailed account of finite-nuclear-size contributions. While the relativistic corrections to the leading finite-size contribution are known, the higher-order effects need an additional consideration. Two results are presented in the paper. One is on the anomalous-magnetic-moment correction to the finite-size effects and the other is due to higher-order effects in Z α m RN . We also present here a method to relate the contributions to the g factor of a bound electron in a hydrogenlike atom to its energy within a nonrelativistic approach.

Neural network disturbance observer-based distributed finite-time formation tracking control for multiple unmanned helicopters.

PubMed

Wang, Dandan; Zong, Qun; Tian, Bailing; Shao, Shikai; Zhang, Xiuyun; Zhao, Xinyi

2018-02-01

The distributed finite-time formation tracking control problem for multiple unmanned helicopters is investigated in this paper. The control object is to maintain the positions of follower helicopters in formation with external interferences. The helicopter model is divided into a second order outer-loop subsystem and a second order inner-loop subsystem based on multiple-time scale features. Using radial basis function neural network (RBFNN) technique, we first propose a novel finite-time multivariable neural network disturbance observer (FMNNDO) to estimate the external disturbance and model uncertainty, where the neural network (NN) approximation errors can be dynamically compensated by adaptive law. Next, based on FMNNDO, a distributed finite-time formation tracking controller and a finite-time attitude tracking controller are designed using the nonsingular fast terminal sliding mode (NFTSM) method. In order to estimate the second derivative of the virtual desired attitude signal, a novel finite-time sliding mode integral filter is designed. Finally, Lyapunov analysis and multiple-time scale principle ensure the realization of control goal in finite-time. The effectiveness of the proposed FMNNDO and controllers are then verified by numerical simulations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Finite-element numerical modeling of atmospheric turbulent boundary layer

NASA Technical Reports Server (NTRS)

Lee, H. N.; Kao, S. K.

1979-01-01

A dynamic turbulent boundary-layer model in the neutral atmosphere is constructed, using a dynamic turbulent equation of the eddy viscosity coefficient for momentum derived from the relationship among the turbulent dissipation rate, the turbulent kinetic energy and the eddy viscosity coefficient, with aid of the turbulent second-order closure scheme. A finite-element technique was used for the numerical integration. In preliminary results, the behavior of the neutral planetary boundary layer agrees well with the available data and with the existing elaborate turbulent models, using a finite-difference scheme. The proposed dynamic formulation of the eddy viscosity coefficient for momentum is particularly attractive and can provide a viable alternative approach to study atmospheric turbulence, diffusion and air pollution.

Parallel, adaptive finite element methods for conservation laws

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Effect of Finite Computational Domain on Turbulence Scaling Law in Both Physical and Spectral Spaces

NASA Technical Reports Server (NTRS)

Hou, Thomas Y.; Wu, Xiao-Hui; Chen, Shiyi; Zhou, Ye

1998-01-01

The well-known translation between the power law of energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems.

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.

An efficient numerical technique for calculating thermal spreading resistance

NASA Technical Reports Server (NTRS)

Gale, E. H., Jr.

1977-01-01

An efficient numerical technique for solving the equations resulting from finite difference analyses of fields governed by Poisson's equation is presented. The method is direct (noniterative)and the computer work required varies with the square of the order of the coefficient matrix. The computational work required varies with the cube of this order for standard inversion techniques, e.g., Gaussian elimination, Jordan, Doolittle, etc.

A Typology for Finite Groups

ERIC Educational Resources Information Center

Tou, Erik R

2013-01-01

This project classifies groups of small order using a group's center as the key feature. Groups of a given order "n" are typed based on the order of each group's center. Students are led through a sequence of exercises that combine proof-writing, independent research, and an analysis of specific classes of finite groups…

Critical temperatures of hybrid laminates using finite elements

NASA Astrophysics Data System (ADS)

Chockalingam, S.; Mathew, T. C.; Singh, G.; Rao, G. V.

1992-06-01

Thermal buckling of antisymmetric cross-ply hybrid laminates is investigated. A one-dimensional finite element based on first-order shear deformation theory, having two nodes and six degrees of freedom per node, namely axial displacement, transverse displacements and rotation of the normal to the beam axis and their derivatives with respect to beam coordinate axis, is employed for this purpose. Various types of hybrid laminates with different combination of glass/epoxy, Kevlar/epoxy and carbon/epoxy are considered. Effects of slenderness ratio, boundary conditions and lay-ups are studied in detail.

Effects of renormalizing the chiral SU(2) quark-meson model

NASA Astrophysics Data System (ADS)

Zacchi, Andreas; Schaffner-Bielich, Jürgen

2018-04-01

We investigate the restoration of chiral symmetry at finite temperature in the SU(2) quark-meson model, where the mean field approximation is compared to the renormalized version for quarks and mesons. In a combined approach at finite temperature, all the renormalized versions show a crossover transition. The inclusion of different renormalization scales leave the order parameter and the mass spectra nearly untouched but strongly influence the thermodynamics at low temperatures and around the phase transition. We find unphysical results for the renormalized version of mesons and the combined one.

Numerical Methods for 2-Dimensional Modeling

DTIC Science & Technology

1980-12-01

high-order finite element methods, and a multidimensional version of the method of lines, both utilizing an optimized stiff integrator for the time...integration. The finite element methods have proved disappointing, but the method of lines has provided an unexpectedly large gain in speed. Two...diffusion problems with the same number of unknowns (a 21 x 41 grid), solved by second-order finite element methods, took over seven minutes on the Cray-i

The Laguerre finite difference one-way equation solver

NASA Astrophysics Data System (ADS)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

Finite element normal mode analysis of resistance welding jointed of dissimilar plate hat structure

NASA Astrophysics Data System (ADS)

Nazri, N. A.; Sani, M. S. M.

2017-10-01

Structural joints offer connection between structural element (beam, plate, solid etc.) in order to build a whole assembled structure. The complex behaviour of connecting elements plays a valuable role in characteristics of dynamic such as natural frequencies and mode shapes. In automotive structures, the trustworthiness arrangement of the structure extremely depends on joints. In this paper, top hat structure is modelled and designed with spot welding joint using dissimilar materials which is mild steel 1010 and stainless steel 304, using finite element software. Different types of connector elements such as rigid body element (RBE2), welding joint element (CWELD), and bar element (CBAR) are applied to represent real connection between two dissimilar plates. Normal mode analysis is simulated with different types of joining element in order to determine modal properties. Natural frequencies using RBE2, CBAR and CWELD are compared to equivalent rigid body method. Connection that gives the lowest percentage error among these three will be selected as the most reliable joining for resistance spot weld. From the analysis, it is shown that CWELD is better compared to others in term of weld joining among dissimilar plate materials. It is expected that joint modelling of finite element plays significant role in structural dynamics.

On Finite Groups and Finite Fields.

ERIC Educational Resources Information Center

Reid, J. D.

1991-01-01

Given a multiplicative group of nonzero elements with order n, the explicit relationship between the number of cyclic subgroups of order d, which divides n, is used in the proof concerning the cyclic nature of that given multiplicative group. (JJK)

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-07-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Parallel solution of high-order numerical schemes for solving incompressible flows

NASA Technical Reports Server (NTRS)

Milner, Edward J.; Lin, Avi; Liou, May-Fun; Blech, Richard A.

1993-01-01

A new parallel numerical scheme for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained.

Analysis of multi lobe journal bearings with surface roughness using finite difference method

NASA Astrophysics Data System (ADS)

PhaniRaja Kumar, K.; Bhaskar, SUdaya; Manzoor Hussain, M.

2018-04-01

Multi lobe journal bearings are used for high operating speeds and high loads in machines. In this paper symmetrical multi lobe journal bearings are analyzed to find out the effect of surface roughnessduring non linear loading. Using the fourth order RungeKutta method, time transient analysis was performed to calculate and plot the journal centre trajectories. Flow factor method is used to evaluate the roughness and the finite difference method (FDM) is used to predict the pressure distribution over the bearing surface. The Transient analysis is done on the multi lobe journal bearings for threedifferent surface roughness orientations. Longitudinal surface roughness is more effective when compared with isotopic and traverse surface roughness.

A reduced-order integral formulation to account for the finite size effect of isotropic square panels using the transfer matrix method.

PubMed

Bonfiglio, Paolo; Pompoli, Francesco; Lionti, Riccardo

2016-04-01

The transfer matrix method is a well-established prediction tool for the simulation of sound transmission loss and the sound absorption coefficient of flat multilayer systems. Much research has been dedicated to enhancing the accuracy of the method by introducing a finite size effect of the structure to be simulated. The aim of this paper is to present a reduced-order integral formulation to predict radiation efficiency and radiation impedance for a panel with equal lateral dimensions. The results are presented and discussed for different materials in terms of radiation efficiency, sound transmission loss, and the sound absorption coefficient. Finally, the application of the proposed methodology for rectangular multilayer systems is also investigated and validated against experimental data.

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.

Given a one-step numerical scheme, on which ordinary differential equations is it exact?

NASA Astrophysics Data System (ADS)

Villatoro, Francisco R.

2009-01-01

A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.

Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks

NASA Astrophysics Data System (ADS)

Zheng, Mingwen; Li, Lixiang; Peng, Haipeng; Xiao, Jinghua; Yang, Yixian; Zhang, Yanping; Zhao, Hui

2018-06-01

This paper mainly studies the finite-time stability and synchronization problems of memristor-based fractional-order fuzzy cellular neural network (MFFCNN). Firstly, we discuss the existence and uniqueness of the Filippov solution of the MFFCNN according to the Banach fixed point theorem and give a sufficient condition for the existence and uniqueness of the solution. Secondly, a sufficient condition to ensure the finite-time stability of the MFFCNN is obtained based on the definition of finite-time stability of the MFFCNN and Gronwall-Bellman inequality. Thirdly, by designing a simple linear feedback controller, the finite-time synchronization criterion for drive-response MFFCNN systems is derived according to the definition of finite-time synchronization. These sufficient conditions are easy to verify. Finally, two examples are given to show the effectiveness of the proposed results.

A point-value enhanced finite volume method based on approximate delta functions

NASA Astrophysics Data System (ADS)

Xuan, Li-Jun; Majdalani, Joseph

2018-02-01

We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.

Fast smooth second-order sliding mode control for systems with additive colored noises.

PubMed

Yang, Pengfei; Fang, Yangwang; Wu, Youli; Liu, Yunxia; Zhang, Danxu

2017-01-01

In this paper, a fast smooth second-order sliding mode control is presented for a class of stochastic systems with enumerable Ornstein-Uhlenbeck colored noises. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the controller. The finite-time convergence of the prescribed sliding variable dynamics system is proved by using stochastic Lyapunov-like techniques. Then the proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are presented comparing with smooth second-order sliding mode control to validate the analysis.

Predictive Rate-Distortion for Infinite-Order Markov Processes

NASA Astrophysics Data System (ADS)

Marzen, Sarah E.; Crutchfield, James P.

2016-06-01

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments confirm a popular intuition: algorithms that cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of finite- and infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting algorithms yield substantial improvements.

High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

Phase ordering in disordered and inhomogeneous systems

NASA Astrophysics Data System (ADS)

Corberi, Federico; Zannetti, Marco; Lippiello, Eugenio; Burioni, Raffaella; Vezzani, Alessandro

2015-06-01

We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of dynamical behaviors characterized by different growth laws of the ordered domain size, namely logarithmic or power law, respectively. It is conjectured that the interplay between these dynamical classes is regulated by the same topological feature that governs the presence or the absence of a finite-temperature phase transition.

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

DOE PAGES

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 (2Δ x) modes. Furthermore, high-order accuracymore » 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. 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

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guerra, Jorge E.; Ullrich, Paul A.

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 (2Δ x) modes. Furthermore, high-order accuracymore » 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. 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

A Unique Finite Element Modeling of the Periodic Wave Transformation over Sloping and Barred Beaches by Beji and Nadaoka's Extended Boussinesq Equations

PubMed Central

Jabbari, Mohammad Hadi; Sayehbani, Mesbah; Reisinezhad, Arsham

2013-01-01

This paper presents a numerical model based on one-dimensional Beji and Nadaoka's Extended Boussinesq equations for simulation of periodic wave shoaling and its decomposition over morphological beaches. A unique Galerkin finite element and Adams-Bashforth-Moulton predictor-corrector methods are employed for spatial and temporal discretization, respectively. For direct application of linear finite element method in spatial discretization, an auxiliary variable is hereby introduced, and a particular numerical scheme is offered to rewrite the equations in lower-order form. Stability of the suggested numerical method is also analyzed. Subsequently, in order to display the ability of the presented model, four different test cases are considered. In these test cases, dispersive and nonlinearity effects of the periodic waves over sloping beaches and barred beaches, which are the common coastal profiles, are investigated. Outputs are compared with other existing numerical and experimental data. Finally, it is concluded that the current model can be further developed to model any morphological development of coastal profiles. PMID:23853534

Entropy stable discontinuous interfaces coupling for the three-dimensional compressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-06-01

Non-linear entropy stability and a summation-by-parts (SBP) framework are used to derive entropy stable interior interface coupling for the semi-discretized three-dimensional (3D) compressible Navier-Stokes equations. A complete semi-discrete entropy estimate for the interior domain is achieved combining a discontinuous entropy conservative operator of any order [1,2] with an entropy stable coupling condition for the inviscid terms, and a local discontinuous Galerkin (LDG) approach with an interior penalty (IP) procedure for the viscous terms. The viscous penalty contributions scale with the inverse of the Reynolds number (Re) so that for Re → ∞ their contributions vanish and only the entropy stable inviscid interface penalty term is recovered. This paper extends the interface couplings presented [1,2] and provides a simple and automatic way to compute the magnitude of the viscous IP term. The approach presented herein is compatible with any diagonal norm summation-by-parts (SBP) spatial operator, including finite element, finite volume, finite difference schemes and the class of high-order accurate methods which include the large family of discontinuous Galerkin discretizations and flux reconstruction schemes.

Phase Transitions in Finite Systems

NASA Astrophysics Data System (ADS)

Chomaz, Philippe; Gulminelli, Francesca

In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermostatistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent.

Hybrid simulation combining two space-time discretization of the discrete-velocity Boltzmann equation

NASA Astrophysics Data System (ADS)

Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel

2017-11-01

Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.

Multitasking 3-D forward modeling using high-order finite difference methods on the Cray X-MP/416

DOE Office of Scientific and Technical Information (OSTI.GOV)

Terki-Hassaine, O.; Leiss, E.L.

1988-01-01

The CRAY X-MP/416 was used to multitask 3-D forward modeling by the high-order finite difference method. Flowtrace analysis reveals that the most expensive operation in the unitasked program is a matrix vector multiplication. The in-core and out-of-core versions of a reentrant subroutine can perform any fraction of the matrix vector multiplication independently, a pattern compatible with multitasking. The matrix vector multiplication routine can be distributed over two to four processors. The rest of the program utilizes the microtasking feature that lets the system treat independent iterations of DO-loops as subtasks to be performed by any available processor. The availability ofmore » the Solid-State Storage Device (SSD) meant the I/O wait time was virtually zero. A performance study determined a theoretical speedup, taking into account the multitasking overhead. Multitasking programs utilizing both macrotasking and microtasking features obtained actual speedups that were approximately 80% of the ideal speedup.« less

Nuclear relaxation and vibrational contributions to the static electrical properties of polyatomic molecules: beyond the Hartree-Fock approximation

NASA Astrophysics Data System (ADS)

Luis, Josep M.; Martí, Josep; Duran, Miquel; Andrés, JoséL.

1997-04-01

Electronic and nuclear contributions to the static molecular electrical properties, along with the Stark tuning rate ( δνE ) and the infrared cross section changes ( δSE) have been calculated at the SCF level and at different correlated levels of theory, using a TZ2P basis set and finite field techniques. Nuclear contributions to these molecular properties have also been calculated using a recent analytical approach that allow both to check the accuracy of the finite field values, and to evaluate the importance of higher-order derivatives. The HF, CO, H 2O, H 2CO, and CH 4 molecules have been studied and the results compared to experimental date when available. The paper shows that nuclear relaxation and vibrational contributions must be included in order to obtain accurate values of the static electrical properties. Two different, combined approaches are proposed to predict experimental values of the electrical properties to an error smaller than 5%.

On the spline-based wavelet differentiation matrix

NASA Technical Reports Server (NTRS)

Jameson, Leland

1993-01-01

The differentiation matrix for a spline-based wavelet basis is constructed. Given an n-th order spline basis it is proved that the differentiation matrix is accurate of order 2n + 2 when periodic boundary conditions are assumed. This high accuracy, or superconvergence, is lost when the boundary conditions are no longer periodic. Furthermore, it is shown that spline-based bases generate a class of compact finite difference schemes.

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

NASA Technical Reports Server (NTRS)

Bui, Trong T.; Mankbadi, Reda R.

1995-01-01

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

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

NASA Technical Reports Server (NTRS)

Carton De Wiart, Corentin; Diosady, Laslo T.; Garai, Anirban; Burgess, Nicholas; Blonigan, Patrick; Ekelschot, Dirk; Murman, Scott M.

2018-01-01

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

Theory and simulation of time-fractional fluid diffusion in porous media

NASA Astrophysics Data System (ADS)

Carcione, José M.; Sanchez-Sesma, Francisco J.; Luzón, Francisco; Perez Gavilán, Juan J.

2013-08-01

We simulate a fluid flow in inhomogeneous anisotropic porous media using a time-fractional diffusion equation and the staggered Fourier pseudospectral method to compute the spatial derivatives. A fractional derivative of the order of 0 < ν < 2 replaces the first-order time derivative in the classical diffusion equation. It implies a time-dependent permeability tensor having a power-law time dependence, which describes memory effects and accounts for anomalous diffusion. We provide a complete analysis of the physics based on plane waves. The concepts of phase, group and energy velocities are analyzed to describe the location of the diffusion front, and the attenuation and quality factors are obtained to quantify the amplitude decay. We also obtain the frequency-domain Green function. The time derivative is computed with the Grünwald-Letnikov summation, which is a finite-difference generalization of the standard finite-difference operator to derivatives of fractional order. The results match the analytical solution obtained from the Green function. An example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of ν. The calculation requires storing the whole pressure field in the computer memory since anomalous diffusion ‘recalls the past’.

Methods for High-Order Multi-Scale and Stochastic Problems Analysis, Algorithms, and Applications

DTIC Science & Technology

2016-10-17

finite volume schemes, discontinuous Galerkin finite element method, and related methods, for solving computational fluid dynamics (CFD) problems and...approximation for finite element methods. (3) The development of methods of simulation and analysis for the study of large scale stochastic systems of...laws, finite element method, Bernstein-Bezier finite elements , weakly interacting particle systems, accelerated Monte Carlo, stochastic networks 16

RAXBOD- INVISCID TRANSONIC FLOW OVER AXISYMMETRIC BODIES

NASA Technical Reports Server (NTRS)

Keller, J. D.

1994-01-01

The problem of axisymmetric transonic flow is of interest not only because of the practical application to missile and launch vehicle aerodynamics, but also because of its relation to fully three-dimensional flow in terms of the area rule. The RAXBOD computer program was developed for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses a finite-difference relaxation method to numerically solve the exact formulation of the disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important. The governing second-order partial differential equation describing the flow potential is replaced by a system of finite difference equations, including Jameson's "rotated" difference scheme at supersonic points. A stretching is applied to both the normal and tangential coordinates such that the infinite physical space is mapped onto a finite computational space. The boundary condition at infinity can be applied directly and there is no need for an asymptotic far-field solution. The system of finite difference equations is solved by a column relaxation method. In order to obtain both rapid convergence and any desired resolution, the relaxation is performed iteratively on successively refined grids. Input to RAXBOD consists of a description of the body geometry, the free stream conditions, and the desired resolution control parameters. Output from RAXBOD includes computed geometric parameters in the normal and tangential directions, iteration history information, drag coefficients, flow field data in the computational plane, and coordinates of the sonic line. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6600 computer with an overlayed central memory requirement of approximately 40K (octal) of 60 bit words. Optional plotted output can be generated for the Calcomp plotting system. The RAXBOD program was developed in 1976.

Maximum likelihood estimation of finite mixture model for economic data

NASA Astrophysics Data System (ADS)

Phoong, Seuk-Yen; Ismail, Mohd Tahir

2014-06-01

Finite mixture model is a mixture model with finite-dimension. This models are provides a natural representation of heterogeneity in a finite number of latent classes. In addition, finite mixture models also known as latent class models or unsupervised learning models. Recently, maximum likelihood estimation fitted finite mixture models has greatly drawn statistician's attention. The main reason is because maximum likelihood estimation is a powerful statistical method which provides consistent findings as the sample sizes increases to infinity. Thus, the application of maximum likelihood estimation is used to fit finite mixture model in the present paper in order to explore the relationship between nonlinear economic data. In this paper, a two-component normal mixture model is fitted by maximum likelihood estimation in order to investigate the relationship among stock market price and rubber price for sampled countries. Results described that there is a negative effect among rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia.

A strategy for optical properties investigation in ABe2BO3F2 (A=K, Rb, Cs) using finite field methods

NASA Astrophysics Data System (ADS)

Mushahali, Hahaer; Mu, Baoxia; Wang, Qian; Mamat, Mamatrishat; Cao, Haibin; Yang, Guang; Jing, Qun

2018-07-01

The finite-field methods can be used to intuitively learn about the optical response and find out the atomic contributions to the birefringence and SHG tensors. In this paper, the linear and second-order nonlinear optical properties of ABe2BO3F2 family (A = K, Rb, Cs) compounds are investigated using the finite-field methods within different exchange-correlation functionals. The results show that the obtained birefringence and SHG tensors are in good agreement with the experimental values. The atomic contribution to the total birefringence was further investigated using the variation of the atomic charges, and the Born effective charges. The results show that the boron-oxygen groups give main contribution to the anisotropic birefringence.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giunta, G.; Belouettar, S.

In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigationsmore » show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family.« less

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)

2002-01-01

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ullrich, Paul A.; Devendran, Dharshi; Johansen, Hans

2016-04-01

The focus on this series of articles is on the generation of accurate, conservative, consistent, and (optionally) monotone linear offline maps. This paper is the second in the series. It extends on the first part by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii)more » from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps.« less

Simulation-aided constitutive law development - Assessment of low triaxiality void nucleation models via extended finite element method

NASA Astrophysics Data System (ADS)

Zhao, Jifeng; Kontsevoi, Oleg Y.; Xiong, Wei; Smith, Jacob

2017-05-01

In this work, a multi-scale computational framework has been established in order to investigate, refine and validate constitutive behaviors in the context of the Gurson-Tvergaard-Needleman (GTN) void mechanics model. The eXtended Finite Element Method (XFEM) has been implemented in order to (1) develop statistical volume elements (SVE) of a matrix material with subscale inclusions and (2) to simulate the multi-void nucleation process due to interface debonding between the matrix and particle phases. Our analyses strongly suggest that under low stress triaxiality the nucleation rate of the voids f˙ can be well described by a normal distribution function with respect to the matrix equivalent stress (σe), as opposed to that proposed (σbar + 1 / 3σkk) in the original form of the single void GTN model. The modified form of the multi-void nucleation model has been validated based on a series of numerical experiments with different loading conditions, material properties, particle shape/size and spatial distributions. The utilization of XFEM allows for an invariant finite element mesh to represent varying microstructures, which implies suitability for drastically reducing complexity in generating the finite element discretizations for large stochastic arrays of microstructure configurations. The modified form of the multi-void nucleation model is further applied to study high strength steels by incorporating first principles calculations. The necessity of using a phenomenological interface separation law has been fully eliminated and replaced by the physics-based cohesive relationship obtained from Density Functional Theory (DFT) calculations in order to provide an accurate macroscopic material response.

A moving mesh finite difference method for equilibrium radiation diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Divergence Free High Order Filter Methods for Multiscale Non-ideal MHD Flows

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, Bjoern

2003-01-01

Low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous MHD flows has been constructed. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field (Delta . B) numerical error in the sense that no standard divergence cleaning is required. For certain 2-D MHD test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.

Heat transfer models for predicting Salmonella enteritidis in shell eggs through supply chain distribution.

PubMed

Almonacid, S; Simpson, R; Teixeira, A

2007-11-01

Egg and egg preparations are important vehicles for Salmonella enteritidis infections. The influence of time-temperature becomes important when the presence of this organism is found in commercial shell eggs. A computer-aided mathematical model was validated to estimate surface and interior temperature of shell eggs under variable ambient and refrigerated storage temperature. A risk assessment of S. enteritidis based on the use of this model, coupled with S. enteritidis kinetics, has already been reported in a companion paper published earlier in JFS. The model considered the actual geometry and composition of shell eggs and was solved by numerical techniques (finite differences and finite elements). Parameters of interest such as local (h) and global (U) heat transfer coefficient, thermal conductivity, and apparent volumetric specific heat were estimated by an inverse procedure from experimental temperature measurement. In order to assess the error in predicting microbial population growth, theoretical and experimental temperatures were applied to a S. enteritidis growth model taken from the literature. Errors between values of microbial population growth calculated from model predicted compared with experimentally measured temperatures were satisfactorily low: 1.1% and 0.8% for the finite difference and finite element model, respectively.

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

NASA Astrophysics Data System (ADS)

Yang, Peng-fei; Fang, Yang-wang; Wu, You-li; Zhang, Dan-xu; Xu, Yang

2018-01-01

A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein-Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.

Numerical integration and optimization of motions for multibody dynamic systems

NASA Astrophysics Data System (ADS)

Aguilar Mayans, Joan

This thesis considers the optimization and simulation of motions involving rigid body systems. It does so in three distinct parts, with the following topics: optimization and analysis of human high-diving motions, efficient numerical integration of rigid body dynamics with contacts, and motion optimization of a two-link robot arm using Finite-Time Lyapunov Analysis. The first part introduces the concept of eigenpostures, which we use to simulate and analyze human high-diving motions. Eigenpostures are used in two different ways: first, to reduce the complexity of the optimal control problem that we solve to obtain such motions, and second, to generate an eigenposture space to which we map existing real world motions to better analyze them. The benefits of using eigenpostures are showcased through different examples. The second part reviews an extensive list of integration algorithms used for the integration of rigid body dynamics. We analyze the accuracy and stability of the different integrators in the three-dimensional space and the rotation space SO(3). Integrators with an accuracy higher than first order perform more efficiently than integrators with first order accuracy, even in the presence of contacts. The third part uses Finite-time Lyapunov Analysis to optimize motions for a two-link robot arm. Finite-Time Lyapunov Analysis diagnoses the presence of time-scale separation in the dynamics of the optimized motion and provides the information and methodology for obtaining an accurate approximation to the optimal solution, avoiding the complications that timescale separation causes for alternative solution methods.

Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modeling

NASA Astrophysics Data System (ADS)

Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.

2015-10-01

We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.

An efficient flexible-order model for 3D nonlinear water waves

NASA Astrophysics Data System (ADS)

Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.

2009-04-01

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.

Development of cost-effective surfactant flooding technology. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pope, G.A.; Sepehrnoori, K.

1996-11-01

Task 1 of this research was the development of a high-resolution, fully implicit, finite-difference, multiphase, multicomponent, compositional simulator for chemical flooding. The major physical phenomena modeled in this simulator are dispersion, heterogeneous permeability and porosity, adsorption, interfacial tension, relative permeability and capillary desaturation, compositional phase viscosity, compositional phase density and gravity effects, capillary pressure, and aqueous-oleic-microemulsion phase behavior. Polymer and its non-Newtonian rheology properties include shear-thinning viscosity, permeability reduction, inaccessible pore volume, and adsorption. Options of constant or variable space grids and time steps, constant-pressure or constant-rate well conditions, horizontal and vertical wells, and multiple slug injections are also availablemore » in the simulator. The solution scheme used in this simulator is fully implicit. The pressure equation and the mass-conservation equations are solved simultaneously for the aqueous-phase pressure and the total concentrations of each component. A third-order-in-space, second-order-in-time finite-difference method and a new total-variation-diminishing (TVD) third-order flux limiter are used that greatly reduce numerical dispersion effects. Task 2 was the optimization of surfactant flooding. The code UTCHEM was used to simulate surfactant polymer flooding.« less

Numerical analysis for finite-range multitype stochastic contact financial market dynamic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Ge; Wang, Jun; Fang, Wen, E-mail: fangwen@bjtu.edu.cn

In an attempt to reproduce and study the dynamics of financial markets, a random agent-based financial price model is developed and investigated by the finite-range multitype contact dynamic system, in which the interaction and dispersal of different types of investment attitudes in a stock market are imitated by viruses spreading. With different parameters of birth rates and finite-range, the normalized return series are simulated by Monte Carlo simulation method and numerical studied by power-law distribution analysis and autocorrelation analysis. To better understand the nonlinear dynamics of the return series, a q-order autocorrelation function and a multi-autocorrelation function are also definedmore » in this work. The comparisons of statistical behaviors of return series from the agent-based model and the daily historical market returns of Shanghai Composite Index and Shenzhen Component Index indicate that the proposed model is a reasonable qualitative explanation for the price formation process of stock market systems.« less

A genuine nonlinear approach for controller design of a boiler-turbine system.

PubMed

Yang, Shizhong; Qian, Chunjiang; Du, Haibo

2012-05-01

This paper proposes a genuine nonlinear approach for controller design of a drum-type boiler-turbine system. Based on a second order nonlinear model, a finite-time convergent controller is first designed to drive the states to their setpoints in a finite time. In the case when the state variables are unmeasurable, the system will be regulated using a constant controller or an output feedback controller. An adaptive controller is also designed to stabilize the system since the model parameters may vary under different operating points. The novelty of the proposed controller design approach lies in fully utilizing the system nonlinearities instead of linearizing or canceling them. In addition, the newly developed techniques for finite-time convergent controller are used to guarantee fast convergence of the system. Simulations are conducted under different cases and the results are presented to illustrate the performance of the proposed controllers. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Continuous and Discrete Structured Population Models with Applications to Epidemiology and Marine Mammals

NASA Astrophysics Data System (ADS)

Tang, Tingting

In this dissertation, we develop structured population models to examine how changes in the environmental affect population processes. In Chapter 2, we develop a general continuous time size structured model describing a susceptible-infected (SI) population coupled with the environment. This model applies to problems arising in ecology, epidemiology, and cell biology. The model consists of a system of quasilinear hyperbolic partial differential equations coupled with a system of nonlinear ordinary differential equations that represent the environment. We develop a second-order high resolution finite difference scheme to numerically solve the model. Convergence of this scheme to a weak solution with bounded total variation is proved. We numerically compare the second order high resolution scheme with a first order finite difference scheme. Higher order of convergence and high resolution property are observed in the second order finite difference scheme. In addition, we apply our model to a multi-host wildlife disease problem, questions regarding the impact of the initial population structure and transition rate within each host are numerically explored. In Chapter 3, we use a stage structured matrix model for wildlife population to study the recovery process of the population given an environmental disturbance. We focus on the time it takes for the population to recover to its pre-event level and develop general formulas to calculate the sensitivity or elasticity of the recovery time to changes in the initial population distribution, vital rates and event severity. Our results suggest that the recovery time is independent of the initial population size, but is sensitive to the initial population structure. Moreover, it is more sensitive to the reduction proportion to the vital rates of the population caused by the catastrophe event relative to the duration of impact of the event. We present the potential application of our model to the amphibian population dynamic and the recovery of a certain plant population. In addition, we explore, in details, the application of the model to the sperm whale population in Gulf of Mexico after the Deepwater Horizon oil spill. In Chapter 4, we summarize the results from Chapter 2 and Chapter 3 and explore some further avenues of our research.

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

DOE PAGES

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

2015-03-11

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

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

NASA Astrophysics Data System (ADS)

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-05-01

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss-Lobatto-Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Kai; Fu, Shubin; Chung, Eric T.

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructsmore » high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss–Lobatto–Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.« less

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

DOE PAGES

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-02-04

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructsmore » high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss–Lobatto–Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.« less

Arbitrary-order corrections for finite-time drift and diffusion coefficients

NASA Astrophysics Data System (ADS)

Anteneodo, C.; Riera, R.

2009-09-01

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations

NASA Astrophysics Data System (ADS)

Christlieb, Andrew J.; Feng, Xiao; Seal, David C.; Tang, Qi

2016-07-01

We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in Christlieb et al. (2015) [23], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (that has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these derivatives to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax-Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton-Jacobi equations in order to construct a non-oscillatory magnetic field. The end result is an algorithm that is similar to our previous work Christlieb et al. (2014) [8], but this time the time stepping is replaced through a Taylor method with the addition of a positivity-preserving limiter. Finally, positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. The choice of the free parameter is then given in such a way that the fluxes are limited towards the low-order solver until positivity is attained. Given the lack of additional degrees of freedom in the system, this positivity limiter lacks energy conservation where the limiter turns on. However, this ingredient can be dropped for problems where the pressure does not become negative. We present two and three dimensional numerical results for several standard test problems including a smooth Alfvén wave (to verify formal order of accuracy), shock tube problems (to test the shock-capturing ability of the scheme), Orszag-Tang, and cloud shock interactions. These results assert the robustness and verify the high-order of accuracy of the proposed scheme.

Revisiting and Extending Interface Penalties for Multi-Domain Summation-by-Parts Operators

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Nordstrom, Jan; Gottlieb, David

2007-01-01

General interface coupling conditions are presented for multi-domain collocation methods, which satisfy the summation-by-parts (SBP) spatial discretization convention. The combined interior/interface operators are proven to be L2 stable, pointwise stable, and conservative, while maintaining the underlying accuracy of the interior SBP operator. The new interface conditions resemble (and were motivated by) those used in the discontinuous Galerkin finite element community, and maintain many of the same properties. Extensive validation studies are presented using two classes of high-order SBP operators: 1) central finite difference, and 2) Legendre spectral collocation.

Computational methods for vortex dominated compressible flows

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The principal objectives were to: understand the mechanisms by which Euler equation computations model leading edge vortex flows; understand the vortical and shock wave structures that may exist for different wing shapes, angles of incidence, and Mach numbers; and compare calculations with experiments in order to ascertain the limitations and advantages of Euler equation models. The initial approach utilized the cell centered finite volume Jameson scheme. The final calculation utilized a cell vertex finite volume method on an unstructured grid. Both methods used Runge-Kutta four stage schemes for integrating the equations. The principal findings are briefly summarized.

Edge effects in angle-ply composite laminates

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1977-01-01

This paper presents the results of a zeroth-order solution for edge effects in angle-ply composite laminates obtained using perturbation techniques and a limiting free body approach. The general solution for edge effects in laminates of arbitrary angle ply is applied to the special case of a (+ or - 45)s graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness-to-width ratio and compared to finite difference results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress and provides mathematical evidence for singular interlaminar shear stresses in (+ or - 45) graphite/epoxy laminates.

Parallel computation of transverse wakes in linear colliders

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhan, Xiaowei; Ko, Kwok

1996-11-01

SLAC has proposed the detuned structure (DS) as one possible design to control the emittance growth of long bunch trains due to transverse wakefields in the Next Linear Collider (NLC). The DS consists of 206 cells with tapering from cell to cell of the order of few microns to provide Gaussian detuning of the dipole modes. The decoherence of these modes leads to two orders of magnitude reduction in wakefield experienced by the trailing bunch. To model such a large heterogeneous structure realistically is impractical with finite-difference codes using structured grids. The authors have calculated the wakefield in the DSmore » on a parallel computer with a finite-element code using an unstructured grid. The parallel implementation issues are presented along with simulation results that include contributions from higher dipole bands and wall dissipation.« less

Finite horizon EOQ model for non-instantaneous deteriorating items with price and advertisement dependent demand and partial backlogging under inflation

NASA Astrophysics Data System (ADS)

Palanivel, M.; Uthayakumar, R.

2015-07-01

This paper deals with an economic order quantity (EOQ) model for non-instantaneous deteriorating items with price and advertisement dependent demand pattern under the effect of inflation and time value of money over a finite planning horizon. In this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. This paper aids the retailer in minimising the total inventory cost by finding the optimal interval and the optimal order quantity. An algorithm is designed to find the optimum solution of the proposed model. Numerical examples are given to demonstrate the results. Also, the effect of changes in the different parameters on the optimal total cost is graphically presented and the implications are discussed in detail.

Algorithms for computing solvents of unilateral second-order matrix polynomials over prime finite fields using lambda-matrices

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-01-01

The paper considers algorithms for finding diagonalizable and non-diagonalizable roots (so called solvents) of monic arbitrary unilateral second-order matrix polynomial over prime finite field. These algorithms are based on polynomial matrices (lambda-matrices). This is an extension of existing general methods for computing solvents of matrix polynomials over field of complex numbers. We analyze how techniques for complex numbers can be adapted for finite field and estimate asymptotic complexity of the obtained algorithms.

Modular synchronization in complex networks.

PubMed

Oh, E; Rho, K; Hong, H; Kahng, B

2005-10-01

We study the synchronization transition (ST) of a modified Kuramoto model on two different types of modular complex networks. It is found that the ST depends on the type of intermodular connections. For the network with decentralized (centralized) intermodular connections, the ST occurs at finite coupling constant (behaves abnormally). Such distinct features are found in the yeast protein interaction network and the Internet, respectively. Moreover, by applying the finite-size scaling analysis to an artificial network with decentralized intermodular connections, we obtain the exponent associated with the order parameter of the ST to be beta approximately 1 different from beta(MF) approximately 1/2 obtained from the scale-free network with the same degree distribution but the absence of modular structure, corresponding to the mean field value.

Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

NASA Technical Reports Server (NTRS)

Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

2011-01-01

A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

Monte-Carlo simulation of a stochastic differential equation

NASA Astrophysics Data System (ADS)

Arif, ULLAH; Majid, KHAN; M, KAMRAN; R, KHAN; Zhengmao, SHENG

2017-12-01

For solving higher dimensional diffusion equations with an inhomogeneous diffusion coefficient, Monte Carlo (MC) techniques are considered to be more effective than other algorithms, such as finite element method or finite difference method. The inhomogeneity of diffusion coefficient strongly limits the use of different numerical techniques. For better convergence, methods with higher orders have been kept forward to allow MC codes with large step size. The main focus of this work is to look for operators that can produce converging results for large step sizes. As a first step, our comparative analysis has been applied to a general stochastic problem. Subsequently, our formulization is applied to the problem of pitch angle scattering resulting from Coulomb collisions of charge particles in the toroidal devices.

Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

NASA Technical Reports Server (NTRS)

Kreider, Kevin L.; Baumeister, Kenneth J.

1996-01-01

An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.

2018-02-01

A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.

Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids

NASA Astrophysics Data System (ADS)

Lee, Euntaek; Ahn, Hyung Taek; Luo, Hong

2018-02-01

We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

Numerical computation of transonic flows by finite-element and finite-difference methods

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

1978-01-01

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

3-D geoelectrical modelling using finite-difference: a new boundary conditions improvement

NASA Astrophysics Data System (ADS)

Maineult, A.; Schott, J.-J.; Ardiot, A.

2003-04-01

Geoelectrical prospecting is a well-known and frequently used method for quantitative and non-destructive subsurface exploration until depths of a few hundreds metres. Thus archeological objects can be efficiently detected as their resistivities often contrast with those of the surrounding media. Nevertheless using the geoelectrical prospecting method has long been restricted due to inhability to model correctly arbitrarily-shaped structures. The one-dimensional modelling and inversion have long been classical, but are of no interest for the majority of field data, since the natural distribution of resistivity is rarely homogeneous or tabular. Since the 1970's some authors developed discrete methods in order to solve the two and three-dimensional problem, using mathematical tools such as finite-element or finite-difference. The finite-difference approach is quite simple, easily understandable and programmable. Since the work of Dey and Morrison (1979), this approach has become quite popular. Nevertheless, one of its major drawbacks is the difficulty to establish satisfying boundary conditions. Recently Lowry et al. (1989) and Zhao and Yedlin (1996) suggested some refinements on the improvement of the boundary problem. We propose a new betterment, based on the splitting of the potential into two terms, the potential due to a reference tabular medium and a secondary potential caused by a disturbance of this medium. The surface response of a tabular medium has long been known (see for example Koefoed 1979). Here we developed the analytical solution for the electrical tabular potential everywhere in the medium, in order to establish more satisfying boundary conditions. The response of the perturbation, that is to say the object of interest, is then solved using volume-difference and preconditioned conjugate gradient. Finally the grid is refined one or more times in the perturbed domain in order to ameliorate the precision. This method of modelling is easy to implement and numerical computations run very fast. Thanks to improved boundary conditions and refinement processes, edges effects are reduced. Moreover, one important conclusion of this work is the necessity to prefer three-dimensional prospecting, since in some cases a unique profile can lead to misinterpretation, as shown by the comparison of transverse profiles through a buried cylinder and through a buried sphere.

Implementation of the high-order schemes QUICK and LECUSSO in the COMMIX-1C Program

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sakai, K.; Sun, J.G.; Sha, W.T.

Multidimensional analysis computer programs based on the finite volume method, such as COMMIX-1C, have been commonly used to simulate thermal-hydraulic phenomena in engineering systems such as nuclear reactors. In COMMIX-1C, the first-order schemes with respect to both space and time are used. In many situations such as flow recirculations and stratifications with steep gradient of velocity and temperature fields, however, high-order difference schemes are necessary for an accurate prediction of the fields. For these reasons, two second-order finite difference numerical schemes, QUICK (Quadratic Upstream Interpolation for Convective Kinematics) and LECUSSO (Local Exact Consistent Upwind Scheme of Second Order), have beenmore » implemented in the COMMIX-1C computer code. The formulations were derived for general three-dimensional flows with nonuniform grid sizes. Numerical oscillation analyses for QUICK and LECUSSO were performed. To damp the unphysical oscillations which occur in calculations with high-order schemes at high mesh Reynolds numbers, a new FRAM (Filtering Remedy and Methodology) scheme was developed and implemented. To be consistent with the high-order schemes, the pressure equation and the boundary conditions for all the conservation equations were also modified to be of second order. The new capabilities in the code are listed. Test calculations were performed to validate the implementation of the high-order schemes. They include the test of the one-dimensional nonlinear Burgers equation, two-dimensional scalar transport in two impinging streams, von Karmann vortex shedding, shear driven cavity flow, Couette flow, and circular pipe flow. The calculated results were compared with available data; the agreement is good.« less

The effects of finite rate chemical processes on high enthalpy nozzle performance - A comparison between SPARK and SEAGULL

NASA Technical Reports Server (NTRS)

Carpenter, M. H.

1988-01-01

The generalized chemistry version of the computer code SPARK is extended to include two higher-order numerical schemes, yielding fourth-order spatial accuracy for the inviscid terms. The new and old formulations are used to study the influences of finite rate chemical processes on nozzle performance. A determination is made of the computationally optimum reaction scheme for use in high-enthalpy nozzles. Finite rate calculations are compared with the frozen and equilibrium limits to assess the validity of each formulation. In addition, the finite rate SPARK results are compared with the constant ratio of specific heats (gamma) SEAGULL code, to determine its accuracy in variable gamma flow situations. Finally, the higher-order SPARK code is used to calculate nozzle flows having species stratification. Flame quenching occurs at low nozzle pressures, while for high pressures, significant burning continues in the nozzle.

Joint modelling rationale for chained equations

PubMed Central

2014-01-01

Background Chained equations imputation is widely used in medical research. It uses a set of conditional models, so is more flexible than joint modelling imputation for the imputation of different types of variables (e.g. binary, ordinal or unordered categorical). However, chained equations imputation does not correspond to drawing from a joint distribution when the conditional models are incompatible. Concurrently with our work, other authors have shown the equivalence of the two imputation methods in finite samples. Methods Taking a different approach, we prove, in finite samples, sufficient conditions for chained equations and joint modelling to yield imputations from the same predictive distribution. Further, we apply this proof in four specific cases and conduct a simulation study which explores the consequences when the conditional models are compatible but the conditions otherwise are not satisfied. Results We provide an additional “non-informative margins” condition which, together with compatibility, is sufficient. We show that the non-informative margins condition is not satisfied, despite compatible conditional models, in a situation as simple as two continuous variables and one binary variable. Our simulation study demonstrates that as a consequence of this violation order effects can occur; that is, systematic differences depending upon the ordering of the variables in the chained equations algorithm. However, the order effects appear to be small, especially when associations between variables are weak. Conclusions Since chained equations is typically used in medical research for datasets with different types of variables, researchers must be aware that order effects are likely to be ubiquitous, but our results suggest they may be small enough to be negligible. PMID:24559129

Influence of electrodes on the 448 kHz electric currents created by radiofrequency: A finite element study.

PubMed

Spottorno, J; Gonzalez de Vega, C; Buenaventura, M; Hernando, A

2017-01-01

Radiofrequency is a technology used in physical rehabilitation by physicians and physiotherapists for more than fifteen years, although there exist doubts on how it works. Indiba is a particular method that applies a voltage difference of 448 KHz between two electrodes, creating an electric current between them. These electrodes are an active one that is placed on different areas of the body and a passive one that is left on the same position during the treatment. There are two different types of active electrodes: the capacitive one and the resistive one. In this paper, it has been studied how the different electrodes affect the current density inside the body and thus how they affect the efficacy of the treatment. It shows how finite element calculations should help physicians in order to better understand its behavior and improve the treatments.

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

Documentation of the Goddard Laboratory for atmospheres fourth-order two-layer shallow water model

NASA Technical Reports Server (NTRS)

Takacs, L. L. (Compiler)

1986-01-01

The theory and numerical treatment used in the 2-level GLA fourth-order shallow water model are described. This model was designed to emulate the horizontal finite differences used by the GLA Fourth-Order General Circulation Model (Kalnay et al., 1983) in addition to its grid structure, form of high-latitude and global filtering, and time-integration schemes. A user's guide is also provided instructing the user on how to create initial conditions, execute the model, and post-process the data history.

Finite element modeling of hyper-viscoelasticity of peripheral nerve ultrastructures.

PubMed

Chang, Cheng-Tao; Chen, Yu-Hsing; Lin, Chou-Ching K; Ju, Ming-Shaung

2015-07-16

The mechanical characteristics of ultrastructures of rat sciatic nerves were investigated through animal experiments and finite element analyses. A custom-designed dynamic testing apparatus was used to conduct in vitro transverse compression experiments on the nerves. The optical coherence tomography (OCT) was utilized to record the cross-sectional images of nerve during the dynamic testing. Two-dimensional finite element models of the nerves were built based on their OCT images. A hyper-viscoelastic model was employed to describe the elastic and stress relaxation response of each ultrastructure of the nerve, namely the endoneurium, the perineurium and the epineurium. The first-order Ogden model was employed to describe the elasticity of each ultrastructure and a generalized Maxwell model for the relaxation. The inverse finite element analysis was used to estimate the material parameters of the ultrastructures. The results show the instantaneous shear modulus of the ultrastructures in decreasing order is perineurium, endoneurium, and epineurium. The FE model combined with the first-order Ogden model and the second-order Prony series is good enough for describing the compress-and-hold response of the nerve ultrastructures. The integration of OCT and the nonlinear finite element modeling may be applicable to study the viscoelasticity of peripheral nerve down to the ultrastructural level. Copyright © 2015 Elsevier Ltd. All rights reserved.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

NASA Technical Reports Server (NTRS)

Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard

1996-01-01

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Thermal History and Mantle Dynamics of Venus

NASA Technical Reports Server (NTRS)

Hsui, Albert T.

1997-01-01

One objective of this research proposal is to develop a 3-D thermal history model for Venus. The basis of our study is a finite-element computer model to simulate thermal convection of fluids with highly temperature- and pressure-dependent viscosities in a three-dimensional spherical shell. A three-dimensional model for thermal history studies is necessary for the following reasons. To study planetary thermal evolution, one needs to consider global heat budgets of a planet throughout its evolution history. Hence, three-dimensional models are necessary. This is in contrasts to studies of some local phenomena or local structures where models of lower dimensions may be sufficient. There are different approaches to treat three-dimensional thermal convection problems. Each approach has its own advantages and disadvantages. Therefore, the choice of the various approaches is subjective and dependent on the problem addressed. In our case, we are interested in the effects of viscosities that are highly temperature dependent and that their magnitudes within the computing domain can vary over many orders of magnitude. In order to resolve the rapid change of viscosities, small grid spacings are often necessary. To optimize the amount of computing, variable grids become desirable. Thus, the finite-element numerical approach is chosen for its ability to place grid elements of different sizes over the complete computational domain. For this research proposal, we did not start from scratch and develop the finite element codes from the beginning. Instead, we adopted a finite-element model developed by Baumgardner, a collaborator of this research proposal, for three-dimensional thermal convection with constant viscosity. Over the duration supported by this research proposal, a significant amount of advancements have been accomplished.

Discontinuous Observers Design for Finite-Time Consensus of Multiagent Systems With External Disturbances.

PubMed

Liu, Xiaoyang; Ho, Daniel W C; Cao, Jinde; Xu, Wenying

This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.

Strictly stable high order difference approximations for computational aeroacoustics

NASA Astrophysics Data System (ADS)

Müller, Bernhard; Johansson, Stefan

2005-09-01

High order finite difference approximations with improved accuracy and stability properties have been developed for computational aeroacoustics (CAA). One of our new difference operators corresponds to Tam and Webb's DRP scheme in the interior, but is modified near the boundaries to be strictly stable. A unified formulation of the nonlinear and linearized Euler equations is used, which can be extended to the Navier-Stokes equations. The approach has been verified for 1D, 2D and axisymmetric test problems. We have simulated the sound propagation from a rocket launch before lift-off. To cite this article: B. Müller, S. Johansson, C. R. Mecanique 333 (2005).

Elasto-Plastic Analysis of Tee Joints Using HOT-SMAC

NASA Technical Reports Server (NTRS)

Arnold, Steve M. (Technical Monitor); Bednarcyk, Brett A.; Yarrington, Phillip W.

2004-01-01

The Higher Order Theory - Structural/Micro Analysis Code (HOT-SMAC) software package is applied to analyze the linearly elastic and elasto-plastic response of adhesively bonded tee joints. Joints of this type are finding an increasing number of applications with the increased use of composite materials within advanced aerospace vehicles, and improved tools for the design and analysis of these joints are needed. The linearly elastic results of the code are validated vs. finite element analysis results from the literature under different loading and boundary conditions, and new results are generated to investigate the inelastic behavior of the tee joint. The comparison with the finite element results indicates that HOT-SMAC is an efficient and accurate alternative to the finite element method and has a great deal of potential as an analysis tool for a wide range of bonded joints.

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

NASA Technical Reports Server (NTRS)

Reynolds, W. C. (Editor); Maccormack, R. W.

1981-01-01

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

Coupled porohyperelastic mass transport (PHEXPT) finite element models for soft tissues using ABAQUS.

PubMed

Vande Geest, Jonathan P; Simon, B R; Rigby, Paul H; Newberg, Tyler P

2011-04-01

Finite element models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) finite element approach developed using a commercially available ABAQUS finite element software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an Eulerian PHE FEM is coupled to a Lagrangian XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS finite element formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark finite element simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including finite deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of finite deformations. The ABAQUS-based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, finite element libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.

Very high order discontinuous Galerkin method in elliptic problems

NASA Astrophysics Data System (ADS)

Jaśkowiec, Jan

2017-09-01

The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

Very high order discontinuous Galerkin method in elliptic problems

NASA Astrophysics Data System (ADS)

Jaśkowiec, Jan

2018-07-01

The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

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.

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

The large-N Yang-Mills S matrix is ultraviolet finite, but the large-N QCD S matrix is only renormalizable

NASA Astrophysics Data System (ADS)

Bochicchio, Marco

2017-03-01

Yang-Mills (YM) theory and QCD are known to be renormalizable, but not ultraviolet (UV) finite, order by order, in perturbation theory. It is a fundamental question whether YM theory or QCD is UV finite, or only renormalizable, order by order, in the large-N 't Hooft or Veneziano expansions. We demonstrate that the renormalization group (RG) and asymptotic freedom imply that in 't Hooft large-N expansion the S matrix in YM theory is UV finite, while in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massless QCD is renormalizable but not UV finite. By the same argument, the large-N N =1 supersymmetry (SUSY) YM S matrix is UV finite as well. Besides, we demonstrate that, in both 't Hooft and Veneziano large-N expansions, the correlators of local gauge-invariant operators, as opposed to the S matrix, are renormalizable but, in general, not UV finite, either in YM theory and N =1 SUSY YM theory or a fortiori in massless QCD. Moreover, we compute explicitly the counterterms that arise from renormalizing the 't Hooft and Veneziano expansions by deriving in confining massless QCD-like theories a low-energy theorem of the Novikov-Shifman-Vainshtein-Zakharov type that relates the log derivative with respect to the gauge coupling of a k -point correlator, or the log derivative with respect to the RG-invariant scale, to a (k +1 )-point correlator with the insertion of Tr F2 at zero momentum. Finally, we argue that similar results hold in the large-N limit of a vast class of confining massive QCD-like theories, provided a renormalization scheme exists—as, for example, MS ¯ —in which the beta function is not dependent on the masses. Specifically, in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massive QCD and massive N =1 SUSY QCD is renormalizable but not UV finite.

Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

NASA Astrophysics Data System (ADS)

Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.

2010-10-01

Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

Pelvic modelling and the comparison between plate position for double pelvic osteotomy using artificial cancellous bone and finite element analysis.

PubMed

McCartney, William; MacDonald, Bryan; Ober, Ciprian Andrei; Lostado-Lorza, Rubén; Gómez, Fátima Somovilla

2018-03-20

Finite element analysis was used to compare fixation methods for double pelvic osteotomy (DPO). Using 3D scanning a stereolithography (stl) image was produced of a canine pelvis and this was subsequently refined in computer aided design (CAD). Using the CAD files, the images were imported in MSC Marc software to produce a working finite element (FE) model with 3 dimensional tetrahedral elements with linear shaped functions. The dimensions of a precontoured pelvic osteotomy plate with eight screws and a twisted seven screw straight plate were used to build the 2 fixations implants for the FE models. An equivalent load of 300 N was applied progressively on all FE models in order to facilitate its convergence. The load was applied in a distributed manner on the femur-hip joint contact area in order to simulate the actual behavior of the joint. The aim of the present study was to analyze the difference in stiffness and behavior under loading between a lateral vs ventral plate fixation, with unlocked screws and different gap scenarios, for stabilization of a pelvic osteotomy using finite element analysis. From both configurations the maximum displacement of the ventral plate with 7 screws without gap had a value of 1.988 mm, while in the DPO plate had a maximum displacement of 2.191 mm. The load applied for each of the different configurations studied when a gap of 1° was considered and also when a condition of no gap was considered. The ventral plate was stiffer than the lateral plate when a gap was not present. When the gap was closed in the ventral plate, the stiffness increased until a point that remained constant. Ventral plate fixation can be as or more stiff as lateral plate fixation and provides flexible fixation. This behavior should reduce screw loosening. Using ventral plate fixation is recommended to reduce screw loosening or failure.

Higher-order ice-sheet modelling accelerated by multigrid on graphics cards

NASA Astrophysics Data System (ADS)

Brædstrup, Christian; Egholm, David

2013-04-01

Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.

Mass-corrections for the conservative coupling of flow and transport on collocated meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Waluga, Christian, E-mail: waluga@ma.tum.de; Wohlmuth, Barbara; Rüde, Ulrich

2016-01-15

Buoyancy-driven flow models demand a careful treatment of the mass-balance equation to avoid spurious source and sink terms in the non-linear coupling between flow and transport. In the context of finite-elements, it is therefore commonly proposed to employ sufficiently rich pressure spaces, containing piecewise constant shape functions to obtain local or even strong mass-conservation. In three-dimensional computations, this usually requires nonconforming approaches, special meshes or higher order velocities, which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code. In this paper, we therefore propose a lean and conservatively coupled scheme based on standard stabilizedmore » linear equal-order finite elements for the Stokes part and vertex-centered finite volumes for the energy equation. We show that in a weak mass-balance it is possible to recover exact conservation properties by a local flux-correction which can be computed efficiently on the control volume boundaries of the transport mesh. We discuss implementation aspects and demonstrate the effectiveness of the flux-correction by different two- and three-dimensional examples which are motivated by geophysical applications.« less

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Flow adjustment inside large finite-size wind farms approaching the infinite wind farm regime

NASA Astrophysics Data System (ADS)

Wu, Ka Ling; Porté-Agel, Fernando

2017-04-01

Due to the increasing number and the growing size of wind farms, the distance among them continues to decrease. Thus, it is necessary to understand how these large finite-size wind farms and their wakes could interfere the atmospheric boundary layer (ABL) dynamics and adjacent wind farms. Fully-developed flow inside wind farms has been extensively studied through numerical simulations of infinite wind farms. The transportation of momentum and energy is only vertical and the advection of them is neglected in these infinite wind farms. However, less attention has been paid to examine the length of wind farms required to reach such asymptotic regime and the ABL dynamics in the leading and trailing edges of the large finite-size wind farms. Large eddy simulations are performed in this study to investigate the flow adjustment inside large finite-size wind farms in conventionally-neutral boundary layer with the effect of Coriolis force and free-atmosphere stratification from 1 to 5 K/km. For the large finite-size wind farms considered in the present work, when the potential temperature lapse rate is 5 K/km, the wind farms exceed the height of the ABL by two orders of magnitude for the incoming flow inside the farms to approach the fully-developed regime. An entrance fetch of approximately 40 times of the ABL height is also required for such flow adjustment. At the fully-developed flow regime of the large finite-size wind farms, the flow characteristics match those of infinite wind farms even though they have different adjustment length scales. The role of advection at the entrance and exit regions of the large finite-size wind farms is also examined. The interaction between the internal boundary layer developed above the large finite-size wind farms and the ABL under different potential temperature lapse rates are compared. It is shown that the potential temperature lapse rate plays a role in whether the flow inside the large finite-size wind farms adjusts to the fully-developed flow regime. The flow characteristics of the wake of these large finite-size wind farms are reported to forecast the effect of large finite-size wind farms on adjacent wind farms. A power deficit as large as 8% is found at a distance of 10 km downwind from the large finite-size wind farms.

Adaptive Low Dissipative High Order Filter Methods for Multiscale MHD Flows

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, Bjoern

2004-01-01

Adaptive low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous MHD flows has been constructed. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field [divergence of B] numerical error in the sense that no standard divergence cleaning is required. For certain 2-D MHD test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.

Local multiplicative Schwarz algorithms for convection-diffusion equations

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Sarkis, Marcus

1995-01-01

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

Transition from two-dimensional photonic crystals to dielectric metasurfaces in the optical diffraction with a fine structure

PubMed Central

Rybin, Mikhail V.; Samusev, Kirill B.; Lukashenko, Stanislav Yu.; Kivshar, Yuri S.; Limonov, Mikhail F.

2016-01-01

We study experimentally a fine structure of the optical Laue diffraction from two-dimensional periodic photonic lattices. The periodic photonic lattices with the C4v square symmetry, orthogonal C2v symmetry, and hexagonal C6v symmetry are composed of submicron dielectric elements fabricated by the direct laser writing technique. We observe surprisingly strong optical diffraction from a finite number of elements that provides an excellent tool to determine not only the symmetry but also exact number of particles in the finite-length structure and the sample shape. Using different samples with orthogonal C2v symmetry and varying the lattice spacing, we observe experimentally a transition between the regime of multi-order diffraction, being typical for photonic crystals to the regime where only the zero-order diffraction can be observed, being is a clear fingerprint of dielectric metasurfaces characterized by effective parameters. PMID:27491952

Finite-time synchronization of fractional-order memristor-based neural networks with time delays.

PubMed

Velmurugan, G; Rakkiyappan, R; Cao, Jinde

2016-01-01

In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall's inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α:1<α<2 and 0<α<1. The results from the theory of fractional-order differential equations with discontinuous right-hand sides are used to investigate the problem under consideration. The derived results are extended to some previous related works on memristor-based neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

An Integrated Approach to Characterizing Bypassed Oil in Heterogeneous and Fractured Reservoirs Using Partitioning Tracers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akhil Datta-Gupta

2006-12-31

We explore the use of efficient streamline-based simulation approaches for modeling partitioning interwell tracer tests in hydrocarbon reservoirs. Specifically, we utilize the unique features of streamline models to develop an efficient approach for interpretation and history matching of field tracer response. A critical aspect here is the underdetermined and highly ill-posed nature of the associated inverse problems. We have investigated the relative merits of the traditional history matching ('amplitude inversion') and a novel travel time inversion in terms of robustness of the method and convergence behavior of the solution. We show that the traditional amplitude inversion is orders of magnitudemore » more non-linear and the solution here is likely to get trapped in local minimum, leading to inadequate history match. The proposed travel time inversion is shown to be extremely efficient and robust for practical field applications. The streamline approach is generalized to model water injection in naturally fractured reservoirs through the use of a dual media approach. The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems. A detailed comparison with a commercial finite difference simulator shows very good agreement. Furthermore, an examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large-scale field applications. We also propose a novel approach to history matching finite-difference models that combines the advantage of the streamline models with the versatility of finite-difference simulation. In our approach, we utilize the streamline-derived sensitivities to facilitate history matching during finite-difference simulation. The use of finite-difference model allows us to account for detailed process physics and compressibility effects. The approach is very fast and avoids much of the subjective judgments and time-consuming trial-and-errors associated with manual history matching. We demonstrate the power and utility of our approach using a synthetic example and two field examples. We have also explored the use of a finite difference reservoir simulator, UTCHEM, for field-scale design and optimization of partitioning interwell tracer tests. The finite-difference model allows us to include detailed physics associated with reactive tracer transport, particularly those related with transverse and cross-streamline mechanisms. We have investigated the potential use of downhole tracer samplers and also the use of natural tracers for the design of partitioning tracer tests. Finally, we discuss several alternative ways of using partitioning interwell tracer tests (PITTs) in oil fields for the calculation of oil saturation, swept pore volume and sweep efficiency, and assess the accuracy of such tests under a variety of reservoir conditions.« less

Validation of non-rigid point-set registration methods using a porcine bladder pelvic phantom

NASA Astrophysics Data System (ADS)

Zakariaee, Roja; Hamarneh, Ghassan; Brown, Colin J.; Spadinger, Ingrid

2016-01-01

The problem of accurate dose accumulation in fractionated radiotherapy treatment for highly deformable organs, such as bladder, has garnered increasing interest over the past few years. However, more research is required in order to find a robust and efficient solution and to increase the accuracy over the current methods. The purpose of this study was to evaluate the feasibility and accuracy of utilizing non-rigid (affine or deformable) point-set registration in accumulating dose in bladder of different sizes and shapes. A pelvic phantom was built to house an ex vivo porcine bladder with fiducial landmarks adhered onto its surface. Four different volume fillings of the bladder were used (90, 180, 360 and 480 cc). The performance of MATLAB implementations of five different methods were compared, in aligning the bladder contour point-sets. The approaches evaluated were coherent point drift (CPD), gaussian mixture model, shape context, thin-plate spline robust point matching (TPS-RPM) and finite iterative closest point (ICP-finite). The evaluation metrics included registration runtime, target registration error (TRE), root-mean-square error (RMS) and Hausdorff distance (HD). The reference (source) dataset was alternated through all four points-sets, in order to study the effect of reference volume on the registration outcomes. While all deformable algorithms provided reasonable registration results, CPD provided the best TRE values (6.4 mm), and TPS-RPM yielded the best mean RMS and HD values (1.4 and 6.8 mm, respectively). ICP-finite was the fastest technique and TPS-RPM, the slowest.

The order of the quantum chromodynamics transition predicted by the standard model of particle physics.

PubMed

Aoki, Y; Endrodi, G; Fodor, Z; Katz, S D; Szabó, K K

2006-10-12

Quantum chromodynamics (QCD) is the theory of the strong interaction, explaining (for example) the binding of three almost massless quarks into a much heavier proton or neutron--and thus most of the mass of the visible Universe. The standard model of particle physics predicts a QCD-related transition that is relevant for the evolution of the early Universe. At low temperatures, the dominant degrees of freedom are colourless bound states of hadrons (such as protons and pions). However, QCD is asymptotically free, meaning that at high energies or temperatures the interaction gets weaker and weaker, causing hadrons to break up. This behaviour underlies the predicted cosmological transition between the low-temperature hadronic phase and a high-temperature quark-gluon plasma phase (for simplicity, we use the word 'phase' to characterize regions with different dominant degrees of freedom). Despite enormous theoretical effort, the nature of this finite-temperature QCD transition (that is, first-order, second-order or analytic crossover) remains ambiguous. Here we determine the nature of the QCD transition using computationally demanding lattice calculations for physical quark masses. Susceptibilities are extrapolated to vanishing lattice spacing for three physical volumes, the smallest and largest of which differ by a factor of five. This ensures that a true transition should result in a dramatic increase of the susceptibilities. No such behaviour is observed: our finite-size scaling analysis shows that the finite-temperature QCD transition in the hot early Universe was not a real phase transition, but an analytic crossover (involving a rapid change, as opposed to a jump, as the temperature varied). As such, it will be difficult to find experimental evidence of this transition from astronomical observations.

Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

NASA Astrophysics Data System (ADS)

Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.

2016-05-01

Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.

Modeling laser-induced periodic surface structures: Finite-difference time-domain feedback simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skolski, J. Z. P., E-mail: j.z.p.skolski@utwente.nl; Vincenc Obona, J.; Römer, G. R. B. E.

2014-03-14

A model predicting the formation of laser-induced periodic surface structures (LIPSSs) is presented. That is, the finite-difference time domain method is used to study the interaction of electromagnetic fields with rough surfaces. In this approach, the rough surface is modified by “ablation after each laser pulse,” according to the absorbed energy profile, in order to account for inter-pulse feedback mechanisms. LIPSSs with a periodicity significantly smaller than the laser wavelength are found to “grow” either parallel or orthogonal to the laser polarization. The change in orientation and periodicity follow from the model. LIPSSs with a periodicity larger than the wavelengthmore » of the laser radiation and complex superimposed LIPSS patterns are also predicted by the model.« less

RISK OF UNSATURATED/SATURATED TRANSPORT AND TRANSFORMATION OF CHEMICAL CONCENTRATIONS (RUSTIC): VOLUME 1. THEORY AND CODE VERIFICATION

EPA Science Inventory

The RUSTIC program links three subordinate models--PRZM, VADOFT, and SAFTMOD--in order to predict pesticide transport and transformation through the crop root zone, the unsaturated zone, and the saturated zone to drinking water wells. PRZM is a one-dimensional finite-difference m...

Second Order Accurate Finite Difference Methods

DTIC Science & Technology

1984-08-20

34Nonlinear Modulation of Torsional Waves in Elastic Rods," 3. Phys. Soc. Japan, V. 42, No. 6, pp. 2056-2064, 1977. 10. S. S. Antman and T. Liu. "Travelling...waves in a circular rod. The equations have been solved for coupling effects in torsional and longitudinal waves. Antman and Liu (10) have studied

A Study into Discontinuous Galerkin Methods for the Second Order Wave Equation

DTIC Science & Technology

2015-06-01

2011, vol. 7. [9] J. Stewart , Calculus . Belmont, CA: Cengage Learning, 2011. [10] J. E. Kozdon and L. C. Wilcox, “Skew-symmetric splitting for...solution directly at a set of points in a domain. In terms of the calculus of finite differences, we are looking to approximate the derivatives by

A method for the computational modeling of the physics of heart murmurs

NASA Astrophysics Data System (ADS)

Seo, Jung Hee; Bakhshaee, Hani; Garreau, Guillaume; Zhu, Chi; Andreou, Andreas; Thompson, William R.; Mittal, Rajat

2017-05-01

A computational method for direct simulation of the generation and propagation of blood flow induced sounds is proposed. This computational hemoacoustic method is based on the immersed boundary approach and employs high-order finite difference methods to resolve wave propagation and scattering accurately. The current method employs a two-step, one-way coupled approach for the sound generation and its propagation through the tissue. The blood flow is simulated by solving the incompressible Navier-Stokes equations using the sharp-interface immersed boundary method, and the equations corresponding to the generation and propagation of the three-dimensional elastic wave corresponding to the murmur are resolved with a high-order, immersed boundary based, finite-difference methods in the time-domain. The proposed method is applied to a model problem of aortic stenosis murmur and the simulation results are verified and validated by comparing with known solutions as well as experimental measurements. The murmur propagation in a realistic model of a human thorax is also simulated by using the computational method. The roles of hemodynamics and elastic wave propagation on the murmur are discussed based on the simulation results.

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

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

Development of solution techniques for nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Vos, R. G.; Andrews, J. S.

1974-01-01

Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.

Solving Fluid Structure Interaction Problems with an Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.

2016-01-01

An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction.

Scattering models for some vegetation samples

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.; Antar, Y. M. M.

1987-01-01

The Helmholtz integral equation is presently derived for a scatterer of arbitrary shape, and reduced in order to obtain the far zone-scattered field in terms of the field within the scatterer. Attention is given to the effect of different approaches to field estimation within the scatterer on the backscattering cross section, as illustrated numerically by the cases of a circular disk, a needle, and a finite-length cylinder. A comparison is made of the results obtained by modeling a leaf by means of a circular disk within the Shifrin approximation, and a tree branch by means of a finite-length cylinder, with measurements from a single leaf and a single branch.

A simple branching model that reproduces language family and language population distributions

NASA Astrophysics Data System (ADS)

Schwämmle, Veit; de Oliveira, Paulo Murilo Castro

2009-07-01

Human history leaves fingerprints in human languages. Little is known about language evolution and its study is of great importance. Here we construct a simple stochastic model and compare its results to statistical data of real languages. The model is based on the recent finding that language changes occur independently of the population size. We find agreement with the data additionally assuming that languages may be distinguished by having at least one among a finite, small number of different features. This finite set is also used in order to define the distance between two languages, similarly to linguistics tradition since Swadesh.

Modeling aluminum-lithium alloy welding characteristics

NASA Technical Reports Server (NTRS)

Bernstein, Edward L.

1996-01-01

The purpose of this project was to develop a finite element model of the heat-affected zone in the vicinity of a weld line on a plate in order to determine an accurate plastic strain history. The resulting plastic strain increments calculated by the finite element program were then to be used to calculate the measure of damage D. It was hoped to determine the effects of varying welding parameters, such as beam power, efficiency, and weld speed, and the effect of different material properties on the occurrence of microfissuring. The results were to be compared first to the previous analysis of Inconel 718, and then extended to aluminum 2195.

Reissner-Mindlin Legendre Spectral Finite Elements with Mixed Reduced Quadrature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brito, K. D.; Sprague, M. A.

2012-10-01

Legendre spectral finite elements (LSFEs) are examined through numerical experiments for static and dynamic Reissner-Mindlin plate bending and a mixed-quadrature scheme is proposed. LSFEs are high-order Lagrangian-interpolant finite elements with nodes located at the Gauss-Lobatto-Legendre quadrature points. Solutions on unstructured meshes are examined in terms of accuracy as a function of the number of model nodes and total operations. While nodal-quadrature LSFEs have been shown elsewhere to be free of shear locking on structured grids, locking is demonstrated here on unstructured grids. LSFEs with mixed quadrature are, however, locking free and are significantly more accurate than low-order finite-elements for amore » given model size or total computation time.« less

Glassy phase in quenched disordered crystalline membranes

NASA Astrophysics Data System (ADS)

Coquand, O.; Essafi, K.; Kownacki, J.-P.; Mouhanna, D.

2018-03-01

We investigate the flat phase of D -dimensional crystalline membranes embedded in a d -dimensional space and submitted to both metric and curvature quenched disorders using a nonperturbative renormalization group approach. We identify a second-order phase transition controlled by a finite-temperature, finite-disorder fixed point unreachable within the leading order of ɛ =4 -D and 1 /d expansions. This critical point divides the flow diagram into two basins of attraction: that associated with the finite-temperature fixed point controlling the long-distance behavior of disorder-free membranes and that associated with the zero-temperature, finite-disorder fixed point. Our work thus strongly suggests the existence of a whole low-temperature glassy phase for quenched disordered crystalline membranes and, possibly, for graphene and graphene-like compounds.

Some implementational issues of convection schemes for finite volume formulations

NASA Technical Reports Server (NTRS)

Thakur, Siddharth; Shyy, Wei

1993-01-01

Two higher-order upwind schemes - second-order upwind and QUICK - are examined in terms of their interpretation, implementation as well as performance for a recirculating flow in a lid-driven cavity, in the context of a control volume formulation using the SIMPLE algorithm. The present formulation of these schemes is based on a unified framework wherein the first-order upwind scheme is chosen as the basis, with the remaining terms being assigned to the source term. The performance of these schemes is contrasted with the first-order upwind and second-order central difference schemes. Also addressed in this study is the issue of boundary treatment associated with these higher-order upwind schemes. Two different boundary treatments - one that uses a two-point scheme consistently within a given control volume at the boundary, and the other that maintains consistency of flux across the interior face between the adjacent control volumes - are formulated and evaluated.

Some implementational issues of convection schemes for finite-volume formulations

NASA Technical Reports Server (NTRS)

Thakur, Siddharth; Shyy, Wei

1993-01-01

Two higher-order upwind schemes - second-order upwind and QUICK - are examined in terms of their interpretation, implementations, as well as performance for a recirculating flow in a lid-driven cavity, in the context of a control-volume formulation using the SIMPLE algorithm. The present formulation of these schemes is based on a unified framework wherein the first-order upwind scheme is chosen as the basis, with the remaining terms being assigned to the source term. The performance of these schemes is contrasted with the first-order upwind and second-order central difference schemes. Also addressed in this study is the issue of boundary treatment associated with these higher-order upwind schemes. Two different boundary treatments - one that uses a two-point scheme consistently within a given control volume at the boundary, and the other that maintains consistency of flux across the interior face between the adjacent control volumes - are formulated and evaluated.

Insights into the Behavior of Potential Structural Failures Originating from Localized High Stress Regions in Configurations Relevant to Solid Rocket Motor Nozzles

NASA Technical Reports Server (NTRS)

McCutcheon, David Matthew

2017-01-01

During the structural certification effort for the Space Launch System solid rocket booster nozzle, it was identified that no consistent method for addressing local negative margins of safety in non-metallic materials had been developed. Relevant areas included bond-line terminations and geometric features in the composite nozzle liners. In order to gain understanding, analog test specimens were designed that very closely mimic the conditions in the actual full scale hardware. Different locations in the nozzle were represented by different analog specimen designs. This paper describes those tests and corresponding results. Finite element analysis results for the tests are presented. Strain gage correlation of the analysis to the test results is addressed. Furthermore, finite fracture mechanics (a coupled stress and energy failure criterion) is utilized to predict the observed crack pop-in loads for the different configurations. The finite fracture mechanics predictions are found to be within a 10% error relative to the average measured pop-in load for each of four configurations. Initiation locations, arrest behaviors, and resistances to further post-arrest crack propagation are also discussed.

An RBF-FD closest point method for solving PDEs on surfaces

NASA Astrophysics Data System (ADS)

Petras, A.; Ling, L.; Ruuth, S. J.

2018-10-01

Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman (2008) [17]) is an embedding method for solving PDEs on surfaces using standard finite difference schemes. In this paper, we formulate an explicit closest point method using finite difference schemes derived from radial basis functions (RBF-FD). Unlike the orthogonal gradients method (Piret (2012) [22]), our proposed method uses RBF centers on regular grid nodes. This formulation not only reduces the computational cost but also avoids the ill-conditioning from point clustering on the surface and is more natural to couple with a grid based manifold evolution algorithm (Leung and Zhao (2009) [26]). When compared to the standard finite difference discretization of the closest point method, the proposed method requires a smaller computational domain surrounding the surface, resulting in a decrease in the number of sampling points on the surface. In addition, higher-order schemes can easily be constructed by increasing the number of points in the RBF-FD stencil. Applications to a variety of examples are provided to illustrate the numerical convergence of the method.

Reduction of the discretization stencil of direct forcing immersed boundary methods on rectangular cells: The ghost node shifting method

NASA Astrophysics Data System (ADS)

Picot, Joris; Glockner, Stéphane

2018-07-01

We present an analytical study of discretization stencils for the Poisson problem and the incompressible Navier-Stokes problem when used with some direct forcing immersed boundary methods. This study uses, but is not limited to, second-order discretization and Ghost-Cell Finite-Difference methods. We show that the stencil size increases with the aspect ratio of rectangular cells, which is undesirable as it breaks assumptions of some linear system solvers. To circumvent this drawback, a modification of the Ghost-Cell Finite-Difference methods is proposed to reduce the size of the discretization stencil to the one observed for square cells, i.e. with an aspect ratio equal to one. Numerical results validate this proposed method in terms of accuracy and convergence, for the Poisson problem and both Dirichlet and Neumann boundary conditions. An improvement on error levels is also observed. In addition, we show that the application of the chosen Ghost-Cell Finite-Difference methods to the Navier-Stokes problem, discretized by a pressure-correction method, requires an additional interpolation step. This extra step is implemented and validated through well known test cases of the Navier-Stokes equations.

Acceleration of FDTD mode solver by high-performance computing techniques.

PubMed

Han, Lin; Xi, Yanping; Huang, Wei-Ping

2010-06-21

A two-dimensional (2D) compact finite-difference time-domain (FDTD) mode solver is developed based on wave equation formalism in combination with the matrix pencil method (MPM). The method is validated for calculation of both real guided and complex leaky modes of typical optical waveguides against the bench-mark finite-difference (FD) eigen mode solver. By taking advantage of the inherent parallel nature of the FDTD algorithm, the mode solver is implemented on graphics processing units (GPUs) using the compute unified device architecture (CUDA). It is demonstrated that the high-performance computing technique leads to significant acceleration of the FDTD mode solver with more than 30 times improvement in computational efficiency in comparison with the conventional FDTD mode solver running on CPU of a standard desktop computer. The computational efficiency of the accelerated FDTD method is in the same order of magnitude of the standard finite-difference eigen mode solver and yet require much less memory (e.g., less than 10%). Therefore, the new method may serve as an efficient, accurate and robust tool for mode calculation of optical waveguides even when the conventional eigen value mode solvers are no longer applicable due to memory limitation.

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

NASA Technical Reports Server (NTRS)

Bui, Trong T.

1999-01-01

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

Finite-Time Stabilization and Adaptive Control of Memristor-Based Delayed Neural Networks.

PubMed

Wang, Leimin; Shen, Yi; Zhang, Guodong

Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.

Nematic order on the surface of a three-dimensional topological insulator

NASA Astrophysics Data System (ADS)

Lundgren, Rex; Yerzhakov, Hennadii; Maciejko, Joseph

2017-12-01

We study the spontaneous breaking of rotational symmetry in the helical surface state of three-dimensional topological insulators due to strong electron-electron interactions, focusing on time-reversal invariant nematic order. Owing to the strongly spin-orbit coupled nature of the surface state, the nematic order parameter is linear in the electron momentum and necessarily involves the electron spin, in contrast with spin-degenerate nematic Fermi liquids. For a chemical potential at the Dirac point (zero doping), we find a first-order phase transition at zero temperature between isotropic and nematic Dirac semimetals. This extends to a thermal phase transition that changes from first to second order at a finite-temperature tricritical point. At finite doping, we find a transition between isotropic and nematic helical Fermi liquids that is second order even at zero temperature. Focusing on finite doping, we discuss various observable consequences of nematic order, such as anisotropies in transport and the spin susceptibility, the partial breakdown of spin-momentum locking, collective modes and induced spin fluctuations, and non-Fermi-liquid behavior at the quantum critical point and in the nematic phase.

Complex Langevin simulation of chiral symmetry restoration at finite baryonic density

NASA Astrophysics Data System (ADS)

Ilgenfritz, Ernst-Michael

1986-12-01

A recently proposed effective SU(3) spin model with chiral order parameter is studied by means of the complex Langevin equation. A first-order chiral symmetry restoring and deconfining transition is observed at sufficiently low temperature at finite baryonic density. Permanent address: Sektion Physik, Karl-Marx Universität, DDR-7010 Leipzig, German Democratic Republic.

New Multigrid Method Including Elimination Algolithm Based on High-Order Vector Finite Elements in Three Dimensional Magnetostatic Field Analysis

NASA Astrophysics Data System (ADS)

Hano, Mitsuo; Hotta, Masashi

A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.

Large-eddy simulation of flow past a circular cylinder

NASA Technical Reports Server (NTRS)

Mittal, R.

1995-01-01

Some of the most challenging applications of large-eddy simulation are those in complex geometries where spectral methods are of limited use. For such applications more conventional methods such as finite difference or finite element have to be used. However, it has become clear in recent years that dissipative numerical schemes which are routinely used in viscous flow simulations are not good candidates for use in LES of turbulent flows. Except in cases where the flow is extremely well resolved, it has been found that upwind schemes tend to damp out a significant portion of the small scales that can be resolved on the grid. Furthermore, it has been found that even specially designed higher-order upwind schemes that have been used successfully in the direct numerical simulation of turbulent flows produce too much dissipation when used in conjunction with large-eddy simulation. The objective of the current study is to perform a LES of incompressible flow past a circular cylinder at a Reynolds number of 3900 using a solver which employs an energy-conservative second-order central difference scheme for spatial discretization and compare the results obtained with those of Beaudan & Moin (1994) and with the experiments in order to assess the performance of the central scheme for this relatively complex geometry.

Steel Alloy Hot Roll Simulations and Through-Thickness Variation Using Dislocation Density-Based Modeling

NASA Astrophysics Data System (ADS)

Jansen Van Rensburg, G. J.; Kok, S.; Wilke, D. N.

2017-10-01

Different roll pass reduction schedules have different effects on the through-thickness properties of hot-rolled metal slabs. In order to assess or improve a reduction schedule using the finite element method, a material model is required that captures the relevant deformation mechanisms and physics. The model should also report relevant field quantities to assess variations in material state through the thickness of a simulated rolled metal slab. In this paper, a dislocation density-based material model with recrystallization is presented and calibrated on the material response of a high-strength low-alloy steel. The model has the ability to replicate and predict material response to a fair degree thanks to the physically motivated mechanisms it is built on. An example study is also presented to illustrate the possible effect different reduction schedules could have on the through-thickness material state and the ability to assess these effects based on finite element simulations.

Acceleration of low order finite element computation with GPUs (Invited)

NASA Astrophysics Data System (ADS)

Knepley, M. G.

2010-12-01

Considerable effort has been focused on the acceleration using GPUs of high order spectral element methods and discontinuous Galerkin finite element methods. However, these methods are not universally applicable, and much of the existing FEM software base employs low order methods. In this talk, we present a formulation of FEM, using the PETSc framework from ANL, which is amenable to GPU acceleration even at very low order. In addition, using the FEniCS system for FEM, we show that the relevant kernels can be automatically generated and optimized using a symbolic manipulation system.

Using Finite Element Method to Estimate the Material Properties of a Bearing Cage

DTIC Science & Technology

2018-02-01

UNCLASSIFIED UNCLASSIFIED AD-E403 988 Technical Report ARMET-TR-17035 USING FINITE ELEMENT METHOD TO ESTIMATE THE MATERIAL...TITLE AND SUBTITLE USING FINITE ELEMENT METHOD TO ESTIMATE THE MATERIAL PROPERTIES OF A BEARING CAGE 5a. CONTRACT NUMBER 5b. GRANT...specifications of non-metallic bearing cages are typically not supplied by the manufacturer. In order to setup a finite element analysis of a

Transient finite element modeling of functional electrical stimulation.

PubMed

Filipovic, Nenad D; Peulic, Aleksandar S; Zdravkovic, Nebojsa D; Grbovic-Markovic, Vesna M; Jurisic-Skevin, Aleksandra J

2011-03-01

Transcutaneous functional electrical stimulation is commonly used for strengthening muscle. However, transient effects during stimulation are not yet well explored. The effect of an amplitude change of the stimulation can be described by static model, but there is no differency for different pulse duration. The aim of this study is to present the finite element (FE) model of a transient electrical stimulation on the forearm. Discrete FE equations were derived by using a standard Galerkin procedure. Different tissue conductive and dielectric properties are fitted using least square method and trial and error analysis from experimental measurement. This study showed that FE modeling of electrical stimulation can give the spatial-temporal distribution of applied current in the forearm. Three different cases were modeled with the same geometry but with different input of the current pulse, in order to fit the tissue properties by using transient FE analysis. All three cases were compared with experimental measurements of intramuscular voltage on one volunteer.

Anisotropic Resistivity Forward Modelling Using Automatic Generated Higher-order Finite Element Codes

NASA Astrophysics Data System (ADS)

Wang, W.; Liu, J.

2016-12-01

Forward modelling is the general way to obtain responses of geoelectrical structures. Field investigators might find it useful for planning surveys and choosing optimal electrode configurations with respect to their targets. During the past few decades much effort has been put into the development of numerical forward codes, such as integral equation method, finite difference method and finite element method. Nowadays, most researchers prefer the finite element method (FEM) for its flexible meshing scheme, which can handle models with complex geometry. Resistivity Modelling with commercial sofewares such as ANSYS and COMSOL is convenient, but like working with a black box. Modifying the existed codes or developing new codes is somehow a long period. We present a new way to obtain resistivity forward modelling codes quickly, which is based on the commercial sofeware FEPG (Finite element Program Generator). Just with several demanding scripts, FEPG could generate FORTRAN program framework which can easily be altered to adjust our targets. By supposing the electric potential is quadratic in each element of a two-layer model, we obtain quite accurate results with errors less than 1%, while more than 5% errors could appear by linear FE codes. The anisotropic half-space model is supposed to concern vertical distributed fractures. The measured apparent resistivities along the fractures are bigger than results from its orthogonal direction, which are opposite of the true resistivities. Interpretation could be misunderstood if this anisotropic paradox is ignored. The technique we used can obtain scientific codes in a short time. The generated powerful FORTRAN codes could reach accurate results by higher-order assumption and can handle anisotropy to make better interpretations. The method we used could be expand easily to other domain where FE codes are needed.

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

PubMed Central

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

PubMed

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface

NASA Astrophysics Data System (ADS)

Coco, Armando; Russo, Giovanni

2018-05-01

In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.

High-Order Energy Stable WENO Schemes

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2009-01-01

A third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables 'energy stable' modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.

Treatment of late time instabilities in finite difference EMP scattering codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Simpson, L.T.; Arman, S.; Holland, R.

1982-12-01

Time-domain solutions to the finite-differenced Maxwell's equations give rise to several well-known nonphysical propagation anomalies. In particular, when a radiative electric-field look back scheme is employed to terminate the calculation, a high-frequency, growing, numerical instability is introduced. This paper describes the constraints made on the mesh to minimize this instability, and a technique of applying an absorbing sheet to damp out this instability without altering the early time solution. Also described are techniques to extend the data record in the presence of high-frequency noise through application of a low-pass digital filter and the fitting of a damped sinusoid to themore » late-time tail of the data record. An application of these techniques is illustrated with numerical models of the FB-111 aircraft and the B-52 aircraft in the in-flight refueling configuration using the THREDE finite difference computer code. Comparisons are made with experimental scale model measurements with agreement typically on the order of 3 to 6 dB near the fundamental resonances.« less

Generation of segmental chips in metal cutting modeled with the PFEM

NASA Astrophysics Data System (ADS)

Rodriguez Prieto, J. M.; Carbonell, J. M.; Cante, J. C.; Oliver, J.; Jonsén, P.

2018-06-01

The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation.

Generation of segmental chips in metal cutting modeled with the PFEM

NASA Astrophysics Data System (ADS)

Rodriguez Prieto, J. M.; Carbonell, J. M.; Cante, J. C.; Oliver, J.; Jonsén, P.

2017-09-01

The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation.

Finite Element Analysis of Absorbable Sheath to Prevent Stress Shielding of Tibial Interlocking Intramedullary Nail

NASA Astrophysics Data System (ADS)

Dong, Yansheng; Wang, Yongqing; Dong, Limin; Jia, Peng; Lu, Fengcheng

2017-07-01

The nail with absorbable sheath (AS nail) is designed to reduce the stress shielding effect of internal fixation with interlocking intramedullary nail. In order to verify its feasibility, two types of the finite element models of internal fixation of tibia with the AS nail and the common metal nail (CM nail) are established using the Softwares of Mimics, Geomagic, SolidWorks and ANSYS according to the CT scanning data of tibia. The result of the finite element analysis shows that the AS nail has great advantages compared with the CM nail in reducing the stress shielding effect in different periods of fracture healing. The conclusion is that the AS nail can realize the static fixation to the dynamic fixation from the early to the later automatically to shorten the time of fracture healing, which also provides a new technique to the interlocking intramedullary nail.

The Effect of Scale Dependent Discretization on the Progressive Failure of Composite Materials Using Multiscale Analyses

NASA Technical Reports Server (NTRS)

Ricks, Trenton M.; Lacy, Thomas E., Jr.; Pineda, Evan J.; Bednarcyk, Brett A.; Arnold, Steven M.

2013-01-01

A multiscale modeling methodology, which incorporates a statistical distribution of fiber strengths into coupled micromechanics/ finite element analyses, is applied to unidirectional polymer matrix composites (PMCs) to analyze the effect of mesh discretization both at the micro- and macroscales on the predicted ultimate tensile (UTS) strength and failure behavior. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a PMC tensile specimen that initiates at the repeating unit cell (RUC) level. Three different finite element mesh densities were employed and each coupled with an appropriate RUC. Multiple simulations were performed in order to assess the effect of a statistical distribution of fiber strengths on the bulk composite failure and predicted strength. The coupled effects of both the micro- and macroscale discretizations were found to have a noticeable effect on the predicted UTS and computational efficiency of the simulations.

Finite element analysis on a medical implant.

PubMed

Semenescu, Augustin; Radu-Ioniță, Florentina; Mateș, Ileana Mariana; Bădică, Petre; Batalu, Nicolae Dan; Negoita, Olivia Doina; Purcarea, Victor Lorin

2016-01-01

Several studies have shown a tight connection between several ocular pathologies and an increased risk of hip fractures due to falling, especially among elderly patients. The total replacement of the hip joint is a major surgical intervention that aims to restore the function of the affected hip by various factors, such as arthritis, injures, and others. A corkscrew-like femoral stem was designed in order to preserve the bone stock and to prevent the occurrence of iatrogenic fractures during the hammering of the implant. In this paper, the finite element analysis for the proposed design was applied, considering different loads and three types of materials. A finite element analysis is a powerful tool to simulate, optimize, design, and select suitable materials for new medical implants. The results showed that the best scenario was for Ti6Al4V alloy, although Ti and 316L stainless steel had a reasonable high safety factor.

Developments in the Gung Ho dynamical core

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2017-04-01

Gung Ho is the new dynamical core being developed for the next generation Met Office weather and climate model, suitable for meeting the exascale challenge on emerging computer architectures. It builds upon the earlier collaborative project between the Met Office, NERC and STFC Daresbury of the same name to investigate suitable numerical methods for dynamical cores. A mixed-finite element approach is used, where different finite element spaces are used to represent various fields. This method provides a number of beneficial improvements over the current model, such a compatibility and inherent conservation on quasi-uniform unstructured meshes, whilst maintaining the accuracy and good dispersion properties of the staggered grid currently used. Furthermore, the mixed finite element approach allows a large degree of flexibility in the type of mesh, order of approximation and discretisation, providing a simple way to test alternative options to obtain the best model possible.

Realistic finite temperature simulations of magnetic systems using quantum statistics

NASA Astrophysics Data System (ADS)

Bergqvist, Lars; Bergman, Anders

2018-01-01

We have performed realistic atomistic simulations at finite temperatures using Monte Carlo and atomistic spin dynamics simulations incorporating quantum (Bose-Einstein) statistics. The description is much improved at low temperatures compared to classical (Boltzmann) statistics normally used in these kind of simulations, while at higher temperatures the classical statistics are recovered. This corrected low-temperature description is reflected in both magnetization and the magnetic specific heat, the latter allowing for improved modeling of the magnetic contribution to free energies. A central property in the method is the magnon density of states at finite temperatures, and we have compared several different implementations for obtaining it. The method has no restrictions regarding chemical and magnetic order of the considered materials. This is demonstrated by applying the method to elemental ferromagnetic systems, including Fe and Ni, as well as Fe-Co random alloys and the ferrimagnetic system GdFe3.

Proper time regularization and the QCD chiral phase transition

PubMed Central

Cui, Zhu-Fang; Zhang, Jin-Li; Zong, Hong-Shi

2017-01-01

We study the QCD chiral phase transition at finite temperature and finite quark chemical potential within the two flavor Nambu–Jona-Lasinio (NJL) model, where a generalization of the proper-time regularization scheme is motivated and implemented. We find that in the chiral limit the whole transition line in the phase diagram is of second order, whereas for finite quark masses a crossover is observed. Moreover, if we take into account the influence of quark condensate to the coupling strength (which also provides a possible way of how the effective coupling varies with temperature and quark chemical potential), it is found that a CEP may appear. These findings differ substantially from other NJL results which use alternative regularization schemes, some explanation and discussion are given at the end. This indicates that the regularization scheme can have a dramatic impact on the study of the QCD phase transition within the NJL model. PMID:28401889

Robust non-fragile finite-frequency H∞ static output-feedback control for active suspension systems

NASA Astrophysics Data System (ADS)

Wang, Gang; Chen, Changzheng; Yu, Shenbo

2017-07-01

This paper deals with the problem of non-fragile H∞ static output-feedback control of vehicle active suspension systems with finite-frequency constraint. The control objective is to improve ride comfort within the given frequency range and ensure the hard constraints in the time-domain. Moreover, in order to enhance the robustness of the controller, the control gain perturbation is also considered in controller synthesis. Firstly, a new non-fragile H∞ finite-frequency control condition is established by using generalized Kalman-Yakubovich-Popov (GKYP) lemma. Secondly, the static output-feedback control gain is directly derived by using a non-iteration algorithm. Different from the existing iteration LMI results, the static output-feedback design is simple and less conservative. Finally, the proposed control algorithm is applied to a quarter-car active suspension model with actuator dynamics, numerical results are made to show the effectiveness and merits of the proposed method.

Fast calculation of the sensitivity matrix in magnetic induction tomography by tetrahedral edge finite elements and the reciprocity theorem.

PubMed

Hollaus, K; Magele, C; Merwa, R; Scharfetter, H

2004-02-01

Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed.

A 2D Daubechies finite wavelet domain method for transient wave response analysis in shear deformable laminated composite plates

NASA Astrophysics Data System (ADS)

Nastos, C. V.; Theodosiou, T. C.; Rekatsinas, C. S.; Saravanos, D. A.

2018-03-01

An efficient numerical method is developed for the simulation of dynamic response and the prediction of the wave propagation in composite plate structures. The method is termed finite wavelet domain method and takes advantage of the outstanding properties of compactly supported 2D Daubechies wavelet scaling functions for the spatial interpolation of displacements in a finite domain of a plate structure. The development of the 2D wavelet element, based on the first order shear deformation laminated plate theory is described and equivalent stiffness, mass matrices and force vectors are calculated and synthesized in the wavelet domain. The transient response is predicted using the explicit central difference time integration scheme. Numerical results for the simulation of wave propagation in isotropic, quasi-isotropic and cross-ply laminated plates are presented and demonstrate the high spatial convergence and problem size reduction obtained by the present method.

On the superconvergence of Galerkin methods for hyperbolic IBVP

NASA Technical Reports Server (NTRS)

Gottlieb, David; Gustafsson, Bertil; Olsson, Pelle; Strand, BO

1993-01-01

Finite element Galerkin methods for periodic first order hyperbolic equations exhibit superconvergence on uniform grids at the nodes, i.e., there is an error estimate 0(h(sup 2r)) instead of the expected approximation order 0(h(sup r)). It will be shown that no matter how the approximating subspace S(sup h) is chosen, the superconvergence property is lost if there are characteristics leaving the domain. The implications of this result when constructing compact implicit difference schemes is also discussed.

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Halem, Milton (Technical Monitor)

2000-01-01

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

Hybrid High-Order methods for finite deformations of hyperelastic materials

NASA Astrophysics Data System (ADS)

Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas

2018-01-01

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order k≥1 on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of a broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order k and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of the two HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. The two HHO methods exhibit robust behavior in the quasi-incompressible regime.

A Spectral Finite Element Approach to Modeling Soft Solids Excited with High-Frequency Harmonic Loads

PubMed Central

Brigham, John C.; Aquino, Wilkins; Aguilo, Miguel A.; Diamessis, Peter J.

2010-01-01

An approach for efficient and accurate finite element analysis of harmonically excited soft solids using high-order spectral finite elements is presented and evaluated. The Helmholtz-type equations used to model such systems suffer from additional numerical error known as pollution when excitation frequency becomes high relative to stiffness (i.e. high wave number), which is the case, for example, for soft tissues subject to ultrasound excitations. The use of high-order polynomial elements allows for a reduction in this pollution error, but requires additional consideration to counteract Runge's phenomenon and/or poor linear system conditioning, which has led to the use of spectral element approaches. This work examines in detail the computational benefits and practical applicability of high-order spectral elements for such problems. The spectral elements examined are tensor product elements (i.e. quad or brick elements) of high-order Lagrangian polynomials with non-uniformly distributed Gauss-Lobatto-Legendre nodal points. A shear plane wave example is presented to show the dependence of the accuracy and computational expense of high-order elements on wave number. Then, a convergence study for a viscoelastic acoustic-structure interaction finite element model of an actual ultrasound driven vibroacoustic experiment is shown. The number of degrees of freedom required for a given accuracy level was found to consistently decrease with increasing element order. However, the computationally optimal element order was found to strongly depend on the wave number. PMID:21461402

Lamb shift and fine structure at n =2 in a hydrogenlike muonic atom with the nuclear spin I =0

NASA Astrophysics Data System (ADS)

Korzinin, Evgeny Yu.; Shelyuto, Valery A.; Ivanov, Vladimir G.; Karshenboim, Savely G.

2018-01-01

The paper is devoted to the Lamb shift and fine structure in a hydrogenlike muonic atom with a spinless nucleus up to the order α5m with all the recoil corrections included. Enhanced contributions of a higher order are also considered. We present the results on the pure QED contribution and on the finite-nuclear-size contribution, proportional to RN2, with the higher-order corrections included. We also consider the consistency of the pure QED theory and the evaluation of the nuclear-structure effects. Most of the QED theory is the same as the theory for the case of the nuclear spin 1/2. Additional nuclear-spin-dependent terms are considered in detail. The issue of the difference for the theories with a spinor nucleus and a scalar one is discussed for the recoil contributions in the order (Zα ) 4m ,α (Zα ) 4m , and (Zα ) 5m . The numerical results are presented for the muonic atoms with two lightest scalar nuclei, helium-4 and beryllium-10. We compare the theory of those muonic atoms with theory for the muonic hydrogen. Some higher-order finite-nuclear-size corrections for the Lamb shift in muonic hydrogen are revisited.

Finite element stress, vibration, and buckling analysis of laminated beams with the use of refined elements

NASA Astrophysics Data System (ADS)

Borovkov, Alexei I.; Avdeev, Ilya V.; Artemyev, A.

1999-05-01

In present work, the stress, vibration and buckling finite element analysis of laminated beams is performed. Review of the equivalent single-layer (ESL) laminate theories is done. Finite element algorithms and procedures integrated into the original FEA program system and based on the classical laminated plate theory (CLPT), first-order shear deformation theory (FSDT), third-order theory of Reddy (TSDT-R) and third- order theory of Kant (TSDT-K) with the use of the Lanczos method for solving of the eigenproblem are developed. Several numerical tests and examples of bending, free vibration and buckling of multilayered and sandwich beams with various material, geometry properties and boundary conditions are solved. New effective higher-order hierarchical element for the accurate calculation of transverse shear stress is proposed. The comparative analysis of results obtained by the considered models and solutions of 2D problems of the heterogeneous anisotropic elasticity is fulfilled.

A projection hybrid high order finite volume/finite element method for incompressible turbulent flows

NASA Astrophysics Data System (ADS)

Busto, S.; Ferrín, J. L.; Toro, E. F.; Vázquez-Cendón, M. E.

2018-01-01

In this paper the projection hybrid FV/FE method presented in [1] is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the k-ε model. Regarding the transport diffusion stage new schemes of high order of accuracy are developed. The CVC Kolgan-type scheme and ADER methodology are extended to 3D. The latter is modified in order to profit from the dual mesh employed by the projection algorithm and the derivatives involved in the diffusion term are discretized using a Galerkin approach. The accuracy and stability analysis of the new method are carried out for the advection-diffusion-reaction equation. Within the projection stage the pressure correction is computed by a piecewise linear finite element method. Numerical results are presented, aimed at verifying the formal order of accuracy of the scheme and to assess the performance of the method on several realistic test problems.

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

NASA Astrophysics Data System (ADS)

Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

2018-06-01

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

User's manual of fd2: A software package for modeling seismological problems with 2-dimensional linear finite-difference method. Special report, 1 May-15 July 1993

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jih, R.S.

1993-07-15

Fd2 is a software package developed at Teledyne Geotech Alexandria Laboratories (TGAL) during the past several years for generating synthetic seismograms and displaying the wavefields. This package consists of primarily a 2-dimensional 2nd-order explicit linear finite-difference (LFD) code. LFD method has the advantage that the solution contains all conversions and all orders of multiple scattering. It permits examinations of fairly general models with arbitrary complex variations in material properties and free-surface geometry. Furthermore, it does not require many assumptions commonly invoked in other theoretical approaches. The basic limitations to the LFD method or the finite-element method are the computational costmore » and memory requirements. These constrain the size of the grid and the number of time steps that can be calculated over a reasonable time frame. Our LFD code has a distinguishable feature in that it allows the inclusion o topographical free surface. This is particularly useful in modeling nuclear explosions buried in mountains. In this topical report, sample scripts are presented to illustrate the usage of fd2 and several supporting routines for plotting out the synthetics, generating 2-dimensional media, as well as the graphic visualization of wavefields. The algorithms for handling the boundary conditions of polygonal topography are reviewed in detail. Thus this topical report serves as both a programmer's guide and the user's manual.« less

A third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

Finite mixture modeling for vehicle crash data with application to hotspot identification.

PubMed

Park, Byung-Jung; Lord, Dominique; Lee, Chungwon

2014-10-01

The application of finite mixture regression models has recently gained an interest from highway safety researchers because of its considerable potential for addressing unobserved heterogeneity. Finite mixture models assume that the observations of a sample arise from two or more unobserved components with unknown proportions. Both fixed and varying weight parameter models have been shown to be useful for explaining the heterogeneity and the nature of the dispersion in crash data. Given the superior performance of the finite mixture model, this study, using observed and simulated data, investigated the relative performance of the finite mixture model and the traditional negative binomial (NB) model in terms of hotspot identification. For the observed data, rural multilane segment crash data for divided highways in California and Texas were used. The results showed that the difference measured by the percentage deviation in ranking orders was relatively small for this dataset. Nevertheless, the ranking results from the finite mixture model were considered more reliable than the NB model because of the better model specification. This finding was also supported by the simulation study which produced a high number of false positives and negatives when a mis-specified model was used for hotspot identification. Regarding an optimal threshold value for identifying hotspots, another simulation analysis indicated that there is a discrepancy between false discovery (increasing) and false negative rates (decreasing). Since the costs associated with false positives and false negatives are different, it is suggested that the selected optimal threshold value should be decided by considering the trade-offs between these two costs so that unnecessary expenses are minimized. Copyright © 2014 Elsevier Ltd. All rights reserved.

Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations

USGS Publications Warehouse

Walters, R.A.; Carey, G.F.

1983-01-01

The origin and nature of spurious oscillation modes that appear in mixed finite element methods are examined. In particular, the shallow water equations are considered and a modal analysis for the one-dimensional problem is developed. From the resulting dispersion relations we find that the spurious modes in elevation are associated with zero frequency and large wave number (wavelengths of the order of the nodal spacing) and consequently are zero-velocity modes. The spurious modal behavior is the result of the finite spatial discretization. By means of an artificial compressibility and limiting argument we are able to resolve the similar problem for the Navier-Stokes equations. The relationship of this simpler analysis to alternative consistency arguments is explained. This modal approach provides an explanation of the phenomenon in question and permits us to deduce the cause of the very complex behavior of spurious modes observed in numerical experiments with the shallow water equations and Navier-Stokes equations. Furthermore, this analysis is not limited to finite element formulations, but is also applicable to finite difference formulations. ?? 1983.

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

PubMed

Xia, Guohua; Lin, Ching-Long

2008-04-01

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

A method for reducing the order of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Masri, S. F.; Miller, R. K.; Sassi, H.; Caughey, T. K.

1984-06-01

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.

Asymmetric finite size of ions and orientational ordering of water in electric double layer theory within lattice model.

PubMed

Gongadze, Ekaterina; Kralj-Iglic, Veronika; Iglic, Ales

2018-06-25

In the present short communication, a brief historical survey of the mean-field theoretical description of electric double layer (EDL) is presented. A special attention is devoted to asymmetric finite size of ions and orientational ordering of water dipoles. A model of Wicke and Eigen, who were first to explicitly derive the ion distribution functions for finite size of ions, is discussed. Arguments are given in favour of changing the recently adopted name of the mean-field EDL model for finite size of ions from Bikerman model to Bikerman-Wicke-Eigen model. Theoretically predicted asymmetric and symmetric camel-like shape of the voltage dependence of the differential capacitance is also discussed. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Improving a complex finite-difference ground water flow model through the use of an analytic element screening model

USGS Publications Warehouse

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

Finite Element Barotropic Model for the Indian and Western Pacific OceanBasin: Tidal Model Data Comparisons and Sensitivities

DTIC Science & Technology

2018-01-11

From - To) 01/11/2018 Final Technical Report June 01 2016 - Dec 30 2017 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Finite - Element Barotropic Model...grid finite - element barotropic fully hydrodynamic model in order to understand the shallow-water dynamics of the Indian Ocean and Western Pacific Ocean...dissipative dissipative processes are explored. 15. SUBJECTTERMS finite - element , unstructured grid, barotropic tides, bathymetry, internal tide

Fractional finite Fourier transform.

PubMed

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

On the Stability of Jump-Linear Systems Driven by Finite-State Machines with Markovian Inputs

NASA Technical Reports Server (NTRS)

Patilkulkarni, Sudarshan; Herencia-Zapana, Heber; Gray, W. Steven; Gonzalez, Oscar R.

2004-01-01

This paper presents two mean-square stability tests for a jump-linear system driven by a finite-state machine with a first-order Markovian input process. The first test is based on conventional Markov jump-linear theory and avoids the use of any higher-order statistics. The second test is developed directly using the higher-order statistics of the machine s output process. The two approaches are illustrated with a simple model for a recoverable computer control system.

Turbine Engine Research Center (TERC) Data System Enhancement and Test Article Evaluation. Delivery Order 0002: TERC Aeromechanical Characterization

DTIC Science & Technology

2005-06-01

test, the entire turbulence model was changed from standard k- epsilon to Spalart- Allmaras. Using these different tools of turbulence models, a few...this research, leaving only pre-existing finite element models to be used. At some point a NASTRAN model was developed for vibrations analysis but

PRZM-2, A MODEL FOR PREDICTING PESTICIDE FATE IN THE CROP ROOT AND UNSATURATED SOIL ZONES: USERS MANUAL FOR RELEASE 2.0

EPA Science Inventory

PRZM-2 links two subordinate models--PRZM and VADOFT--in order to predict pesticide transport and transformation down through the crop root and unsaturated zones. RZM is a one-dimensional, finite difference model that accounts for pesticide fate in the crop root zone. his release...

High Order Well-balanced WENO Scheme for the Gas Dynamics Equations under Gravitational Fields

DTIC Science & Technology

2011-11-12

there exists the hydrostatic balance where the flux produced by the pressure is canceled by the gravitational source term. Many astro - physical...approximation to W (x) to obtain an approximation to W ′(xi) = fx (U(xi, yj)). See again [7, 15] for more details of finite difference WENO schemes in

Fourth-order partial differential equation noise removal on welding images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Halim, Suhaila Abd; Ibrahim, Arsmah; Sulong, Tuan Nurul Norazura Tuan

2015-10-22

Partial differential equation (PDE) has become one of the important topics in mathematics and is widely used in various fields. It can be used for image denoising in the image analysis field. In this paper, a fourth-order PDE is discussed and implemented as a denoising method on digital images. The fourth-order PDE is solved computationally using finite difference approach and then implemented on a set of digital radiographic images with welding defects. The performance of the discretized model is evaluated using Peak Signal to Noise Ratio (PSNR). Simulation is carried out on the discretized model on different level of Gaussianmore » noise in order to get the maximum PSNR value. The convergence criteria chosen to determine the number of iterations required is measured based on the highest PSNR value. Results obtained show that the fourth-order PDE model produced promising results as an image denoising tool compared with median filter.« less

Targeted ENO schemes with tailored resolution property for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-11-01

In this paper, we extend the range of targeted ENO (TENO) schemes (Fu et al. (2016) [18]) by proposing an eighth-order TENO8 scheme. A general formulation to construct the high-order undivided difference τK within the weighting strategy is proposed. With the underlying scale-separation strategy, sixth-order accuracy for τK in the smooth solution regions is designed for good performance and robustness. Furthermore, a unified framework to optimize independently the dispersion and dissipation properties of high-order finite-difference schemes is proposed. The new framework enables tailoring of dispersion and dissipation as function of wavenumber. The optimal linear scheme has minimum dispersion error and a dissipation error that satisfies a dispersion-dissipation relation. Employing the optimal linear scheme, a sixth-order TENO8-opt scheme is constructed. A set of benchmark cases involving strong discontinuities and broadband fluctuations is computed to demonstrate the high-resolution properties of the new schemes.

Subleading soft graviton theorem for loop amplitudes

NASA Astrophysics Data System (ADS)

Sen, Ashoke

2017-11-01

Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.

ACCURATE SOLUTION AND GRADIENT COMPUTATION FOR ELLIPTIC INTERFACE PROBLEMS WITH VARIABLE COEFFICIENTS

PubMed Central

LI, ZHILIN; JI, HAIFENG; CHEN, XIAOHONG

2016-01-01

A new augmented method is proposed for elliptic interface problems with a piecewise variable coefficient that has a finite jump across a smooth interface. The main motivation is not only to get a second order accurate solution but also a second order accurate gradient from each side of the interface. The key of the new method is to introduce the jump in the normal derivative of the solution as an augmented variable and re-write the interface problem as a new PDE that consists of a leading Laplacian operator plus lower order derivative terms near the interface. In this way, the leading second order derivatives jump relations are independent of the jump in the coefficient that appears only in the lower order terms after the scaling. An upwind type discretization is used for the finite difference discretization at the irregular grid points near or on the interface so that the resulting coefficient matrix is an M-matrix. A multi-grid solver is used to solve the linear system of equations and the GMRES iterative method is used to solve the augmented variable. Second order convergence for the solution and the gradient from each side of the interface has also been proved in this paper. Numerical examples for general elliptic interface problems have confirmed the theoretical analysis and efficiency of the new method. PMID:28983130

Stability and Drag Reduction in a Boundary Layer with Microbubbles.

DTIC Science & Technology

1988-02-01

order accurate. .’ Since the numerical methods are not the object of this % dissertation, we decline from including the finite difference equations...previous appendix must be the special case of zero pressure gradient. Some entries of the matrices of the block tridiagonal system will be different ...of the wall mean velocity gradient was observed to be associated with the migration of the bubbles away from the boundary layer. The time scale of the

Direct numerical simulation of transitional and turbulent flow over a heated flat plate using finite-difference schemes

NASA Technical Reports Server (NTRS)

Madavan, Nateri K.

1995-01-01

This report deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a heated flat plate in the presence of relatively high freestream turbulence was performed. The geometry and flow conditions were chosen to match earlier experiments. The development of the momentum and thermal boundary layers was documented. Velocity and temperature profiles, as well as distributions of skin friction, surface heat transfer rate, Reynolds shear stress, and turbulent heat flux, were shown to compare well with experiment. The results indicate that the essential features of the transition process have been captured. The numerical method used here can be applied to complex geometries in a straightforward manner.

Full numerical simulation of coflowing, axisymmetric jet diffusion flames

NASA Technical Reports Server (NTRS)

Mahalingam, S.; Cantwell, B. J.; Ferziger, J. H.

1990-01-01

The near field of a non-premixed flame in a low speed, coflowing axisymmetric jet is investigated numerically using full simulation. The time-dependent governing equations are solved by a second-order, explicit finite difference scheme and a single-step, finite rate model is used to represent the chemistry. Steady laminar flame results show the correct dependence of flame height on Peclet number and reaction zone thickness on Damkoehler number. Forced simulations reveal a large difference in the instantaneous structure of scalar dissipation fields between nonbuoyant and buoyant cases. In the former, the scalar dissipation marks intense reaction zones, supporting the flamelet concept; however, results suggest that flamelet modeling assumptions need to be reexamined. In the latter, this correspondence breaks down, suggesting that modifications to the flamelet modeling approach are needed in buoyant turbulent diffusion flames.

High surface plasmon resonance sensitivity enabled by optical disks.

PubMed

Dou, Xuan; Phillips, Blayne M; Chung, Pei-Yu; Jiang, Peng

2012-09-01

We report a systematic, experimental, and theoretical investigation on the surface plasmon resonance (SPR) sensing using optical disks with different track pitches, including Blu-ray disk (BD), digital versatile disk (DVD), and compact disk (CD). Optical reflection measurements indicate that CD and DVD exhibit much higher SPR sensitivity than BD. Both experiments and finite-difference time-domain simulations reveal that the SPR sensitivity is significantly affected by the diffraction order of the SPR peaks and higher diffraction order results in lower sensitivity. Numerical simulations also show that very high sensitivity (∼1600  nm per refractive index unit) is achievable by CDs.

Technical report series on global modeling and data assimilation. Volume 5: Documentation of the AIRES/GEOS dynamical core, version 2

NASA Technical Reports Server (NTRS)

Suarez, Max J. (Editor); Takacs, Lawrence L.

1995-01-01

A detailed description of the numerical formulation of Version 2 of the ARIES/GEOS 'dynamical core' is presented. This code is a nearly 'plug-compatible' dynamics for use in atmospheric general circulation models (GCMs). It is a finite difference model on a staggered latitude-longitude C-grid. It uses second-order differences for all terms except the advection of vorticity by the rotation part of the flow, which is done at fourth-order accuracy. This dynamical core is currently being used in the climate (ARIES) and data assimilation (GEOS) GCMs at Goddard.

Wavelet-based adaptation methodology combined with finite difference WENO to solve ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Do, Seongju; Li, Haojun; Kang, Myungjoo

2017-06-01

In this paper, we present an accurate and efficient wavelet-based adaptive weighted essentially non-oscillatory (WENO) scheme for hydrodynamics and ideal magnetohydrodynamics (MHD) equations arising from the hyperbolic conservation systems. The proposed method works with the finite difference weighted essentially non-oscillatory (FD-WENO) method in space and the third order total variation diminishing (TVD) Runge-Kutta (RK) method in time. The philosophy of this work is to use the lifted interpolating wavelets as not only detector for singularities but also interpolator. Especially, flexible interpolations can be performed by an inverse wavelet transformation. When the divergence cleaning method introducing auxiliary scalar field ψ is applied to the base numerical schemes for imposing divergence-free condition to the magnetic field in a MHD equation, the approximations to derivatives of ψ require the neighboring points. Moreover, the fifth order WENO interpolation requires large stencil to reconstruct high order polynomial. In such cases, an efficient interpolation method is necessary. The adaptive spatial differentiation method is considered as well as the adaptation of grid resolutions. In order to avoid the heavy computation of FD-WENO, in the smooth regions fixed stencil approximation without computing the non-linear WENO weights is used, and the characteristic decomposition method is replaced by a component-wise approach. Numerical results demonstrate that with the adaptive method we are able to resolve the solutions that agree well with the solution of the corresponding fine grid.

Distributed finite-time trajectory tracking control for multiple nonholonomic mobile robots with uncertainties and external disturbances

NASA Astrophysics Data System (ADS)

Ou, Meiying; Sun, Haibin; Gu, Shengwei; Zhang, Yangyi

2017-11-01

This paper investigates the distributed finite-time trajectory tracking control for a group of nonholonomic mobile robots with time-varying unknown parameters and external disturbances. At first, the tracking error system is derived for each mobile robot with the aid of a global invertible transformation, which consists of two subsystems, one is a first-order subsystem and another is a second-order subsystem. Then, the two subsystems are studied respectively, and finite-time disturbance observers are proposed for each robot to estimate the external disturbances. Meanwhile, distributed finite-time tracking controllers are developed for each mobile robot such that all states of each robot can reach the desired value in finite time, where the desired reference value is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers, and the followers are assumed to have only local interaction. The effectiveness of the theoretical results is finally illustrated by numerical simulations.

Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays.

PubMed

Peng, Xiao; Wu, Huaiqin; Song, Ka; Shi, Jiaxin

2017-10-01

This paper is concerned with the global Mittag-Leffler synchronization and the synchronization in finite time for fractional-order neural networks (FNNs) with discontinuous activations and time delays. Firstly, the properties with respect to Mittag-Leffler convergence and convergence in finite time, which play a critical role in the investigation of the global synchronization of FNNs, are developed, respectively. Secondly, the novel state-feedback controller, which includes time delays and discontinuous factors, is designed to realize the synchronization goal. By applying the fractional differential inclusion theory, inequality analysis technique and the proposed convergence properties, the sufficient conditions to achieve the global Mittag-Leffler synchronization and the synchronization in finite time are addressed in terms of linear matrix inequalities (LMIs). In addition, the upper bound of the setting time of the global synchronization in finite time is explicitly evaluated. Finally, two examples are given to demonstrate the validity of the proposed design method and theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

NASA Astrophysics Data System (ADS)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

A finite element beam propagation method for simulation of liquid crystal devices.

PubMed

Vanbrabant, Pieter J M; Beeckman, Jeroen; Neyts, Kristiaan; James, Richard; Fernandez, F Anibal

2009-06-22

An efficient full-vectorial finite element beam propagation method is presented that uses higher order vector elements to calculate the wide angle propagation of an optical field through inhomogeneous, anisotropic optical materials such as liquid crystals. The full dielectric permittivity tensor is considered in solving Maxwell's equations. The wide applicability of the method is illustrated with different examples: the propagation of a laser beam in a uniaxial medium, the tunability of a directional coupler based on liquid crystals and the near-field diffraction of a plane wave in a structure containing micrometer scale variations in the transverse refractive index, similar to the pixels of a spatial light modulator.

Design of an optomechanical filter based on solid/solid phoxonic crystals

NASA Astrophysics Data System (ADS)

Moradi, Pedram; Bahrami, Ali

2018-03-01

We simulate a phoxonic crystal which shows complete phononic and TM-polarized photonic bandgaps. The constituent materials are tungsten and polymethyl methacrylate, and we obtained these bandgaps with a filling factor of only 28%, which is very compatible with the fabrication method. A cavity was then defined that selects narrow passbands of optical and elastic waves. In order to maximize the quality factor, a defect rod is added in the output waveguide. The final structure filters an optical wavelength of 840 nm (with corresponding frequency of 357 THz) and an elastic frequency of 3.6703 GHz. Simulations are done by using finite element, plane wave expansion, and finite difference time domain methods.

Assessment of the performance of rigid pavement back-calculation through finite element modeling

NASA Astrophysics Data System (ADS)

Shoukry, Samir N.; William, Gergis W.; Martinelli, David R.

1999-02-01

This study focuses on examining the behavior of rigid pavement layers during the Falling Weight Deflectometer (FWD) test. Factors affecting the design of a concrete slab, such as whether the joints are doweled or undoweled and the spacing between the transverse joints, were considered in this study. Explicit finite element analysis was employed to investigate pavement layers' responses to the action of the impulse of the FWD test. Models of various dimensions were developed to satisfy the factors under consideration. The accuracy of the finite element models developed in this investigation was verified by comparing the finite element- generated deflection basin with that experimentally measured during an actual test. The results showed that the measured deflection basin can be reproduced through finite element modeling of the pavement structure. The resulting deflection basins from the use FE modeling was processed in order to backcalculate pavement layer moduli. This approach provides a method for the evaluation of the performance of existing backcalculation programs which are based on static elastic layer analysis. Based upon the previous studies conducted for the selection of software, three different backcalculation programs were chosen for the evaluation: MODULUS5.0, EVERCALC4.0, and MODCOMP3. The results indicate that ignoring the dynamic nature of the load may lead to crude results, especially during backcalculation procedures.

Higher-order nonclassicalities of finite dimensional coherent states: A comparative study

NASA Astrophysics Data System (ADS)

Alam, Nasir; Verma, Amit; Pathak, Anirban

2018-07-01

Conventional coherent states (CSs) are defined in various ways. For example, CS is defined as an infinite Poissonian expansion in Fock states, as displaced vacuum state, or as an eigenket of annihilation operator. In the infinite dimensional Hilbert space, these definitions are equivalent. However, these definitions are not equivalent for the finite dimensional systems. In this work, we present a comparative description of the lower- and higher-order nonclassical properties of the finite dimensional CSs which are also referred to as qudit CSs (QCSs). For the comparison, nonclassical properties of two types of QCSs are used: (i) nonlinear QCS produced by applying a truncated displacement operator on the vacuum and (ii) linear QCS produced by the Poissonian expansion in Fock states of the CS truncated at (d - 1)-photon Fock state. The comparison is performed using a set of nonclassicality witnesses (e.g., higher order antibunching, higher order sub-Poissonian statistics, higher order squeezing, Agarwal-Tara parameter, Klyshko's criterion) and a set of quantitative measures of nonclassicality (e.g., negativity potential, concurrence potential and anticlassicality). The higher order nonclassicality witnesses have found to reveal the existence of higher order nonclassical properties of QCS for the first time.

Finite amplitude instability of second-order fluids in plane Poiseuille flow.

NASA Technical Reports Server (NTRS)

Mcintire, L. V.; Lin, C. H.

1972-01-01

The hydrodynamic stability of plane Poiseuille flow of second-order fluids to finite amplitude disturbances is examined using the method of Stuart and Watson as extended by Reynolds and Potter. For slightly non-Newtonian fluids subcritical instabilities are predicted. No supercritical equilibrium states are expected if the entire spectrum of disturbance wavelengths is present. Possible implications with respect to the Toms phenomenon are discussed.

New Fukui, dual and hyper-dual kernels as bond reactivity descriptors.

PubMed

Franco-Pérez, Marco; Polanco-Ramírez, Carlos-A; Ayers, Paul W; Gázquez, José L; Vela, Alberto

2017-06-21

We define three new linear response indices with promising applications for bond reactivity using the mathematical framework of τ-CRT (finite temperature chemical reactivity theory). The τ-Fukui kernel is defined as the ratio between the fluctuations of the average electron density at two different points in the space and the fluctuations in the average electron number and is designed to integrate to the finite-temperature definition of the electronic Fukui function. When this kernel is condensed, it can be interpreted as a site-reactivity descriptor of the boundary region between two atoms. The τ-dual kernel corresponds to the first order response of the Fukui kernel and is designed to integrate to the finite temperature definition of the dual descriptor; it indicates the ambiphilic reactivity of a specific bond and enriches the traditional dual descriptor by allowing one to distinguish between the electron-accepting and electron-donating processes. Finally, the τ-hyper dual kernel is defined as the second-order derivative of the Fukui kernel and is proposed as a measure of the strength of ambiphilic bonding interactions. Although these quantities have never been proposed, our results for the τ-Fukui kernel and for τ-dual kernel can be derived in zero-temperature formulation of the chemical reactivity theory with, among other things, the widely-used parabolic interpolation model.

A solver for General Unilateral Polynomial Matrix Equation with Second-Order Matrices Over Prime Finite Fields

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-03-01

The paper firstly considers the problem of finding solvents for arbitrary unilateral polynomial matrix equations with second-order matrices over prime finite fields from the practical point of view: we implement the solver for this problem. The solver’s algorithm has two step: the first is finding solvents, having Jordan Normal Form (JNF), the second is finding solvents among the rest matrices. The first step reduces to the finding roots of usual polynomials over finite fields, the second is essentially exhaustive search. The first step’s algorithms essentially use the polynomial matrices theory. We estimate the practical duration of computations using our software implementation (for example that one can’t construct unilateral matrix polynomial over finite field, having any predefined number of solvents) and answer some theoretically-valued questions.

Scattering and Emission from Inhomogeneous Vegetation Canopy and Alien Target by Using Three-Dimensional Vector Radiative Transfer (3D-VRT) Equation

NASA Astrophysics Data System (ADS)

Jin, Ya-Qiu; Liang, Zichang

2005-01-01

To solve 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both the vertical z and horizontal (x,y) directions, to form very thin multi-boxes. The zero-th order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to deriving high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency and under different radiometer's resolutions from inhomogeneous scatter model such as vegetation canopy and embedded alien target are simulated and discussed.

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.

Simulations of viscous and compressible gas-gas flows using high-order finite difference schemes

NASA Astrophysics Data System (ADS)

Capuano, M.; Bogey, C.; Spelt, P. D. M.

2018-05-01

A computational method for the simulation of viscous and compressible gas-gas flows is presented. It consists in solving the Navier-Stokes equations associated with a convection equation governing the motion of the interface between two gases using high-order finite-difference schemes. A discontinuity-capturing methodology based on sensors and a spatial filter enables capturing shock waves and deformable interfaces. One-dimensional test cases are performed as validation and to justify choices in the numerical method. The results compare well with analytical solutions. Shock waves and interfaces are accurately propagated, and remain sharp. Subsequently, two-dimensional flows are considered including viscosity and thermal conductivity. In Richtmyer-Meshkov instability, generated on an air-SF6 interface, the influence of the mesh refinement on the instability shape is studied, and the temporal variations of the instability amplitude is compared with experimental data. Finally, for a plane shock wave propagating in air and impacting a cylindrical bubble filled with helium or R22, numerical Schlieren pictures obtained using different grid refinements are found to compare well with experimental shadow-photographs. The mass conservation is verified from the temporal variations of the mass of the bubble. The mean velocities of pressure waves and bubble interface are similar to those obtained experimentally.

A Systematic Methodology for Constructing High-Order Energy-Stable WENO Schemes

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2008-01-01

A third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter (AIAA 2008-2876, 2008) was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables \\energy stable" modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.

A Systematic Methodology for Constructing High-Order Energy Stable WENO Schemes

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2009-01-01

A third-order Energy Stable Weighted Essentially Non{Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter [1] was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables "energy stable" modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.

Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions

NASA Astrophysics Data System (ADS)

Gordon, Dan; Gordon, Rachel; Turkel, Eli

2015-09-01

We consider several compact high order absorbing boundary conditions (ABCs) for the Helmholtz equation in three dimensions. A technique called "the gradient method" (GM) for ABCs is also introduced and combined with the high order ABCs. GM is based on the principle of using directional derivatives in the direction of the wavefront propagation. The new ABCs are used together with the recently introduced compact sixth order finite difference scheme for variable wave numbers. Experiments on problems with known analytic solutions produced very accurate results, demonstrating the efficacy of the high order schemes, particularly when combined with GM. The new ABCs are then applied to the SEG/EAGE Salt model, showing the advantages of the new schemes.

Computer-Aided Engineering of Semiconductor Integrated Circuits

DTIC Science & Technology

1979-07-01

equation using a five point finite difference approximation. Section 4.3.6 describes the numerical techniques and iterative algorithms which are used...neighbor points. This is generally referred to as a five point finite difference scheme on a rectangular grid, as described below. The finite difference ...problems in steady state have been analyzed by the finite difference method [4. 16 ] [4.17 3 or finite element method [4. 18 3, [4. 19 3 as reported last

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

PubMed

Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

2013-09-01

Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

A study on the uniqueness of the plastic flow direction for granular assemblies of ductile particles using discrete finite-element simulations

NASA Astrophysics Data System (ADS)

Abdelmoula, Nouha; Harthong, Barthélémy; Imbault, Didier; Dorémus, Pierre

2017-12-01

The multi-particle finite element method involving assemblies of meshed particles interacting through finite-element contact conditions is adopted to study the plastic flow of a granular material with highly deformable elastic-plastic grains. In particular, it is investigated whether the flow rule postulate applies for such materials. Using a spherical stress probing method, the influence of incremental stress on plastic strain increment vectors was assessed for numerical samples compacted along two different loading paths up to different values of relative density. Results show that the numerical samples studied behave reasonably well according to an associated flow rule, except in the vicinity of the loading point where the influence of the stress increment proved to be very significant. A plausible explanation for the non-uniqueness of the direction of plastic flow is proposed, based on the idea that the resistance of the numerical sample to plastic straining can vary by an order of magnitude depending on the direction of the accumulated stress. The above-mentioned dependency of the direction of plastic flow on the direction of the stress increment was related to the difference in strength between shearing and normal stressing at the scale of contact surfaces between particles.

Numerical Modelling of Ground Penetrating Radar Antennas

NASA Astrophysics Data System (ADS)

Giannakis, Iraklis; Giannopoulos, Antonios; Pajewski, Lara

2014-05-01

Numerical methods are needed in order to solve Maxwell's equations in complicated and realistic problems. Over the years a number of numerical methods have been developed to do so. Amongst them the most popular are the finite element, finite difference implicit techniques, frequency domain solution of Helmontz equation, the method of moments, transmission line matrix method. However, the finite-difference time-domain method (FDTD) is considered to be one of the most attractive choice basically because of its simplicity, speed and accuracy. FDTD first introduced in 1966 by Kane Yee. Since then, FDTD has been established and developed to be a very rigorous and well defined numerical method for solving Maxwell's equations. The order characteristics, accuracy and limitations are rigorously and mathematically defined. This makes FDTD reliable and easy to use. Numerical modelling of Ground Penetrating Radar (GPR) is a very useful tool which can be used in order to give us insight into the scattering mechanisms and can also be used as an alternative approach to aid data interpretation. Numerical modelling has been used in a wide range of GPR applications including archeology, geophysics, forensic, landmine detection etc. In engineering, some applications of numerical modelling include the estimation of the effectiveness of GPR to detect voids in bridges, to detect metal bars in concrete, to estimate shielding effectiveness etc. The main challenges in numerical modelling of GPR for engineering applications are A) the implementation of the dielectric properties of the media (soils, concrete etc.) in a realistic way, B) the implementation of the geometry of the media (soils inhomogeneities, rough surface, vegetation, concrete features like fractures and rock fragments etc.) and C) the detailed modelling of the antenna units. The main focus of this work (which is part of the COST Action TU1208) is the accurate and realistic implementation of GPR antenna units into the FDTD model. Accurate models based on general characteristics of the commercial antennas GSSI 1.5 GHz and MALA 1.2 GHz have been already incorporated in GprMax, a free software which solves Maxwell's equation using a second order in space and time FDTD algorithm. This work presents the implementation of horn antennas with different parameters as well as ridged horn antennas into this FDTD model and their effectiveness is tested in realistic modelled situations. Accurate models of soils and concrete are used to test and compare different antenna units. Stochastic methods are used in order to realistically simulate the geometrical characteristics of the medium. Regarding the dielectric properties, Debye approximations are incorporated in order to simulate realistically the dielectric properties of the medium on the frequency range of interest.

Nonstandard and Higher-Order Finite-Difference Methods for Electromagnetics

DTIC Science & Technology

2009-10-26

Simplified Fuselage filled with 90 passengers. . . . . . . . . 135 4.4. A top view photograph of the expanded polystyrene passenger support, and the... expanded polystyrene supports. . . . . . . . . . . . . . . . . . . . . . . 140 4.10. Measured S11 (the exterior antenna) of the simplified fuselage...escape. To keep the passengers in their designated locations and upright, an expanded polystyrene support system was made. In a sheet of 1” thick

Direct numerical simulation of transition and turbulence in a spatially evolving boundary layer

NASA Technical Reports Server (NTRS)

Rai, Man M.; Moin, Parviz

1991-01-01

A high-order-accurate finite-difference approach to direct simulations of transition and turbulence in compressible flows is described. Attention is given to the high-free-stream disturbance case in which transition to turbulence occurs close to the leading edge. In effect, computation requirements are reduced. A method for numerically generating free-stream disturbances is presented.

One-dimensional simulation of temperature and moisture in atmospheric and soil boundary layers

NASA Technical Reports Server (NTRS)

Bornstein, R. D.; Santhanam, K.

1981-01-01

Meteorologists are interested in modeling the vertical flow of heat and moisture through the soil in order to better simulate the vertical and temporal variations of the atmospheric boundary layer. The one dimensional planetary boundary layer model of is modified by the addition of transport equations to be solved by a finite difference technique to predict soil moisture.

Finite-difference time-domain synthesis of infrasound propagation through an absorbing atmosphere.

PubMed

de Groot-Hedlin, C

2008-09-01

Equations applicable to finite-difference time-domain (FDTD) computation of infrasound propagation through an absorbing atmosphere are derived and examined in this paper. It is shown that over altitudes up to 160 km, and at frequencies relevant to global infrasound propagation, i.e., 0.02-5 Hz, the acoustic absorption in dB/m varies approximately as the square of the propagation frequency plus a small constant term. A second-order differential equation is presented for an atmosphere modeled as a compressible Newtonian fluid with low shear viscosity, acted on by a small external damping force. It is shown that the solution to this equation represents pressure fluctuations with the attenuation indicated above. Increased dispersion is predicted at altitudes over 100 km at infrasound frequencies. The governing propagation equation is separated into two partial differential equations that are first order in time for FDTD implementation. A numerical analysis of errors inherent to this FDTD method shows that the attenuation term imposes additional stability constraints on the FDTD algorithm. Comparison of FDTD results for models with and without attenuation shows that the predicted transmission losses for the attenuating media agree with those computed from synthesized waveforms.

Stability of streamwise vortices

NASA Technical Reports Server (NTRS)

Khorrami, M. K.; Grosch, C. E.; Ash, R. L.

1987-01-01

A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Application of a Third Order Upwind Scheme to Viscous Flow over Clean and Iced Wings

NASA Technical Reports Server (NTRS)

Bangalore, A.; Phaengsook, N.; Sankar, L. N.

1994-01-01

A 3-D compressible Navier-Stokes solver has been developed and applied to 3-D viscous flow over clean and iced wings. This method uses a third order accurate finite volume scheme with flux difference splitting to model the inviscid fluxes, and second order accurate symmetric differences to model the viscous terms. The effects of turbulence are modeled using a Kappa-epsilon model. In the vicinity of the sold walls the kappa and epsilon values are modeled using Gorski's algebraic model. Sampling results are presented for surface pressure distributions, for untapered swept clean and iced wings made of NACA 0012 airfoil sections. The leading edge of these sections is modified using a simulated ice shape. Comparisons with experimental data are given.

The Reverse Time Migration technique coupled with Interior Penalty Discontinuous Galerkin method.

NASA Astrophysics Data System (ADS)

Baldassari, C.; Barucq, H.; Calandra, H.; Denel, B.; Diaz, J.

2009-04-01

Seismic imaging is based on the seismic reflection method which produces an image of the subsurface from reflected waves recordings by using a tomography process and seismic migration is the industrial standard to improve the quality of the images. The migration process consists in replacing the recorded wavefields at their actual place by using various mathematical and numerical methods but each of them follows the same schedule, according to the pioneering idea of Claerbout: numerical propagation of the source function (propagation) and of the recorded wavefields (retropropagation) and next, construction of the image by applying an imaging condition. The retropropagation step can be realized accouting for the time reversibility of the wave equation and the resulting algorithm is currently called Reverse Time Migration (RTM). To be efficient, especially in three dimensional domain, the RTM requires the solution of the full wave equation by fast numerical methods. Finite element methods are considered as the best discretization method for solving the wave equation, even if they lead to the solution of huge systems with several millions of degrees of freedom, since they use meshes adapted to the domain topography and the boundary conditions are naturally taken into account in the variational formulation. Among the different finite element families, the spectral element one (SEM) is very interesting because it leads to a diagonal mass matrix which dramatically reduces the cost of the numerical computation. Moreover this method is very accurate since it allows the use of high order finite elements. However, SEM uses meshes of the domain made of quadrangles in 2D or hexaedra in 3D which are difficult to compute and not always suitable for complex topographies. Recently, Grote et al. applied the IPDG (Interior Penalty Discontinuous Galerkin) method to the wave equation. This approach is very interesting since it relies on meshes with triangles in 2D or tetrahedra in 3D, which allows to handle the topography of the domain very accurately. Moreover, the fact that the resulting mass matrix is block-diagonal and that IPDG is compatible with the use of high-order finite element may let us suppose that its performances are similar to the ones of the SEM. In this presentation, we study the performances of IDPG through numerical comparisons with the SEM in 1D and 2D. We compare in particular the accuracy of the solutions obtained by the two methods with various order of approximation and the computational burden of the algorithms. The conclusion is IPDG and SEM perform similarly when considering low order finite elements while IPDG outperforms SEM in case of high order finite elements. Next we illustrate the impact of IPDG on the RTM, first through a simple configuration test (two-layered medium), then through realistic industrial applications in 2D.

Second-Order Consensus in Multiagent Systems via Distributed Sliding Mode Control.

PubMed

Yu, Wenwu; Wang, He; Cheng, Fei; Yu, Xinghuo; Wen, Guanghui

2016-11-22

In this paper, the new decoupled distributed sliding-mode control (DSMC) is first proposed for second-order consensus in multiagent systems, which finally solves the fundamental unknown problem for sliding-mode control (SMC) design of coupled networked systems. A distributed full-order sliding-mode surface is designed based on the homogeneity with dilation for reaching second-order consensus in multiagent systems, under which the sliding-mode states are decoupled. Then, the SMC is applied to the decoupled sliding-mode states to reach their origin in finite time, which is the sliding-mode surface. The states of agents can first reach the designed sliding-mode surface in finite time and then move to the second-order consensus state along the surface in finite time as well. The DSMC designed in this paper can eliminate the influence of singularity problems and weaken the influence of chattering, which is still very difficult in the SMC systems. In addition, DSMC proposes a general decoupling framework for designing SMC in networked multiagent systems. Simulations are presented to verify the theoretical results in this paper.

Generation of deterministic tsunami hazard maps in the Bay of Cadiz, south-west Spain

NASA Astrophysics Data System (ADS)

Álvarez-Gómez, J. A.; Otero, L.; Olabarrieta, M.; González, M.; Carreño, E.; Baptista, M. A.; Miranda, J. M.; Medina, R.; Lima, V.

2009-04-01

The bay of Cádiz is a densely populated and industrialized area, and an important centre of tourism which multiplies its population in the summer months. This bay is situated in the Gulf of Cádiz, the south-west Atlantic margin of the Iberian Peninsula. From a tectonic point of view this area can be defined as a diffuse plate boundary, comprising the eastern edge of the Gloria and Tydeman transforms (where the deformation is mainly concentrated in these shear corridors), the Gorringe Bank, the Horseshoe Abyssal plain, the Portimao and Guadalquivir banks, and the western termination of the arcuated Gibraltar Arc. This deformation zone is the eastern edge of the Azores - Gibraltar seismic zone, being the present day boundary between the Eurasian and African plates. The motion between the plates is mainly convergent in the Gulf of Cádiz, but gradually changes to almost pure transcurrent along the Gloria Fault. The relative motion between the two plates is of the order of 4-5 mm/yr. In order to define the different tsunamigenic zones and to characterize its worst tsunamigenic source we have used seismic, structural and geological data. The numerical model used to simulate the wave propagation and coastal inundation is the C3 (Cantabria, COMCOT and Tsunami-Claw) model. C3 is a hybrid finite difference-finite volume method which balances between efficiency and accuracy. For offshore domain in deep waters the model applies an explicit finite difference scheme (FD), which is computationally fast and accurate in large grids. For near coast domains in coastal areas, it applies a finite volume scheme (VOF). It solves correctly the bore formation and the bore propagation. It is very effective solving the run-up and the run down. A set of five worst case tsunamigenic sources has been used with four different sea levels (minimum tide, most probable low tide, most probable high tide and maximum tide), in order to produce the following thematic maps with the C3 model: maximum free surface elevation, maximum water depth, maximum current speed, maximum Froude number and maximum impact forces (hydrostatic and dynamic forces). The fault rupture and sea bottom displacement has been computed by means of the Okada equations. As result, a set of more than 100 deterministic thematic maps have been created in a GIS environment incorporating geographical data and high resolution orthorectified satellite images. These thematic maps form an atlas of inundation maps that will be distributed to different government authorities and civil protection and emergency agencies. The authors gratefully acknowledge the financial support provided by the EU under the frame of the European Project TRANSFER (Tsunami Risk And Strategies For the European Region), 6th Framework Programme.

Prediction of muscle activation for an eye movement with finite element modeling.

PubMed

Karami, Abbas; Eghtesad, Mohammad; Haghpanah, Seyyed Arash

2017-10-01

In this paper, a 3D finite element (FE) modeling is employed in order to predict extraocular muscles' activation and investigate force coordination in various motions of the eye orbit. A continuum constitutive hyperelastic model is employed for material description in dynamic modeling of the extraocular muscles (EOMs). Two significant features of this model are accurate mass modeling with FE method and stimulating EOMs for motion through muscle activation parameter. In order to validate the eye model, a forward dynamics simulation of the eye motion is carried out by variation of the muscle activation. Furthermore, to realize muscle activation prediction in various eye motions, two different tracking-based inverse controllers are proposed. The performance of these two inverse controllers is investigated according to their resulted muscle force magnitude and muscle force coordination. The simulation results are compared with the available experimental data and the well-known existing neurological laws. The comparison authenticates both the validation and the prediction results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Equation of State of Structured Matter at Finite Temperature

NASA Astrophysics Data System (ADS)

Maruyama, T.; Yasutake, N.; Tatsumi, T.

We investigate the properties of nuclear matter at the first-order phase transitions such as liquid-gas phase transition and hadron-quark phase transition. As a general feature of the first-order phase transitions of matter consisting of many species of charged particles, there appears a mixed phases with geometrical structures called ``pasta'' due to the balance of the Coulomb repulsion and the surface tension between two phases [G.~D.~Ravenhall, C.~J.~Pethick and J.~R.~Wilson, Phys. Rev. Lett. 50 (1983), 2066. M.~Hashimoto, H.~Seki and M.~Yamada, Prog. Theor. Phys. 71 (1984), 320.] The equation of state (EOS) of mixed phase is different from the one obtained by a bulk application of the Gibbs conditions or by the Maxwell construction due to the effects of the non-uniform structure. We show that the charge screening and strong surface tension make the EOS close to that of the Maxwell construction. The thermal effects are elucidated as well as the above finite-size effects.

CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anninos, Peter; Lau, Cheuk; Bryant, Colton

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performedmore » separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.« less

End point of a first-order phase transition in many-flavor lattice QCD at finite temperature and density.

PubMed

Ejiri, Shinji; Yamada, Norikazu

2013-04-26

Towards the feasibility study of the electroweak baryogenesis in realistic technicolor scenario, we investigate the phase structure of (2+N(f))-flavor QCD, where the mass of two flavors is fixed to a small value and the others are heavy. For the baryogenesis, an appearance of a first-order phase transition at finite temperature is a necessary condition. Using a set of configurations of two-flavor lattice QCD and applying the reweighting method, the effective potential defined by the probability distribution function of the plaquette is calculated in the presence of additional many heavy flavors. Through the shape of the effective potential, we determine the critical mass of heavy flavors separating the first-order and crossover regions and find it to become larger with N(f). We moreover study the critical line at finite density and the first-order region is found to become wider as increasing the chemical potential. Possible applications to real (2+1)-flavor QCD are discussed.

CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

NASA Astrophysics Data System (ADS)

Anninos, Peter; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Lau, Cheuk; Nemergut, Daniel

2017-08-01

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge-Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.

Experimental study of uncentralized squeeze film dampers

NASA Technical Reports Server (NTRS)

Quinn, R. D.

1983-01-01

The vibration response of a rotor system supported by a squeeze film damper (SFD) was experimentally investigated in order to provide experimental data in support of the Rotor/Stator Interactive Finite Element theoretical development. Part of the investigation required the designing and building of a rotor/SFD system that could operate with or without end seals in order to accommodate different SFD lengths. SFD variables investigated included clearance, eccentricity mass, fluid pressure, and viscosity and temperature. The results show inlet pressure, viscosity and clearance have significant influence on the damper performance and accompanying rotor response.

Computation of Nonlinear Backscattering Using a High-Order Numerical Method

NASA Technical Reports Server (NTRS)

Fibich, G.; Ilan, B.; Tsynkov, S.

2001-01-01

The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

A fast direct solver for a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. Wayne

1992-01-01

An efficient, direct, second-order solver for the discrete solution of two-dimensional separable elliptic equations on the sphere is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wavenumber and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

High Order Filter Methods for the Non-ideal Compressible MHD Equations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, Bjoern

2003-01-01

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard divergence cleaning is not required by the present filter approach. For certain non-ideal MHD test cases, divergence free preservation of the magnetic fields has been achieved.

High-order ENO schemes applied to two- and three-dimensional compressible flow

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Erlebacher, Gordon; Zang, Thomas A.; Whitaker, David; Osher, Stanley

1991-01-01

High order essentially non-oscillatory (ENO) finite difference schemes are applied to the 2-D and 3-D compressible Euler and Navier-Stokes equations. Practical issues, such as vectorization, efficiency of coding, cost comparison with other numerical methods, and accuracy degeneracy effects, are discussed. Numerical examples are provided which are representative of computational problems of current interest in transition and turbulence physics. These require both nonoscillatory shock capturing and high resolution for detailed structures in the smooth regions and demonstrate the advantage of ENO schemes.

Divergence Free High Order Filter Methods for the Compressible MHD Equations

NASA Technical Reports Server (NTRS)

Yea, H. C.; Sjoegreen, Bjoern

2003-01-01

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard diver- gence cleaning is not required by the present filter approach. For certain MHD test cases, divergence free preservation of the magnetic fields has been achieved.

On the Definition of Surface Potentials for Finite-Difference Operators

NASA Technical Reports Server (NTRS)

Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

For a class of linear constant-coefficient finite-difference operators of the second order, we introduce the concepts similar to those of conventional single- and double-layer potentials for differential operators. The discrete potentials are defined completely independently of any notion related to the approximation of the continuous potentials on the grid. We rather use all approach based on differentiating, and then inverting the differentiation of a function with surface discontinuity of a particular kind, which is the most general way of introducing surface potentials in the theory of distributions. The resulting finite-difference "surface" potentials appear to be solutions of the corresponding continuous potentials. Primarily, this pertains to the possibility of representing a given solution to the homogeneous equation on the domain as a variety of surface potentials, with the density defined on the domain's boundary. At the same time the discrete surface potentials can be interpreted as one specific realization of the generalized potentials of Calderon's type, and consequently, their approximation properties can be studied independently in the framework of the difference potentials method by Ryaben'kii. The motivation for introducing and analyzing the discrete surface potentials was provided by the problems of active shielding and control of sound, in which the aforementioned source terms that drive the potentials are interpreted as the acoustic control sources that cancel out the unwanted noise on a predetermined region of interest.

The use of the Finite Element method for the earthquakes modelling in different geodynamic environments

NASA Astrophysics Data System (ADS)

Castaldo, Raffaele; Tizzani, Pietro

2016-04-01

Many numerical models have been developed to simulate the deformation and stress changes associated to the faulting process. This aspect is an important topic in fracture mechanism. In the proposed study, we investigate the impact of the deep fault geometry and tectonic setting on the co-seismic ground deformation pattern associated to different earthquake phenomena. We exploit the impact of the structural-geological data in Finite Element environment through an optimization procedure. In this framework, we model the failure processes in a physical mechanical scenario to evaluate the kinematics associated to the Mw 6.1 L'Aquila 2009 earthquake (Italy), the Mw 5.9 Ferrara and Mw 5.8 Mirandola 2012 earthquake (Italy) and the Mw 8.3 Gorkha 2015 earthquake (Nepal). These seismic events are representative of different tectonic scenario: the normal, the reverse and thrust faulting processes, respectively. In order to simulate the kinematic of the analyzed natural phenomena, we assume, under the plane stress approximation (is defined to be a state of stress in which the normal stress, sz, and the shear stress sxz and syz, directed perpendicular to x-y plane are assumed to be zero), the linear elastic behavior of the involved media. The performed finite element procedure consist of through two stages: (i) compacting under the weight of the rock successions (gravity loading), the deformation model reaches a stable equilibrium; (ii) the co-seismic stage simulates, through a distributed slip along the active fault, the released stresses. To constrain the models solution, we exploit the DInSAR deformation velocity maps retrieved by satellite data acquired by old and new generation sensors, as ENVISAT, RADARSAT-2 and SENTINEL 1A, encompassing the studied earthquakes. More specifically, we first generate 2D several forward mechanical models, then, we compare these with the recorded ground deformation fields, in order to select the best boundaries setting and parameters. Finally, the performed multi-parametric finite element models allow us to verify the effect of the crustal structures on the ground deformation and evaluate the stress-drop associated to the studied earthquakes on the surrounding structures.

Subresolution Displacements in Finite Difference Simulations of Ultrasound Propagation and Imaging.

PubMed

Pinton, Gianmarco F

2017-03-01

Time domain finite difference simulations are used extensively to simulate wave propagation. They approximate the wave field on a discrete domain with a grid spacing that is typically on the order of a tenth of a wavelength. The smallest displacements that can be modeled by this type of simulation are thus limited to discrete values that are integer multiples of the grid spacing. This paper presents a method to represent continuous and subresolution displacements by varying the impedance of individual elements in a multielement scatterer. It is demonstrated that this method removes the limitations imposed by the discrete grid spacing by generating a continuum of displacements as measured by the backscattered signal. The method is first validated on an ideal perfect correlation case with a single scatterer. It is subsequently applied to a more complex case with a field of scatterers that model an acoustic radiation force-induced displacement used in ultrasound elasticity imaging. A custom finite difference simulation tool is used to simulate propagation from ultrasound imaging pulses in the scatterer field. These simulated transmit-receive events are then beamformed into images, which are tracked with a correlation-based algorithm to determine the displacement. A linear predictive model is developed to analytically describe the relationship between element impedance and backscattered phase shift. The error between model and simulation is λ/ 1364 , where λ is the acoustical wavelength. An iterative method is also presented that reduces the simulation error to λ/ 5556 over one iteration. The proposed technique therefore offers a computationally efficient method to model continuous subresolution displacements of a scattering medium in ultrasound imaging. This method has applications that include ultrasound elastography, blood flow, and motion tracking. This method also extends generally to finite difference simulations of wave propagation, such as electromagnetic or seismic waves.

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

DOE PAGES

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

2015-09-04

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. 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 themore » 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 discretization 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 solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble.

PubMed

Gross, Markus; Gambassi, Andrea; Dietrich, S

2017-08-01

The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ε=4-d, where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ε and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble

NASA Astrophysics Data System (ADS)

Gross, Markus; Gambassi, Andrea; Dietrich, S.

2017-08-01

The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ɛ =4 -d , where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ɛ and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.