Finite-volume scheme for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: bramiozo@gmail.com [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands)
2016-02-01
In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.
Sman, van der R.G.M.
2006-01-01
In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the
International Nuclear Information System (INIS)
Botchorishvili, Ramaz; Pironneau, Olivier
2003-01-01
We develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms. The schemes are of equilibrium type, hence with uniform bounds on approximate solutions, valid in cell entropy inequalities and exact for some equilibrium states. Convergence is investigated in the framework of kinetic schemes. Numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms. Equilibrium type schemes produce accurate results even on test problems for which the standard approach fails. For some numerical tests they exhibit exponential type convergence rate. In two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 5000 2 grid points
A hybrid finite-volume and finite difference scheme for depth-integrated non-hydrostatic model
Yin, Jing; Sun, Jia-wen; Wang, Xing-gang; Yu, Yong-hai; Sun, Zhao-chen
2017-06-01
A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.
Saad, Bilal Mohammed; Saad, Mazen Naufal B M
2014-01-01
We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.
Saad, Bilal Mohammed
2014-06-28
We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.
An assessment of unstructured grid finite volume schemes for cold gas hypersonic flow calculations
Directory of Open Access Journals (Sweden)
João Luiz F. Azevedo
2009-06-01
Full Text Available A comparison of five different spatial discretization schemes is performed considering a typical high speed flow application. Flowfields are simulated using the 2-D Euler equations, discretized in a cell-centered finite volume procedure on unstructured triangular meshes. The algorithms studied include a central difference-type scheme, and 1st- and 2nd-order van Leer and Liou flux-vector splitting schemes. These methods are implemented in an efficient, edge-based, unstructured grid procedure which allows for adaptive mesh refinement based on flow property gradients. Details of the unstructured grid implementation of the methods are presented together with a discussion of the data structure and of the adaptive refinement strategy. The application of interest is the cold gas flow through a typical hypersonic inlet. Results for different entrance Mach numbers and mesh topologies are discussed in order to assess the comparative performance of the various spatial discretization schemes.
CSIR Research Space (South Africa)
Suliman, Ridhwaan
2012-07-01
Full Text Available -linear deformations are accounted for. As will be demonstrated, the finite volume approach exhibits similar disad- vantages to the linear Q4 finite element formulation when undergoing bending. An enhanced finite volume approach is discussed and compared with finite...
Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping
Smith, Timothy; Pantano, Carlos
2017-11-01
We present a new method to enforce field bounds in high-order Legendre-WENO finite volume schemes. The strategy consists of reconstructing each field through an intermediate mapping, which by design satisfies realizability constraints. Determination of the coefficients of the polynomial reconstruction involves nonlinear equations that are solved using Newton's method. The selection between the original or mapped reconstruction is implemented dynamically to minimize computational cost. The method has also been generalized to fields that exhibit interdependencies, requiring multi-dimensional mappings. Further, the method does not depend on the existence of a numerical flux function. We will discuss details of the proposed scheme and show results for systems in conservation and non-conservation form. This work was funded by the NSF under Grant DMS 1318161.
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Ismagilov, Timur Z., E-mail: ismagilov@academ.org
2015-02-01
This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.
Botti, Lorenzo; Paliwal, Nikhil; Conti, Pierangelo; Antiga, Luca; Meng, Hui
2018-06-01
Image-based computational fluid dynamics (CFD) has shown potential to aid in the clinical management of intracranial aneurysms (IAs) but its adoption in the clinical practice has been missing, partially due to lack of accuracy assessment and sensitivity analysis. To numerically solve the flow-governing equations CFD solvers generally rely on two spatial discretization schemes: Finite Volume (FV) and Finite Element (FE). Since increasingly accurate numerical solutions are obtained by different means, accuracies and computational costs of FV and FE formulations cannot be compared directly. To this end, in this study we benchmark two representative CFD solvers in simulating flow in a patient-specific IA model: (1) ANSYS Fluent, a commercial FV-based solver and (2) VMTKLab multidGetto, a discontinuous Galerkin (dG) FE-based solver. The FV solver's accuracy is improved by increasing the spatial mesh resolution (134k, 1.1m, 8.6m and 68.5m tetrahedral element meshes). The dGFE solver accuracy is increased by increasing the degree of polynomials (first, second, third and fourth degree) on the base 134k tetrahedral element mesh. Solutions from best FV and dGFE approximations are used as baseline for error quantification. On average, velocity errors for second-best approximations are approximately 1cm/s for a [0,125]cm/s velocity magnitude field. Results show that high-order dGFE provide better accuracy per degree of freedom but worse accuracy per Jacobian non-zero entry as compared to FV. Cross-comparison of velocity errors demonstrates asymptotic convergence of both solvers to the same numerical solution. Nevertheless, the discrepancy between under-resolved velocity fields suggests that mesh independence is reached following different paths. This article is protected by copyright. All rights reserved.
A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension
Energy Technology Data Exchange (ETDEWEB)
Garrick, Daniel P. [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States); Owkes, Mark [Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, MT (United States); Regele, Jonathan D., E-mail: jregele@iastate.edu [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States)
2017-06-15
Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.
A computationally efficient 3D finite-volume scheme for violent liquid–gas sloshing
CSIR Research Space (South Africa)
Oxtoby, Oliver F
2015-10-01
Full Text Available We describe a semi-implicit volume-of-fluid free-surface-modelling methodology for flow problems involving violent free-surface motion. For efficient computation, a hybrid-unstructured edge-based vertex-centred finite volume discretisation...
Traoré, Philippe; Ahipo, Yves Marcel; Louste, Christophe
2009-08-01
In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla [P.K. Khosla, S.G. Rubin, A diagonally dominant second-order accurate implicit scheme, Computers and Fluids 2 (1974) 207-209] and known as deferred correction, has been intensively utilized by Muzaferija [S. Muzaferija, Adaptative finite volume method for flow prediction using unstructured meshes and multigrid approach, Ph.D. Thesis, Imperial College, 1994] and later Fergizer and Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002] to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of the normal gradient, our scheme gives accurate solutions in geometries where the basic idea of Muzaferija fails. First the performances of both schemes are compared for a Poisson problem solved in quadrangular domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are not degraded even on extremely skewed mesh. Next, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid as well as on an anisotropically distorted one. Finally we compare the solution obtained for quadrilateral control volumes to the ones obtained with a finite element code and with an unstructured version of our finite volume code for triangular control volumes. No differences can be observed between the different solutions, which demonstrates the effectiveness of our approach.
Energy Technology Data Exchange (ETDEWEB)
Saas, L.
2004-05-01
This Thesis deals with sedimentary basin modeling whose goal is the prediction through geological times of the localizations and appraisal of hydrocarbons quantities present in the ground. Due to the natural and evolutionary decomposition of the sedimentary basin in blocks and stratigraphic layers, domain decomposition methods are requested to simulate flows of waters and of hydrocarbons in the ground. Conservations laws are used to model the flows in the ground and form coupled partial differential equations which must be discretized by finite volume method. In this report we carry out a study on finite volume methods on non-matching grids solved by domain decomposition methods. We describe a family of finite volume schemes on non-matching grids and we prove that the associated global discretized problem is well posed. Then we give an error estimate. We give two examples of finite volume schemes on non matching grids and the corresponding theoretical results (Constant scheme and Linear scheme). Then we present the resolution of the global discretized problem by a domain decomposition method using arbitrary interface conditions (for example Robin conditions). Finally we give numerical results which validate the theoretical results and study the use of finite volume methods on non-matching grids for basin modeling. (author)
Boscheri, Walter; Dumbser, Michael
2017-10-01
We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total
Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri
2018-04-01
In this paper we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.
Keslerová, Radka; Trdlička, David
2015-09-01
This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.
International Nuclear Information System (INIS)
Farhanieh, B.; Amanifard, N.; Ghorbanian, K.
2002-01-01
An unsteady two-dimensional numerical investigation was performed on the viscous flow passing through a multi-blade cascade. A Cartesian finite-volume approach was linked to Van-Leer's and Roe's flux splitting schemes to evaluate inviscid flux terms. To prevent the oscillatory behavior of numerical results and to increase the accuracy, Mon tonic Upstream Scheme for Conservation Laws was added to flux splitting schemes. The Baldwin-Lo max (B L) turbulence model was implemented to solve the turbulent case studies. Implicit solution was also provided using Lower and Upper (L U) decomposition technique to compare with explicit solutions. To validate the numerical procedure, two test cases are prepared and flow over a Na Ca 0012 airfoil was investigated and the pressure coefficients were compared to the reference data. The numerical solver was implemented to study the flow passing over a compressor cascade. The results of various combinations of splitting schemes and the Mon tonic Upstream Scheme for Conventional Laws limiter were compared with each other to find the suitable methods in cascade problems. Finally the convergence histories of implemented schemes were compared to each other to show the behavior of the solver in using various methods before implementation of them in flow instability studies
International Nuclear Information System (INIS)
Xing Yulong; Shu Chiwang
2006-01-01
Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) 206-227; J. Sci. Comput., accepted], we designed a well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which at the same time maintains genuine high order accuracy for general solutions, to a class of hyperbolic systems with separable source terms including the shallow water equations, the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. In this paper, we generalize high order finite volume WENO schemes and Runge-Kutta discontinuous Galerkin (RKDG) finite element methods to the same class of hyperbolic systems to maintain a well-balanced property. Finite volume and discontinuous Galerkin finite element schemes are more flexible than finite difference schemes to treat complicated geometry and adaptivity. However, because of a different computational framework, the maintenance of the well-balanced property requires different technical approaches. After the description of our well-balanced high order finite volume WENO and RKDG schemes, we perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions
A positive and entropy-satisfying finite volume scheme for the Baer–Nunziato model
Energy Technology Data Exchange (ETDEWEB)
Coquel, Frédéric, E-mail: frederic.coquel@cmap.polytechnique.fr [CMAP, École Polytechnique CNRS, UMR 7641, Route de Saclay, F-91128 Palaiseau cedex (France); Hérard, Jean-Marc, E-mail: jean-marc.herard@edf.fr [EDF-R& D, Département MFEE, 6 Quai Watier, F-78401 Chatou Cedex (France); Saleh, Khaled, E-mail: saleh@math.univ-lyon1.fr [Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 bd 11 novembre 1918, F-69622 Villeurbanne cedex (France)
2017-02-01
We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer–Nunziato model, namely Schwendeman–Wahle–Kapila's Godunov-type scheme and Tokareva–Toro's HLLC scheme . The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.
A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model
Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled
2017-02-01
We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Tokareva-Toro's HLLC scheme [44]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.
Balsara, Dinshaw S.; Dumbser, Michael
2015-10-01
Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on
Schwing, Alan Michael
For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable
A perturbative study of two four-quark operators in finite volume renormalization schemes
Palombi, Filippo; Sint, S
2006-01-01
Starting from the QCD Schroedinger functional (SF), we define a family of renormalization schemes for two four-quark operators, which are, in the chiral limit, protected against mixing with other operators. With the appropriate flavour assignments these operators can be interpreted as part of either the $\\Delta F=1$ or $\\Delta F=2$ effective weak Hamiltonians. In view of lattice QCD with Wilson-type quarks, we focus on the parity odd components of the operators, since these are multiplicatively renormalized both on the lattice and in continuum schemes. We consider 9 different SF schemes and relate them to commonly used continuum schemes at one-loop order of perturbation theory. In this way the two-loop anomalous dimensions in the SF schemes can be inferred. As a by-product of our calculation we also obtain the one-loop cutoff effects in the step-scaling functions of the respective renormalization constants, for both O(a) improved and unimproved Wilson quarks. Our results will be needed in a separate study of ...
Yu, Guojun
2012-10-01
In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.
Yu, Guojun; Yu, Bo; Sun, Shuyu; Tao, Wenquan
2012-01-01
In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.
International Nuclear Information System (INIS)
Ansanay-Alex, G.
2009-01-01
The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)
Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael
2018-06-01
In this work, we present a novel second-order accurate well-balanced arbitrary Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.
Boscheri, Walter; Dumbser, Michael
2014-10-01
In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with
International Nuclear Information System (INIS)
Popov, Pavel P.; Pope, Stephen B.
2014-01-01
This work addresses the issue of particle mass consistency in Large Eddy Simulation/Probability Density Function (LES/PDF) methods for turbulent reactive flows. Numerical schemes for the implicit and explicit enforcement of particle mass consistency (PMC) are introduced, and their performance is examined in a representative LES/PDF application, namely the Sandia–Sydney Bluff-Body flame HM1. A new combination of interpolation schemes for velocity and scalar fields is found to better satisfy PMC than multilinear and fourth-order Lagrangian interpolation. A second-order accurate time-stepping scheme for stochastic differential equations (SDE) is found to improve PMC relative to Euler time stepping, which is the first time that a second-order scheme is found to be beneficial, when compared to a first-order scheme, in an LES/PDF application. An explicit corrective velocity scheme for PMC enforcement is introduced, and its parameters optimized to enforce a specified PMC criterion with minimal corrective velocity magnitudes
Development and analysis of finite volume methods
International Nuclear Information System (INIS)
Omnes, P.
2010-05-01
This document is a synthesis of a set of works concerning the development and the analysis of finite volume methods used for the numerical approximation of partial differential equations (PDEs) stemming from physics. In the first part, the document deals with co-localized Godunov type schemes for the Maxwell and wave equations, with a study on the loss of precision of this scheme at low Mach number. In the second part, discrete differential operators are built on fairly general, in particular very distorted or nonconforming, bidimensional meshes. These operators are used to approach the solutions of PDEs modelling diffusion, electro and magneto-statics and electromagnetism by the discrete duality finite volume method (DDFV) on staggered meshes. The third part presents the numerical analysis and some a priori as well as a posteriori error estimations for the discretization of the Laplace equation by the DDFV scheme. The last part is devoted to the order of convergence in the L2 norm of the finite volume approximation of the solution of the Laplace equation in one dimension and on meshes with orthogonality properties in two dimensions. Necessary and sufficient conditions, relatively to the mesh geometry and to the regularity of the data, are provided that ensure the second-order convergence of the method. (author)
Directory of Open Access Journals (Sweden)
Kodwo Annan
2012-01-01
Full Text Available The efficiency of a high-flux dialyzer in terms of buffering and toxic solute removal largely depends on the ability to use convection-diffusion mechanism inside the membrane. A two-dimensional transient convection-diffusion model coupled with acid-base correction term was developed. A finite volume technique was used to discretize the model and to numerically simulate it using MATLAB software tool. We observed that small solute concentration gradients peaked and were large enough to activate solute diffusion process in the membrane. While CO2 concentration gradients diminished from their maxima and shifted toward the end of the membrane, concentration gradients peaked at the same position. Also, CO2 concentration decreased rapidly within the first 47 minutes while optimal concentration was achieved within 30 minutes of the therapy. Abnormally high diffusion fluxes were observed near the blood-membrane interface that increased diffusion driving force and enhanced the overall diffusive process. While convective flux dominated total flux during the dialysis session, there was a continuous interference between convection and diffusion fluxes that call for the need to seek minimal interference between these two mechanisms. This is critical for the effective design and operation of high-flux dialyzers.
Finite Difference Schemes as Algebraic Correspondences between Layers
Malykh, Mikhail; Sevastianov, Leonid
2018-02-01
For some differential equations, especially for Riccati equation, new finite difference schemes are suggested. These schemes define protective correspondences between the layers. Calculation using these schemes can be extended to the area beyond movable singularities of exact solution without any error accumulation.
An introduction to the UNCLE finite element scheme
International Nuclear Information System (INIS)
Enderby, J.A.
1983-01-01
UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)
A Note on Symplectic, Multisymplectic Scheme in Finite Element Method
Institute of Scientific and Technical Information of China (English)
GUO Han-Ying; JI Xiao-Mei; LI Yu-Qi; WU Ke
2001-01-01
We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case respectively. These results are in fact the intrinsic reason why the numerical experiments show that such finite element algorithms are accurate in practice.``
An introduction to the UNCLE finite element scheme
Energy Technology Data Exchange (ETDEWEB)
Enderby, J A [UK Atomic Energy Authority, Northern Division, Risley Nuclear Power Development Establishment, Risley, Warrington (United Kingdom)
1983-05-01
UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)
Finite Volumes for Complex Applications VII
Ohlberger, Mario; Rohde, Christian
2014-01-01
The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications. The second volume of the proceedings covers reviewed contributions reporting successful applications in the fields of fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative propert...
Finite-difference schemes for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: es@cwi.nl [Centrum Wiskunde and Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands)
2014-09-01
In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.
Fourier analysis of finite element preconditioned collocation schemes
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
Non Standard Finite Difference Scheme for Mutualistic Interaction Description
Gabbriellini, Gianluca
2012-01-01
One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource mutualism description, this work deals with the application of the Mickens Non Standard Finite Difference method to transform the continuous-time scheme into a discrete-time one. It has been proved that the Mickens scheme is dynamically consistent with the o...
Chiral crossover transition in a finite volume
Shi, Chao; Jia, Wenbao; Sun, An; Zhang, Liping; Zong, Hongshi
2018-02-01
Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudo-transition temperature {T}{{c}} of the crossover, showing a significant decrease in {T}{{c}} as L decreases below 3 fm. Supported by National Natural Science Foundation of China (11475085, 11535005, 11690030, 51405027), the Fundamental Research Funds for the Central Universities (020414380074), China Postdoctoral Science Foundation (2016M591808) and Open Research Foundation of State Key Lab. of Digital Manufacturing Equipment & Technology in Huazhong University of Science & Technology (DMETKF2015015)
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
Yamamoto, Naoki; Kanazawa, Takuya
2009-01-01
We study the properties of QCD at high baryon density in a finite volume where color superconductivity occurs. We derive exact sum rules for complex eigenvalues of the Dirac operator at finite chemical potential, and show that the Dirac spectrum is directly related to the color superconducting gap $\\Delta$. Also, we find a characteristic signature of color superconductivity: an X-shaped spectrum of partition function zeros in the complex quark mass plane near the origin, reflecting the $Z(2)_...
Finite volume QCD at fixed topological charge
Aoki, Sinya; Fukaya, Hidenori; Hashimoto, Shoji; Onogi, Tetsuya
2007-01-01
In finite volume the partition function of QCD with a given $\\theta$ is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed topological sector, the result deviates from the true expectation value by an amount proportional to the inverse space-time volume 1/V. Using the saddle point expansion, we derive formulas to express the correction due to the fixed topological charge in terms of...
International Nuclear Information System (INIS)
Kriventsev, Vladimir
2000-09-01
Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed
Nonlinear Conservation Laws and Finite Volume Methods
Leveque, Randall J.
Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References
Computational Aero-Acoustic Using High-order Finite-Difference Schemes
DEFF Research Database (Denmark)
Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær
2007-01-01
are solved using the in-house flow solver EllipSys2D/3D which is a second-order finite volume code. The acoustic solution is found by solving the acoustic equations using high-order finite difference schemes. The incompressible flow equations and the acoustic equations are solved at the same time levels......In this paper, a high-order technique to accurately predict flow-generated noise is introduced. The technique consists of solving the viscous incompressible flow equations and inviscid acoustic equations using a incompressible/compressible splitting technique. The incompressible flow equations...
Solving hyperbolic equations with finite volume methods
Vázquez-Cendón, M Elena
2015-01-01
Finite volume methods are used in numerous applications and by a broad multidisciplinary scientific community. The book communicates this important tool to students, researchers in training and academics involved in the training of students in different science and technology fields. The selection of content is based on the author’s experience giving PhD and master courses in different universities. In the book the introduction of new concepts and numerical methods go together with simple exercises, examples and applications that contribute to reinforce them. In addition, some of them involve the execution of MATLAB codes. The author promotes an understanding of common terminology with a balance between mathematical rigor and physical intuition that characterizes the origin of the methods. This book aims to be a first contact with finite volume methods. Once readers have studied it, they will be able to follow more specific bibliographical references and use commercial programs or open source software withi...
Hidden charm molecules in a finite volume
International Nuclear Information System (INIS)
Albaladejo, M.; Hidalgo-Duque, C.; Nieves, J.; Oset, E.
2014-01-01
In the present paper we address the interaction of charmed mesons in hidden charm channels in a finite box. We use the interaction from a recent model based on heavy quark spin symmetry that predicts molecules of hidden charm in the infinite volume. The energy levels in the box are generated within this model, and several methods for the analysis of these levels ("inverse problem") are investigated. (author)
Call Admission Scheme for Multidimensional Traffic Assuming Finite Handoff User
Directory of Open Access Journals (Sweden)
Md. Baitul Al Sadi
2017-01-01
Full Text Available Usually, the number of users within a cell in a mobile cellular network is considered infinite; hence, M/M/n/k model is appropriate for new originated traffic, but the number of ongoing calls around a cell is always finite. Hence, the traffic model of handoff call will be M/M/n/k/N. In this paper, a K-dimensional traffic model of a mobile cellular network is proposed using the combination of limited and unlimited users case. A new call admission scheme (CAS is proposed based on both thinning scheme and fading condition. The fading condition of the wireless channel access to a handoff call is prioritized compared to newly originated calls.
Energy Technology Data Exchange (ETDEWEB)
Ansanay-Alex, G.
2009-06-17
The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)
Biquartic Finite Volume Element Metho d Based on Lobatto-Guass Structure
Institute of Scientific and Technical Information of China (English)
Gao Yan-ni; Chen Yan-li
2015-01-01
In this paper, a biquartic finite volume element method based on Lobatto-Guass structure is presented for variable coeﬃcient elliptic equation on rectangular partition. Not only the optimal H1 and L2 error estimates but also some super-convergent properties are available and could be proved for this method. The numer-ical results obtained by this finite volume element scheme confirm the validity of the theoretical analysis and the effectiveness of this method.
International Nuclear Information System (INIS)
Yamamoto, Naoki; Kanazawa, Takuya
2009-01-01
We study the properties of QCD at high baryon density in a finite volume where color superconductivity occurs. We derive exact sum rules for complex eigenvalues of the Dirac operator at a finite chemical potential, and show that the Dirac spectrum is directly related to the color superconducting gap Δ. Also, we find a characteristic signature of color superconductivity: an X-shaped spectrum of partition function zeros in the complex quark mass plane near the origin, reflecting the Z(2) L xZ(2) R symmetry of the diquark pairing. Our results are universal in the domain Δ -1 π -1 where L is the linear size of the system and m π is the pion mass at high density.
Finite Volume Method for Pricing European Call Option with Regime-switching Volatility
Lista Tauryawati, Mey; Imron, Chairul; Putri, Endah RM
2018-03-01
In this paper, we present a finite volume method for pricing European call option using Black-Scholes equation with regime-switching volatility. In the first step, we formulate the Black-Scholes equations with regime-switching volatility. we use a finite volume method based on fitted finite volume with spatial discretization and an implicit time stepping technique for the case. We show that the regime-switching scheme can revert to the non-switching Black Scholes equation, both in theoretical evidence and numerical simulations.
Auction dynamics: A volume constrained MBO scheme
Jacobs, Matt; Merkurjev, Ekaterina; Esedoǧlu, Selim
2018-02-01
We show how auction algorithms, originally developed for the assignment problem, can be utilized in Merriman, Bence, and Osher's threshold dynamics scheme to simulate multi-phase motion by mean curvature in the presence of equality and inequality volume constraints on the individual phases. The resulting algorithms are highly efficient and robust, and can be used in simulations ranging from minimal partition problems in Euclidean space to semi-supervised machine learning via clustering on graphs. In the case of the latter application, numerous experimental results on benchmark machine learning datasets show that our approach exceeds the performance of current state-of-the-art methods, while requiring a fraction of the computation time.
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
Liu, Meilin; Bagci, Hakan
2011-01-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results
Topology optimization using the finite volume method
DEFF Research Database (Denmark)
in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...... derivative of the system matrix K and in how one computes the discretized version of certain objective functions. Thus for a cost function for minimum dissipated energy (like minimum compliance for an elastic structure) one obtains an expression c = u^\\T \\tilde{K}u $, where \\tilde{K} is different from K...... the well known Reuss lower bound. [1] Bendsøe, M.P.; Sigmund, O. 2004: Topology Optimization - Theory, Methods, and Applications. Berlin Heidelberg: Springer Verlag [2] Versteeg, H. K.; W. Malalasekera 1995: An introduction to Computational Fluid Dynamics: the Finite Volume Method. London: Longman...
Finite Volume Method for Unstructured Grid
International Nuclear Information System (INIS)
Casmara; Kardana, N.D.
1997-01-01
The success of a computational method depends on the solution algorithm and mesh generation techniques. cell distributions are needed, which allow the solution to be calculated over the entire body surface with sufficient accuracy. to handle the mesh generation for multi-connected region such as multi-element bodies, the unstructured finite volume method will be applied. the advantages of the unstructured meshes are it provides a great deal more flexibility for generating meshes about complex geometries and provides a natural setting for the use of adaptive meshing. the governing equations to be discretized are inviscid and rotational euler equations. Applications of the method will be evaluated on flow around single and multi-component bodies
Hybrid finite volume/ finite element method for radiative heat transfer in graded index media
Zhang, L.; Zhao, J. M.; Liu, L. H.; Wang, S. Y.
2012-09-01
The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89-101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.
Hybrid finite volume/ finite element method for radiative heat transfer in graded index media
International Nuclear Information System (INIS)
Zhang, L.; Zhao, J.M.; Liu, L.H.; Wang, S.Y.
2012-01-01
The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89-101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.
Hadronic electroweak processes in a finite volume
International Nuclear Information System (INIS)
Agadjanov, Andria
2017-01-01
In the present thesis, we study a number of hadronic electroweak processes in a finite volume. Our work is motivated by the ongoing and future lattice simulations of the strong interaction theory called quantum chromodynamics. According to the available computational resources, the numerical calculations are necessarily performed on lattices with a finite spatial extension. The first part of the thesis is based on the finite volume formalism which is a standard method to investigate the processes with the final state interactions, and in particular, the elastic hadron resonances, on the lattice. Throughout the work, we systematically apply the non-relativistic effective field theory. The great merit of this approach is that it encodes the low-energy dynamics directly in terms of the effective range expansion parameters. After a brief introduction into the subject, we formulate a framework for the extraction of the ΔNγ * as well as the B→K * transition form factors from lattice data. Both processes are of substantial phenomenological interest, including the search for physics beyond the Standard Model. Moreover, we provide a proper field-theoretical definition of the resonance matrix elements, and advocate it in comparison to the one based on the infinitely narrow width approximation. In the second part we consider certain aspects of the doubly virtual nucleon Compton scattering. The main objective of the work is to answer the question whether there is, in the Regge language, a so-called fixed pole in the process. To answer this question, the unknown subtraction function, which enters one of the dispersion relations for the invariant amplitudes, has to be determined. The external field method provides a feasible approach to tackle this problem on the lattice. Considering the nucleon in a periodic magnetic field, we derive a simple relation for the ground state energy shift up to a second order in the field strength. The obtained result encodes the value of the
Hadronic electroweak processes in a finite volume
Energy Technology Data Exchange (ETDEWEB)
Agadjanov, Andria
2017-11-07
In the present thesis, we study a number of hadronic electroweak processes in a finite volume. Our work is motivated by the ongoing and future lattice simulations of the strong interaction theory called quantum chromodynamics. According to the available computational resources, the numerical calculations are necessarily performed on lattices with a finite spatial extension. The first part of the thesis is based on the finite volume formalism which is a standard method to investigate the processes with the final state interactions, and in particular, the elastic hadron resonances, on the lattice. Throughout the work, we systematically apply the non-relativistic effective field theory. The great merit of this approach is that it encodes the low-energy dynamics directly in terms of the effective range expansion parameters. After a brief introduction into the subject, we formulate a framework for the extraction of the ΔNγ{sup *} as well as the B→K{sup *} transition form factors from lattice data. Both processes are of substantial phenomenological interest, including the search for physics beyond the Standard Model. Moreover, we provide a proper field-theoretical definition of the resonance matrix elements, and advocate it in comparison to the one based on the infinitely narrow width approximation. In the second part we consider certain aspects of the doubly virtual nucleon Compton scattering. The main objective of the work is to answer the question whether there is, in the Regge language, a so-called fixed pole in the process. To answer this question, the unknown subtraction function, which enters one of the dispersion relations for the invariant amplitudes, has to be determined. The external field method provides a feasible approach to tackle this problem on the lattice. Considering the nucleon in a periodic magnetic field, we derive a simple relation for the ground state energy shift up to a second order in the field strength. The obtained result encodes the
A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation
International Nuclear Information System (INIS)
Banks, J.W.; Hittinger, J.A.
2010-01-01
Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.
Finite spatial volume approach to finite temperature field theory
International Nuclear Information System (INIS)
Weiss, Nathan
1981-01-01
A relativistic quantum field theory at finite temperature T=β -1 is equivalent to the same field theory at zero temperature but with one spatial dimension of finite length β. This equivalence is discussed for scalars, for fermions, and for gauge theories. The relationship is checked for free field theory. The translation of correlation functions between the two formulations is described with special emphasis on the nonlocal order parameters of gauge theories. Possible applications are mentioned. (auth)
Kou, Jisheng
2017-06-09
In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated by piecewise constant functions or Q1 functions, while the velocity and pressure are discretized by the lowest-order Raviart-Thomas element and the piecewise constant functions, respectively. Using quadrature rules, we demonstrate that this scheme can be reduced into a finite volume method on staggered grid, which is extensively used in computational fluid mechanics and engineering.
Finite volume form factors in the presence of integrable defects
International Nuclear Information System (INIS)
Bajnok, Z.; Buccheri, F.; Hollo, L.; Konczer, J.; Takacs, G.
2014-01-01
We developed the theory of finite volume form factors in the presence of integrable defects. These finite volume form factors are expressed in terms of the infinite volume form factors and the finite volume density of states and incorporate all polynomial corrections in the inverse of the volume. We tested our results, in the defect Lee–Yang model, against numerical data obtained by truncated conformal space approach (TCSA), which we improved by renormalization group methods adopted to the defect case. To perform these checks we determined the infinite volume defect form factors in the Lee–Yang model exactly, including their vacuum expectation values. We used these data to calculate the two point functions, which we compared, at short distance, to defect CFT. We also derived explicit expressions for the exact finite volume one point functions, which we checked numerically. In all of these comparisons excellent agreement was found
Well balanced finite volume methods for nearly hydrostatic flows
International Nuclear Information System (INIS)
Botta, N.; Klein, R.; Langenberg, S.; Luetzenkirchen, S.
2004-01-01
In numerical approximations of nearly hydrostatic flows, a proper representation of the dominant hydrostatic balance is of crucial importance: unbalanced truncation errors can induce unacceptable spurious motions, e.g., in dynamical cores of models for numerical weather prediction (NWP) in particular near steep topography. In this paper we develop a new strategy for the construction of discretizations that are 'well-balanced' with respect to dominant hydrostatics. The classical idea of formulating the momentum balance in terms of deviations of pressure from a balanced background distribution is realized here through local, time dependent hydrostatic reconstructions. Balanced discretizations of the pressure gradient and of the gravitation source term are achieved through a 'discrete Archimedes' buoyancy principle'. This strategy is applied to extend an explicit standard finite volume Godunov-type scheme for compressible flows with minimal modifications. The resulting method has the following features: (i) It inherits its conservation properties from the underlying base scheme. (ii) It is exactly balanced, even on curvilinear grids, for a large class of near-hydrostatic flows. (iii) It solves the full compressible flow equations without reference to a background state that is defined for an entire vertical column of air. (iv) It is robust with respect to details of the implementation, such as the choice of slope limiting functions, or the particularities of boundary condition discretizations
International Nuclear Information System (INIS)
Vidovic, D.; Segal, A.; Wesseling, P.
2004-01-01
A method for linear reconstruction of staggered vector fields with special treatment of the divergence is presented. An upwind-biased finite volume scheme for solving the unsteady incompressible Navier-Stokes equations on staggered unstructured triangular grids that uses this reconstruction is described. The scheme is applied to three benchmark problems and is found to be superlinearly convergent in space
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids
Directory of Open Access Journals (Sweden)
Sudi Mungkasi
2016-01-01
Full Text Available This paper presents a numerical entropy production (NEP scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.
A lattice Boltzmann coupled to finite volumes method for solving phase change problems
Directory of Open Access Journals (Sweden)
El Ganaoui Mohammed
2009-01-01
Full Text Available A numerical scheme coupling lattice Boltzmann and finite volumes approaches has been developed and qualified for test cases of phase change problems. In this work, the coupled partial differential equations of momentum conservation equations are solved with a non uniform lattice Boltzmann method. The energy equation is discretized by using a finite volume method. Simulations show the ability of this developed hybrid method to model the effects of convection, and to predict transfers. Benchmarking is operated both for conductive and convective situation dominating solid/liquid transition. Comparisons are achieved with respect to available analytical solutions and experimental results.
8th conference on Finite Volumes for Complex Applications
Omnes, Pascal
2017-01-01
This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier–Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including m...
An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics
International Nuclear Information System (INIS)
Kühnlein, Christian; Smolarkiewicz, Piotr K.
2017-01-01
An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.
An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics
Energy Technology Data Exchange (ETDEWEB)
Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int
2017-04-01
An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.
High-order finite volume advection
Shaw, James
2018-01-01
The cubicFit advection scheme is limited to second-order convergence because it uses a polynomial reconstruction fitted to point values at cell centres. The highOrderFit advection scheme achieves higher than second order by calculating high-order moments over the mesh geometry.
A perturbational h4 exponential finite difference scheme for the convective diffusion equation
International Nuclear Information System (INIS)
Chen, G.Q.; Gao, Z.; Yang, Z.F.
1993-01-01
A perturbational h 4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h 2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes. Besides, the h 4 accuracy of the perturbational scheme is verified using double precision arithmetic
Three-body unitarity in the finite volume
Energy Technology Data Exchange (ETDEWEB)
Mai, M. [The George Washington University, Washington, DC (United States); Doering, M. [The George Washington University, Washington, DC (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
2017-12-15
The physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic 3 → 3 amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. The corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated. (orig.)
A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method
Directory of Open Access Journals (Sweden)
Feng Wu
Full Text Available Abstract A modified computational scheme of the stochastic perturbation finite element method (SPFEM is developed for structures with low-level uncertainties. The proposed scheme can provide second-order estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.
Directory of Open Access Journals (Sweden)
Peng Jiang
2013-01-01
Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
The finite precision computation and the nonconvergence of difference scheme
Pengfei, Wang; Jianping, Li
2008-01-01
The authors show that the round-off error can break the consistency which is the premise of using the difference equation to replace the original differential equations. We therefore proposed a theoretical approach to investigate this effect, and found that the difference scheme can not guarantee the convergence of the actual compute result to the analytical one. A conservation scheme experiment is applied to solve a simple linear differential equation satisfing the LAX equivalence theorem in...
International Nuclear Information System (INIS)
Benasser Algehawi, Mohammed; Samsudin, Azman
2010-01-01
We present a method to extract key pairs needed for the Identity Based Encryption (IBE) scheme from extended Chebyshev polynomial over finite fields Z p . Our proposed scheme relies on the hard problem and the bilinear property of the extended Chebyshev polynomial over Z p . The proposed system is applicable, secure, and reliable.
International Nuclear Information System (INIS)
Fedon-Magnaud, C.; Hennart, J.P.; Lautard, J.J.
1983-03-01
An unified formulation of non conforming finite elements with quadrature formula and simple nodal scheme is presented. The theoretical convergence is obtained for the previous scheme when the mesh is refined. Numerical tests are provided in order to bear out the theorical results
A novel finite volume discretization method for advection-diffusion systems on stretched meshes
Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.
2018-06-01
This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.
Accuracy of spectral and finite difference schemes in 2D advection problems
DEFF Research Database (Denmark)
Naulin, V.; Nielsen, A.H.
2003-01-01
In this paper we investigate the accuracy of two numerical procedures commonly used to solve 2D advection problems: spectral and finite difference (FD) schemes. These schemes are widely used, simulating, e.g., neutral and plasma flows. FD schemes have long been considered fast, relatively easy...... that the accuracy of FD schemes can be significantly improved if one is careful in choosing an appropriate FD scheme that reflects conservation properties of the nonlinear terms and in setting up the grid in accordance with the problem....
Liu, Meilin
2011-07-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.
Four-level conservative finite-difference schemes for Boussinesq paradigm equation
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.
A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers
Bagci, Hakan
2015-01-01
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability
A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers
Bagci, Hakan
2015-01-07
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability
6th international symposium on finite volumes for complex applications
Halama, Jan; Herbin, Raphaèle; Hubert, Florence; Fort, Jaroslav; FVCA 6; Finite Volumes for Complex Applications VI : Problems and perspectives
2011-01-01
Finite volume methods are used for various applications in fluid dynamics, magnetohydrodynamics, structural analysis or nuclear physics. A closer look reveals many interesting phenomena and mathematical or numerical difficulties, such as true error analysis and adaptivity, modelling of multi-phase phenomena or fitting problems, stiff terms in convection/diffusion equations and sources. To overcome existing problems and to find solution methods for future applications requires many efforts and always new developments. The goal of The International Symposium on Finite Volumes for Complex Applica
Application of compact finite-difference schemes to simulations of stably stratified fluid flows
Czech Academy of Sciences Publication Activity Database
Bodnár, Tomáš; Beneš, L.; Fraunie, P.; Kozel, Karel
2012-01-01
Roč. 219, č. 7 (2012), s. 3336-3353 ISSN 0096-3003 Institutional support: RVO:61388998 Keywords : stratification * finite- difference * finite-volume * Runge-Kutta Subject RIV: BA - General Mathematics Impact factor: 1.349, year: 2012 http://www.sciencedirect.com/science/article/pii/S0096300311010988
Five-point Element Scheme of Finite Analytic Method for Unsteady Groundwater Flow
Institute of Scientific and Technical Information of China (English)
Xiang Bo; Mi Xiao; Ji Changming; Luo Qingsong
2007-01-01
In order to improve the finite analytic method's adaptability for irregular unit, by using coordinates rotation technique this paper establishes a five-point element scheme of finite analytic method. It not only solves unsteady groundwater flow equation but also gives the boundary condition. This method can be used to calculate the three typical questions of groundwater. By compared with predecessor's computed result, the result of this method is more satisfactory.
The finite volume element (FVE) and multigrid method for the incompressible Navier-Stokes equations
International Nuclear Information System (INIS)
Gu Lizhen; Bao Weizhu
1992-01-01
The authors apply FVE method to discrete INS equations with the original variable, in which the bilinear square finite element and the square finite volume are chosen. The discrete schemes of INS equations are presented. The FMV multigrid algorithm is applied to solve that discrete system, where DGS iteration is used as smoother, DGS distributive mode for the INS discrete system is also presented. The sample problems for the square cavity flow with Reynolds number Re≤100 are successfully calculated. The numerical solutions show that the results with 1 FMV is satisfactory and when Re is not large, The FVE discrete scheme of the conservative INS equations and that of non-conservative INS equations with linearization both can provide almost same accuracy
Finite Volume Effect of Baryons in Strange Hadronic Matter
Institute of Scientific and Technical Information of China (English)
SUN Bao-Xi; LI Lei; NING Ping-Zhi; ZHAO En-Guang
2001-01-01
The finite volume effect of baryons in strange hadronic matter (SHM) is studied within the framework of relativistic mean-field theory. As this effect is concerned, the saturation density of SHM turns lower, and the binding energy per baryon decreases. Its influence to the compression modulus of SHM is also discussed.
Finite volume at two-loops in chiral perturbation theory
International Nuclear Information System (INIS)
Bijnens, Johan; Rössler, Thomas
2015-01-01
We calculate the finite volume corrections to meson masses and decay constants in two and three flavour Chiral Perturbation Theory to two-loop order. The analytical results are compared with the existing result for the pion mass in two-flavour ChPT and the partial results for the other quantities. We present numerical results for all quantities.
Treating network junctions in finite volume solution of transient gas flow models
Bermúdez, Alfredo; López, Xián; Vázquez-Cendón, M. Elena
2017-09-01
A finite volume scheme for the numerical solution of a non-isothermal non-adiabatic compressible flow model for gas transportation networks on non-flat topography is introduced. Unlike standard Euler equations, the model takes into account wall friction, variable height and heat transfer between the pipe and the environment which are source terms. The case of one single pipe was considered in a previous reference by the authors, [8], where a finite volume method with upwind discretization of the flux and source terms has been proposed in order to get a well-balanced scheme. The main goal of the present paper is to go a step further by considering a network of pipes. The main issue is the treatment of junctions for which container-like 2D finite volumes are introduced. The couplings between pipes (1D) and containers (2D) are carefully described and the conservation properties are analyzed. Numerical tests including real gas networks are solved showing the performance of the proposed methodology.
A multigrid algorithm for the cell-centered finite difference scheme
Ewing, Richard E.; Shen, Jian
1993-01-01
In this article, we discuss a non-variational V-cycle multigrid algorithm based on the cell-centered finite difference scheme for solving a second-order elliptic problem with discontinuous coefficients. Due to the poor approximation property of piecewise constant spaces and the non-variational nature of our scheme, one step of symmetric linear smoothing in our V-cycle multigrid scheme may fail to be a contraction. Again, because of the simple structure of the piecewise constant spaces, prolongation and restriction are trivial; we save significant computation time with very promising computational results.
Development of a hip joint model for finite volume simulations.
Cardiff, P; Karač, A; FitzPatrick, D; Ivanković, A
2014-01-01
This paper establishes a procedure for numerical analysis of a hip joint using the finite volume method. Patient-specific hip joint geometry is segmented directly from computed tomography and magnetic resonance imaging datasets and the resulting bone surfaces are processed into a form suitable for volume meshing. A high resolution continuum tetrahedral mesh has been generated, where a sandwich model approach is adopted; the bones are represented as a stiffer cortical shells surrounding more flexible cancellous cores. Cartilage is included as a uniform thickness extruded layer and the effect of layer thickness is investigated. To realistically position the bones, gait analysis has been performed giving the 3D positions of the bones for the full gait cycle. Three phases of the gait cycle are examined using a finite volume based custom structural contact solver implemented in open-source software OpenFOAM.
High-order asynchrony-tolerant finite difference schemes for partial differential equations
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.
Stability of finite difference schemes for generalized von Foerster equations with renewal
Directory of Open Access Journals (Sweden)
Henryk Leszczyński
2014-01-01
Full Text Available We consider a von Foerster-type equation describing the dynamics of a population with the production of offsprings given by the renewal condition. We construct a finite difference scheme for this problem and give sufficient conditions for its stability with respect to \\(l^1\\ and \\(l^\\infty\\ norms.
International Nuclear Information System (INIS)
Berthe, P.M.
2013-01-01
In the context of nuclear waste repositories, we consider the numerical discretization of the non stationary convection diffusion equation. Discontinuous physical parameters and heterogeneous space and time scales lead us to use different space and time discretizations in different parts of the domain. In this work, we choose the discrete duality finite volume (DDFV) scheme and the discontinuous Galerkin scheme in time, coupled by an optimized Schwarz waveform relaxation (OSWR) domain decomposition method, because this allows the use of non-conforming space-time meshes. The main difficulty lies in finding an upwind discretization of the convective flux which remains local to a sub-domain and such that the multi domain scheme is equivalent to the mono domain one. These difficulties are first dealt with in the one-dimensional context, where different discretizations are studied. The chosen scheme introduces a hybrid unknown on the cell interfaces. The idea of up winding with respect to this hybrid unknown is extended to the DDFV scheme in the two-dimensional setting. The well-posedness of the scheme and of an equivalent multi domain scheme is shown. The latter is solved by an OSWR algorithm, the convergence of which is proved. The optimized parameters in the Robin transmission conditions are obtained by studying the continuous or discrete convergence rates. Several test-cases, one of which inspired by nuclear waste repositories, illustrate these results. (author) [fr
Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation
International Nuclear Information System (INIS)
Sha, Wei; Huang, Zhixiang; Wu, Xianliang; Chen, Mingsheng
2007-01-01
An explicit fourth-order finite-difference time-domain (FDTD) scheme using the symplectic integrator is applied to electromagnetic simulation. A feasible numerical implementation of the symplectic FDTD (SFDTD) scheme is specified. In particular, new strategies for the air-dielectric interface treatment and the near-to-far-field (NFF) transformation are presented. By using the SFDTD scheme, both the radiation and the scattering of three-dimensional objects are computed. Furthermore, the energy-conserving characteristic hold for the SFDTD scheme is verified under long-term simulation. Numerical results suggest that the SFDTD scheme is more efficient than the traditional FDTD method and other high-order methods, and can save computational resources
A point-value enhanced finite volume method based on approximate delta functions
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.
Precise determination of universal finite volume observables in the Gross-Neveu model
Energy Technology Data Exchange (ETDEWEB)
Korzec, T.
2007-01-26
The Gross-Neveu model is a quantum field theory in two space time dimensions that shares many features with quantum chromo dynamics. In this thesis the continuum model and its discretized versions are reviewed and a finite volume renormalization scheme is introduced and tested. Calculations in the limit of infinitely many fermion flavors as well as perturbative computations are carried out. In extensive Monte-Carlo simulations of the one flavor and the four flavor lattice models with Wilson fermions a set of universal finite volume observables is calculated to a high precision. In the one flavor model which is equivalent to the massless Thirring model the continuum extrapolated Monte-Carlo results are confronted with an exact solution of the model. (orig.)
Precise determination of universal finite volume observables in the Gross-Neveu model
International Nuclear Information System (INIS)
Korzec, T.
2007-01-01
The Gross-Neveu model is a quantum field theory in two space time dimensions that shares many features with quantum chromo dynamics. In this thesis the continuum model and its discretized versions are reviewed and a finite volume renormalization scheme is introduced and tested. Calculations in the limit of infinitely many fermion flavors as well as perturbative computations are carried out. In extensive Monte-Carlo simulations of the one flavor and the four flavor lattice models with Wilson fermions a set of universal finite volume observables is calculated to a high precision. In the one flavor model which is equivalent to the massless Thirring model the continuum extrapolated Monte-Carlo results are confronted with an exact solution of the model. (orig.)
International Nuclear Information System (INIS)
Masoud Ziaei-Rad
2010-01-01
In this paper, a two-dimensional numerical scheme is presented for the simulation of turbulent, viscous, transient compressible flows in the simultaneously developing hydraulic and thermal boundary layer region. The numerical procedure is a finite-volume-based finite-element method applied to unstructured grids. This combination together with a new method applied for the boundary conditions allows for accurate computation of the variables in the entrance region and for a wide range of flow fields from subsonic to transonic. The Roe-Riemann solver is used for the convective terms, whereas the standard Galerkin technique is applied for the viscous terms. A modified κ-ε model with a two-layer equation for the near-wall region combined with a compressibility correction is used to predict the turbulent viscosity. Parallel processing is also employed to divide the computational domain among the different processors to reduce the computational time. The method is applied to some test cases in order to verify the numerical accuracy. The results show significant differences between incompressible and compressible flows in the friction coefficient, Nusselt number, shear stress and the ratio of the compressible turbulent viscosity to the molecular viscosity along the developing region. A transient flow generated after an accidental rupture in a pipeline was also studied as a test case. The results show that the present numerical scheme is stable, accurate and efficient enough to solve the problem of transient wall-bounded flow.
Mimetic Theory for Cell-Centered Lagrangian Finite Volume Formulation on General Unstructured Grids
Energy Technology Data Exchange (ETDEWEB)
Sambasivan, Shiv Kumar [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory; Burton, Donald E. [Los Alamos National Laboratory; Christon, Mark A. [Los Alamos National Laboratory
2012-07-19
A finite volume cell-centered Lagrangian scheme for solving large deformation problems is constructed based on the hypo-elastic model and using the mimetic theory. Rigorous analysis in the context of gas and solid dynamics, and arbitrary polygonal meshes, is presented to demonstrate the ability of cell-centered schemes in mimicking the continuum properties and principles at the discrete level. A new mimetic formulation based gradient evaluation technique and physics-based, frame independent and symmetry preserving slope limiters are proposed. Furthermore, a physically consistent dissipation model is employed which is both robust and inexpensive to implement. The cell-centered scheme along with these additional new features are applied to solve solids undergoing elasto-plastic deformation.
DEFF Research Database (Denmark)
Fasano, Andrea; Rasmussen, Henrik K.
2017-01-01
A third order accurate, in time and space, finite element scheme for the numerical simulation of three- dimensional time-dependent flow of the molecular stress function type of fluids in a generalized formu- lation is presented. The scheme is an extension of the K-BKZ Lagrangian finite element me...
International Nuclear Information System (INIS)
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region
Confining dyon gas with finite-volume effects under control
Energy Technology Data Exchange (ETDEWEB)
Bruckmann, Falk [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Dinter, Simon [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Ilgenfritz, Ernst-Michael [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Joint Institute for Nuclear Research, VBLHEP, Dubna (Russian Federation); Maier, Benjamin; Mueller-Preussker, Michael [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Wagner, Marc [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik
2011-11-15
As an approach to describe the long-range properties of non-Abelian gauge theories at non-zero temperature T
Confining dyon gas with finite-volume effects under control
International Nuclear Information System (INIS)
Bruckmann, Falk; Maier, Benjamin; Mueller-Preussker, Michael; Wagner, Marc; Frankfurt Univ.
2011-11-01
As an approach to describe the long-range properties of non-Abelian gauge theories at non-zero temperature T c , we consider a non-interacting ensemble of dyons (magnetic monopoles) with non-trivial holonomy. We show analytically, that the quark-antiquark free energy from the Polyakov loop correlator grows linearly with the distance, and how the string tension scales with the dyon density. In numerical treatments, the long-range tails of the dyon fields cause severe finite-volume effects. Therefore, we demonstrate the application of Ewald's summation method to this system. Finite-volume effects are shown to be under control, which is a crucial requirement for numerical studies of interacting dyon ensembles. (orig.)
Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation
Litaker, Eric T.
1994-12-01
The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.
Infinite volume of noncommutative black hole wrapped by finite surface
Energy Technology Data Exchange (ETDEWEB)
Zhang, Baocheng, E-mail: zhangbc.zhang@yahoo.com [School of Mathematics and Physics, China University of Geosciences, Wuhan 430074 (China); You, Li, E-mail: lyou@mail.tsinghua.edu.cn [State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084 (China)
2017-02-10
The volume of a black hole under noncommutative spacetime background is found to be infinite, in contradiction with the surface area of a black hole, or its Bekenstein–Hawking (BH) entropy, which is well-known to be finite. Our result rules out the possibility of interpreting the entropy of a black hole by counting the number of modes wrapped inside its surface if the final evaporation stage can be properly treated. It implies the statistical interpretation for the BH entropy can be independent of the volume, provided spacetime is noncommutative. The effect of radiation back reaction is found to be small and doesn't influence the above conclusion.
Renormalization in self-consistent approximation schemes at finite temperature I: theory
International Nuclear Information System (INIS)
Hees, H. van; Knoll, J.
2001-07-01
Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)
An Elgamal Encryption Scheme of Fibonacci Q-Matrix and Finite State Machine
Directory of Open Access Journals (Sweden)
B. Ravi Kumar
2015-12-01
Full Text Available Cryptography is the science of writing messages in unknown form using mathematical models. In Cryptography, several ciphers were introduced for the encryption schemes. Recent research focusing on designing various mathematical models in such a way that tracing the inverse of the designed mathematical models is infeasible for the eve droppers. In the present work, the ELGamal encryption scheme is executed using the generator of a cyclic group formed by the points on choosing elliptic curve, finite state machines and key matrices obtained from the Fibonacci sequences.
Finite-volume cumulant expansion in QCD-colorless plasma
Energy Technology Data Exchange (ETDEWEB)
Ladrem, M. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); Physics Department, Algiers (Algeria); ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Ahmed, M.A.A. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Taiz University in Turba, Physics Department, Taiz (Yemen); Alfull, Z.Z. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); Cherif, S. [ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Ghardaia University, Sciences and Technologies Department, Ghardaia (Algeria)
2015-09-15
Due to the finite-size effects, the localization of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite-volume transition point T{sub 0}(V) of the QCD deconfinement phase transition to a colorless QGP, we have developed a new approach using the finite-size cumulant expansion of the order parameter and the L{sub mn}-method. The first six cumulants C{sub 1,2,3,4,5,6} with the corresponding under-normalized ratios (skewness Σ, kurtosis κ, pentosis Π{sub ±}, and hexosis H{sub 1,2,3}) and three unnormalized combinations of them, (O = σ{sup 2}κΣ{sup -1},U = σ{sup -2}Σ{sup -1},N = σ{sup 2}κ) are calculated and studied as functions of (T, V). A new approach, unifying in a clear and consistent way the definitions of cumulant ratios, is proposed.Anumerical FSS analysis of the obtained results has allowed us to locate accurately the finite-volume transition point. The extracted transition temperature value T{sub 0}(V) agrees with that expected T{sub 0}{sup N}(V) from the order parameter and the thermal susceptibility χ{sub T} (T, V), according to the standard procedure of localization to within about 2%. In addition to this, a very good correlation factor is obtained proving the validity of our cumulants method. The agreement of our results with those obtained by means of other models is remarkable. (orig.)
A non-perturbative analysis in finite volume gauge theory
International Nuclear Information System (INIS)
Koller, J.; State Univ. of New York, Stony Brook; Van Baal, P.; State Univ. of New York, Stony Brook
1988-01-01
We discuss SU(2) gauge theory on a three-torus using a finite volume expansion. Our discovery of natural coordinates allows us to obtain continuum results in a region where Monte Carlo data are also available. The obtained results agree well with the perturbative and semiclassical analysis for small volumes, and there is fair agreement with the Monte Carlo results in intermediate volumes. The simple picture which emerges for the approximate low energy dynamics is that of three interacting particles enclosed in a sphere, with zero total 'angular momentum'. The validity of an adiabatic approximation is investigated. The fundamentally new understanding gained, is that non-perturbative dynamics can be incorporated by imposing boundary conditions which arise through the nontrivial topology of configuration space. (orig.)
Development op finite volume methods for fluid dynamics
International Nuclear Information System (INIS)
Delcourte, S.
2007-09-01
We aim to develop a finite volume method which applies to a greater class of meshes than other finite volume methods, restricted by orthogonality constraints. We build discrete differential operators over the three staggered tessellations needed for the construction of the method. These operators verify some analogous properties to those of the continuous operators. At first, the method is applied to the Div-Curl problem, which can be viewed as a building block of the Stokes problem. Then, the Stokes problem is dealt with with various boundary conditions. It is well known that when the computational domain is polygonal and non-convex, the order of convergence of numerical methods is deteriorated. Consequently, we have studied how an appropriate local refinement is able to restore the optimal order of convergence for the Laplacian problem. At last, we have discretized the non-linear Navier-Stokes problem, using the rotational formulation of the convection term, associated to the Bernoulli pressure. With an iterative algorithm, we are led to solve a saddle-point problem at each iteration. We give a particular interest to this linear problem by testing some pre-conditioners issued from finite elements, which we adapt to our method. Each problem is illustrated by numerical results on arbitrary meshes, such as strongly non-conforming meshes. (author)
Discrete memory schemes for finite strain thermoplasticity and application to shape memory alloys
International Nuclear Information System (INIS)
Favier, D.; Guelin, P.; Pegon, P.; Nowacki, W.K.
1987-01-01
A theory of finite strain plasticity has been proposed: The scheme of pure hysteresis with mixed transport has been extended to the case of non-rotational kinematics. Secondly, the simple shear case has been studied, taking into account Drucker's recent analysis regarding the 'appropriate simple idealizations for finite plasticity'. Illustrations are provided for general stress/strain paths. Also a new theory of isotropic hyperelasticity has been proposed. The 'reversible' relative Cauchy stress tensor (of type (1,1) and weight one) is defined in the dragged along coordinates as a tensorial isotropic function of the Almansi tensor and of its invariants (through the partial derivatives of the actual scalar density of elastic energy per unit extent of dragged along coordinates). The correspondance between strain and stress paths is then defined in a general form which is particularly convenient for the study of first order effects, limit behaviours, coupling and second order effects. Illustrations are provided. The addition of the pure hysteresis stress contribution σ a and of the reversible contribution σ rev leads to a scheme of 'superelasticity' departure to obtain a provisional scheme of shape memory effects. Some remarks are given regarding some of the possible generalizations of the scheme. (orig./GL)
DEFF Research Database (Denmark)
Kolmogorov, Dmitry
turbine computations, collocated grid-based SIMPLE-like algorithms are developed for computations on block-structured grids with nonconformal interfaces. A technique to enhance both the convergence speed and the solution accuracy of the SIMPLE-like algorithms is presented. The erroneous behavior, which...... versions of the SIMPLE algorithm. The new technique is implemented in an existing conservative 2nd order finite-volume scheme flow solver (EllipSys), which is extended to cope with grids with nonconformal interfaces. The behavior of the discrete Navier-Stokes equations is discussed in detail...... Block LU relaxation scheme is shown to possess several optimal conditions, which enables to preserve high efficiency of the multigrid solver on both conformal and nonconformal grids. The developments are done using a parallel MPI algorithm, which can handle multiple numbers of interfaces with multiple...
Development of a high-order finite volume method with multiblock partition techniques
Directory of Open Access Journals (Sweden)
E. M. Lemos
2012-03-01
Full Text Available This work deals with a new numerical methodology to solve the Navier-Stokes equations based on a finite volume method applied to structured meshes with co-located grids. High-order schemes used to approximate advective, diffusive and non-linear terms, connected with multiblock partition techniques, are the main contributions of this paper. Combination of these two techniques resulted in a computer code that involves high accuracy due the high-order schemes and great flexibility to generate locally refined meshes based on the multiblock approach. This computer code has been able to obtain results with higher or equal accuracy in comparison with results obtained using classical procedures, with considerably less computational effort.
Directory of Open Access Journals (Sweden)
Fan Yuxin
2014-12-01
Full Text Available A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute transient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute inflation is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hilber–Hughes–Taylor (HHT time integration method is employed. For the fluid dynamic simulations, the Roe and HLLC (Harten–Lax–van Leer contact scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.
Finite volume gauge theory partition functions in three dimensions
International Nuclear Information System (INIS)
Szabo, Richard J.
2005-01-01
We determine the fermion mass dependence of Euclidean finite volume partition functions for three-dimensional QCD in the ε-regime directly from the effective field theory of the pseudo-Goldstone modes by using zero-dimensional non-linear σ-models. New results are given for an arbitrary number of flavours in all three cases of complex, pseudo-real and real fermions, extending some previous considerations based on random matrix theory. They are used to describe the microscopic spectral correlation functions and smallest eigenvalue distributions of the QCD 3 Dirac operator, as well as the corresponding massive spectral sum rules
International Nuclear Information System (INIS)
Ishiguro, Misako; Higuchi, Kenji
1983-01-01
The finite element method is applied in Galerkin-type approximation to three-dimensional neutron diffusion equations of fast reactors. A hexagonal element scheme is adopted for treating the hexagonal lattice which is typical for fast reactors. The validity of the scheme is verified by applying the scheme as well as alternative schemes to the neutron diffusion calculation of a gas-cooled fast reactor of actual scale. The computed results are compared with corresponding values obtained using the currently applied triangular-element and also with conventional finite difference schemes. The hexagonal finite element scheme is found to yield a reasonable solution to the problem taken up here, with some merit in terms of saving in computing time, but the resulting multiplication factor differs by 1% and the flux by 9% compared with the triangular mesh finite difference scheme. The finite element method, even in triangular element scheme, would appear to incur error in inadmissible amount and which could not be easily eliminated by refining the nodes. (author)
Enhanced finite difference scheme for the neutron diffusion equation using the importance function
International Nuclear Information System (INIS)
Vagheian, Mehran; Vosoughi, Naser; Gharib, Morteza
2016-01-01
Highlights: • An enhanced finite difference scheme for the neutron diffusion equation is proposed. • A seven-step algorithm is considered based on the importance function. • Mesh points are distributed through entire reactor core with respect to the importance function. • The results all proved that the proposed algorithm is highly efficient. - Abstract: Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function. In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in regions with greater neutron importance, density of mesh elements is higher than that in regions with less importance. The forward calculations are then performed for both of the uniform and improved non-uniform mesh point distributions and the results (the neutron fluxes along with the corresponding eigenvalues) for the two cases are compared with each other. The results are benchmarked against the reference values (with fine meshes) for Kang and Rod Bundle BWR benchmark problems. These benchmark cases revealed that the improved non-uniform mesh point distribution is highly efficient.
International Nuclear Information System (INIS)
Surya Mohan, P.; Tarvainen, Tanja; Schweiger, Martin; Pulkkinen, Aki; Arridge, Simon R.
2011-01-01
Highlights: → We developed a variable order global basis scheme to solve light transport in 3D. → Based on finite elements, the method can be applied to a wide class of geometries. → It is computationally cheap when compared to the fixed order scheme. → Comparisons with local basis method and other models demonstrate its accuracy. → Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P N approximation is compared against Monte Carlo simulations and other state-of-the-art methods.
Multichannel 1 → 2 transition amplitudes in a finite volume
Energy Technology Data Exchange (ETDEWEB)
Briceno, Raul A. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Hansen, Maxwell T. [Univ. of Washington, Seattle, WA (United States); Walker-Loud, Andre [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States)
2015-02-03
We perform a model-independent, non-perturbative investigation of two-point and three-point finite-volume correlation functions in the energy regime where two-particle states can go on-shell. We study three-point functions involving a single incoming particle and an outgoing two-particle state, relevant, for example, for studies of meson decays (e.g., B⁰ → K*l⁺l⁻) or meson photo production (e.g., πγ* → ππ). We observe that, while the spectrum solely depends upon the on-shell scattering amplitude, the correlation functions also depend upon off-shell amplitudes. The main result of this work is a non-perturbative generalization of the Lellouch-Luscher formula relating matrix elements of currents in finite and infinite spatial volumes. We extend that work by considering a theory with multiple, strongly-coupled channels and by accommodating external currents which inject arbitrary four-momentum as well as arbitrary angular-momentum. The result is exact up to exponentially suppressed corrections governed by the pion mass times the box size. We also apply our master equation to various examples, including two processes mentioned above as well as examples where the final state is an admixture of two open channels.
Secure diversity-multiplexing tradeoff of zero-forcing transmit scheme at finite-SNR
Rezki, Zouheir
2012-04-01
In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secrecy multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secrecy diversity gain estimates of ZF are derived. Through asymptotic analysis, we show that the upper bound underestimates the secrecy diversity gain, whereas the lower bound is tight at high-SNR, and thus its related diversity gain estimate is equal to the actual asymptotic secrecy diversity gain of the MIMO wiretap channel. © 2012 IEEE.
Development and application of a third order scheme of finite differences centered in mesh
International Nuclear Information System (INIS)
Delfin L, A.; Alonso V, G.; Valle G, E. del
2003-01-01
In this work the development of a third order scheme of finite differences centered in mesh is presented and it is applied in the numerical solution of those diffusion equations in multi groups in stationary state and X Y geometry. Originally this scheme was developed by Hennart and del Valle for the monoenergetic diffusion equation with a well-known source and they show that the one scheme is of third order when comparing the numerical solution with the analytical solution of a model problem using several mesh refinements and boundary conditions. The scheme by them developed it also introduces the application of numeric quadratures to evaluate the rigidity matrices and of mass that its appear when making use of the finite elements method of Galerkin. One of the used quadratures is the open quadrature of 4 points, no-standard, of Newton-Cotes to evaluate in approximate form the elements of the rigidity matrices. The other quadrature is that of 3 points of Radau that it is used to evaluate the elements of all the mass matrices. One of the objectives of these quadratures are to eliminate the couplings among the Legendre moments 0 and 1 associated to the left and right faces as those associated to the inferior and superior faces of each cell of the discretization. The other objective is to satisfy the particles balance in weighed form in each cell. In this work it expands such development to multiplicative means considering several energy groups. There are described diverse details inherent to the technique, particularly those that refer to the simplification of the algebraic systems that appear due to the space discretization. Numerical results for several test problems are presented and are compared with those obtained with other nodal techniques. (Author)
A finite area scheme for shallow granular flows on three-dimensional surfaces
Rauter, Matthias
2017-04-01
Shallow granular flow models have become a popular tool for the estimation of natural hazards, such as landslides, debris flows and avalanches. The shallowness of the flow allows to reduce the three-dimensional governing equations to a quasi two-dimensional system. Three-dimensional flow fields are replaced by their depth-integrated two-dimensional counterparts, which yields a robust and fast method [1]. A solution for a simple shallow granular flow model, based on the so-called finite area method [3] is presented. The finite area method is an adaption of the finite volume method [4] to two-dimensional curved surfaces in three-dimensional space. This method handles the three dimensional basal topography in a simple way, making the model suitable for arbitrary (but mildly curved) topography, such as natural terrain. Furthermore, the implementation into the open source software OpenFOAM [4] is shown. OpenFOAM is a popular computational fluid dynamics application, designed so that the top-level code mimics the mathematical governing equations. This makes the code easy to read and extendable to more sophisticated models. Finally, some hints on how to get started with the code and how to extend the basic model will be given. I gratefully acknowledge the financial support by the OEAW project "beyond dense flow avalanches". Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199, 177-215. Ferziger, J. & Peric, M. 2002 Computational methods for fluid dynamics, 3rd edn. Springer. Tukovic, Z. & Jasak, H. 2012 A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow. Computers & fluids 55, 70-84. Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics 12(6), 620-631.
Numerical investigation of finite-volume effects for the HVP
Boyle, Peter; Gülpers, Vera; Harrison, James; Jüttner, Andreas; Portelli, Antonin; Sachrajda, Christopher
2018-03-01
It is important to correct for finite-volume (FV) effects in the presence of QED, since these effects are typically large due to the long range of the electromagnetic interaction. We recently made the first lattice calculation of electromagnetic corrections to the hadronic vacuum polarisation (HVP). For the HVP, an analytical derivation of FV corrections involves a two-loop calculation which has not yet been carried out. We instead calculate the universal FV corrections numerically, using lattice scalar QED as an effective theory. We show that this method gives agreement with known analytical results for scalar mass FV effects, before applying it to calculate FV corrections for the HVP. This method for numerical calculation of FV effects is also widely applicable to quantities beyond the HVP.
Numerical investigation of finite-volume effects for the HVP
Directory of Open Access Journals (Sweden)
Boyle Peter
2018-01-01
Full Text Available It is important to correct for finite-volume (FV effects in the presence of QED, since these effects are typically large due to the long range of the electromagnetic interaction. We recently made the first lattice calculation of electromagnetic corrections to the hadronic vacuum polarisation (HVP. For the HVP, an analytical derivation of FV corrections involves a two-loop calculation which has not yet been carried out. We instead calculate the universal FV corrections numerically, using lattice scalar QED as an effective theory. We show that this method gives agreement with known analytical results for scalar mass FV effects, before applying it to calculate FV corrections for the HVP. This method for numerical calculation of FV effects is also widely applicable to quantities beyond the HVP.
SU(N) multi-Skyrmions at finite volume
Energy Technology Data Exchange (ETDEWEB)
Canfora, Fabrizio [Centro de Estudios Cientificos (CECS), Casilla, Valdivia (Chile); Di Mauro, Marco; Naddeo, Adele [Universita di Salerno, Dipartimento di Fisica ' ' E.R. Caianiello' ' , Fisciano, SA (Italy); Kurkov, Maxim A. [Universita di Napoli Federico II, Dipartimento di Matematica e Applicazioni ' ' R. Caccioppoli' ' , Napoli (Italy)
2015-09-15
We study multi-soliton solutions of the fourdimensional SU(N) Skyrme model by combining the hedgehog ansatz for SU(N) based on the harmonic maps of S{sup 2} into CP{sup N-1} and a geometrical trick which allows to analyze explicitly finite-volume effects without breaking the relevant symmetries of the ansatz. The geometric set-up allows to introduce a parameter which is related to the ft Hooft coupling of a suitable large N limit, in which N → ∞ and the curvature of the background metric approaches zero, in such a way that their product is constant. The relevance of such a parameter to the physics of the system is pointed out. In particular, we discuss how the discrete symmetries of the configurations depend on it. (orig.)
Finite volume model for two-dimensional shallow environmental flow
Simoes, F.J.M.
2011-01-01
This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.
International Nuclear Information System (INIS)
Khan, A.A.; Goeckeler, M.; Haegler, P.
2006-03-01
We present data for the axial coupling constant g A of the nucleon obtained in lattice QCD with two degenerate flavours of dynamical non-perturbatively improved Wilson quarks. The renormalisation is also performed non-perturbatively. For the analysis we give a chiral extrapolation formula for g A based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavours. Applying this formalism in a finite volume we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattice data in finite volume we are able to determine the axial coupling of the nucleon in the chiral limit without imposing the known value at the physical point. (Orig.)
Energy Technology Data Exchange (ETDEWEB)
Khan, A.A.; Goeckeler, M. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Haegler, P. [Technische Univ. Muenchen (DE). Physik-Department, Theoretische Physik] (and others)
2006-03-15
We present data for the axial coupling constant g{sub A} of the nucleon obtained in lattice QCD with two degenerate flavours of dynamical non-perturbatively improved Wilson quarks. The renormalisation is also performed non-perturbatively. For the analysis we give a chiral extrapolation formula for g{sub A} based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavours. Applying this formalism in a finite volume we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattice data in finite volume we are able to determine the axial coupling of the nucleon in the chiral limit without imposing the known value at the physical point. (Orig.)
Lu, Qiang; Han, Qing-Long; Zhang, Botao; Liu, Dongliang; Liu, Shirong
2017-12-01
This paper deals with the problem of environmental monitoring by developing an event-triggered finite-time control scheme for mobile sensor networks. The proposed control scheme can be executed by each sensor node independently and consists of two parts: one part is a finite-time consensus algorithm while the other part is an event-triggered rule. The consensus algorithm is employed to enable the positions and velocities of sensor nodes to quickly track the position and velocity of a virtual leader in finite time. The event-triggered rule is used to reduce the updating frequency of controllers in order to save the computational resources of sensor nodes. Some stability conditions are derived for mobile sensor networks with the proposed control scheme under both a fixed communication topology and a switching communication topology. Finally, simulation results illustrate the effectiveness of the proposed control scheme for the problem of environmental monitoring.
Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure
Szafran, J.; Juszczyk, K.; Kamiński, M.
2017-12-01
The main goal of this paper is to present coupled Computational Fluid Dynamics and structural analysis for the precise determination of wind impact on internal forces and deformations of structural elements of a longspan roof structure. The Finite Volume Method (FVM) serves for a solution of the fluid flow problem to model the air flow around the structure, whose results are applied in turn as the boundary tractions in the Finite Element Method problem structural solution for the linear elastostatics with small deformations. The first part is carried out with the use of ANSYS 15.0 computer system, whereas the FEM system Robot supports stress analysis in particular roof members. A comparison of the wind pressure distribution throughout the roof surface shows some differences with respect to that available in the engineering designing codes like Eurocode, which deserves separate further numerical studies. Coupling of these two separate numerical techniques appears to be promising in view of future computational models of stochastic nature in large scale structural systems due to the stochastic perturbation method.
Directory of Open Access Journals (Sweden)
G. F. Sun
2015-01-01
Full Text Available A novel explicit finite-difference (FD method is presented to simulate the positive and bounded development process of a microbial colony subjected to a substrate of nutrients, which is governed by a nonlinear parabolic partial differential equations (PDE system. Our explicit FD scheme is uniquely designed in such a way that it transfers the nonlinear terms in the original PDE into discrete sets of linear ones in the algebraic equation system that can be solved very efficiently, while ensuring the stability and the boundedness of the solution. This is achieved through (1 a proper design of intertwined FD approximations for the diffusion function term in both time and spatial variations and (2 the control of the time-step through establishing theoretical stability criteria. A detailed theoretical stability analysis is conducted to reveal that our FD method is indeed stable. Our examples verified the fact that the numerical solution can be ensured nonnegative and bounded to simulate the actual physics. Numerical examples have also been presented to demonstrate the efficiency of the proposed scheme. The present scheme is applicable for solving similar systems of PDEs in the investigation of the dynamics of biological films.
DEFF Research Database (Denmark)
Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter
2011-01-01
We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal......, whereas the convergence of the coefficients happens only with respect to the "volumetric" Lebesgue measure. Additionally, depending on whether the stationarity conditions are stated for the discretized or the original continuous problem, two distinct concepts of stationarity at a discrete level arise. We...... provide characterizations of limit points, with respect to FV mesh size, of globally optimal solutions and two types of stationary points to the discretized problems. We illustrate the practical behaviour of our cell-based FV discretization algorithm on a numerical example....
An efficient coupled polynomial interpolation scheme for shear mode sandwich beam finite element
Directory of Open Access Journals (Sweden)
Litesh N. Sulbhewar
Full Text Available An efficient piezoelectric sandwich beam finite element is presented here. It employs the coupled polynomial field interpolation scheme for field variables which incorporates electromechanical coupling at interpolation level itself; unlike conventional sandwich beam theory (SBT based formulations available in the literature. A variational formulation is used to derive the governing equations, which are used to establish the relationships between field variables. These relations lead to the coupled polynomial field descriptions of variables, unlike conventional SBT formulations which use assumed independent polynomials. The relative axial displacement is expressed only by coupled terms containing contributions from other mechanical and electrical variables, thus eliminating use of the transverse displacement derivative as a degree of freedom. A set of coupled shape function based on these polynomials has shown the improvement in the convergence characteristics of the SBT based formulation. This improvement in the performance is achieved with one nodal degree of freedom lesser than the conventional SBT formulations.
Symplectic finite element scheme: application to a driven problem with a regular singularity
Energy Technology Data Exchange (ETDEWEB)
Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-02-01
A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear `tent` elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs.
Symplectic finite element scheme: application to a driven problem with a regular singularity
International Nuclear Information System (INIS)
Pletzer, A.
1996-02-01
A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear 'tent' elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs
An enhanced finite volume method to model 2D linear elastic structures
CSIR Research Space (South Africa)
Suliman, Ridhwaan
2014-04-01
Full Text Available . Suliman) Preprint submitted to Applied Mathematical Modelling July 22, 2013 Keywords: finite volume, finite element, locking, error analysis 1. Introduction Since the 1960s, the finite element method has mainly been used for modelling the mechanics... formulation provides higher accuracy 2 for displacement solutions. It is well known that the linear finite element formulation suffers from sensitivity to element aspect ratio or shear locking when subjected to bend- ing [16]. Fallah [8] and Wheel [6] present...
Finite volume thermal-hydraulics and neutronics coupled calculations - 15300
International Nuclear Information System (INIS)
Araujo Silva, V.; Campagnole dos Santos, A.A.; Mesquit, A.Z.; Bernal, A.; Miro, R.; Verdu, G.; Pereira, C.
2015-01-01
The computational power available nowadays allows the coupling of neutronics and thermal-hydraulics codes for reactor studies. The present methodology foresees at least one constraint to the separated codes in order to perform coupled calculations: both codes must use the same geometry, however, meshes can be different for each code as long as the internal surfaces stays the same. Using the finite volume technique, a 3D diffusion nodal code was implemented to deal with neutron transport. This code can handle non-structured meshes which allows for complicated geometries calculations and therefore more flexibility. A computational fluid dynamics (CFD) code was used in order to obtain the same level of details for the thermal hydraulics calculations. The chosen code is OpenFOAM, an open-source CFD tool. Changes in OpenFOAM allow simple coupled calculations of a PWR fuel rod with neutron transport code. OpenFOAM sends coolant density information and fuel temperature to the neutron transport code that sends back power information. A mapping function is used to average values when one node in one side corresponds to many nodes in the other side. Data is exchanged between codes by library calls. As the results of a fuel rod calculations progress, more complicated and processing demanding geometries will be simulated, aiming to the simulation of a real scale PWR fuel assembly
1D and 2D Numerical Modeling for Solving Dam-Break Flow Problems Using Finite Volume Method
Directory of Open Access Journals (Sweden)
Szu-Hsien Peng
2012-01-01
Full Text Available The purpose of this study is to model the flow movement in an idealized dam-break configuration. One-dimensional and two-dimensional motion of a shallow flow over a rigid inclined bed is considered. The resulting shallow water equations are solved by finite volumes using the Roe and HLL schemes. At first, the one-dimensional model is considered in the development process. With conservative finite volume method, splitting is applied to manage the combination of hyperbolic term and source term of the shallow water equation and then to promote 1D to 2D. The simulations are validated by the comparison with flume experiments. Unsteady dam-break flow movement is found to be reasonably well captured by the model. The proposed concept could be further developed to the numerical calculation of non-Newtonian fluid or multilayers fluid flow.
Chronopoulos, D
2017-01-01
A systematic expression quantifying the wave energy skewing phenomenon as a function of the mechanical characteristics of a non-isotropic structure is derived in this study. A structure of arbitrary anisotropy, layering and geometric complexity is modelled through Finite Elements (FEs) coupled to a periodic structure wave scheme. A generic approach for efficiently computing the angular sensitivity of the wave slowness for each wave type, direction and frequency is presented. The approach does not involve any finite differentiation scheme and is therefore computationally efficient and not prone to the associated numerical errors. Copyright © 2016 Elsevier B.V. All rights reserved.
Hybrid finite-volume/transported PDF method for the simulation of turbulent reactive flows
Raman, Venkatramanan
A novel computational scheme is formulated for simulating turbulent reactive flows in complex geometries with detailed chemical kinetics. A Probability Density Function (PDF) based method that handles the scalar transport equation is coupled with an existing Finite Volume (FV) Reynolds-Averaged Navier-Stokes (RANS) flow solver. The PDF formulation leads to closed chemical source terms and facilitates the use of detailed chemical mechanisms without approximations. The particle-based PDF scheme is modified to handle complex geometries and grid structures. Grid-independent particle evolution schemes that scale linearly with the problem size are implemented in the Monte-Carlo PDF solver. A novel algorithm, in situ adaptive tabulation (ISAT) is employed to ensure tractability of complex chemistry involving a multitude of species. Several non-reacting test cases are performed to ascertain the efficiency and accuracy of the method. Simulation results from a turbulent jet-diffusion flame case are compared against experimental data. The effect of micromixing model, turbulence model and reaction scheme on flame predictions are discussed extensively. Finally, the method is used to analyze the Dow Chlorination Reactor. Detailed kinetics involving 37 species and 158 reactions as well as a reduced form with 16 species and 21 reactions are used. The effect of inlet configuration on reactor behavior and product distribution is analyzed. Plant-scale reactors exhibit quenching phenomena that cannot be reproduced by conventional simulation methods. The FV-PDF method predicts quenching accurately and provides insight into the dynamics of the reactor near extinction. The accuracy of the fractional time-stepping technique in discussed in the context of apparent multiple-steady states observed in a non-premixed feed configuration of the chlorination reactor.
Modelling of a 400 kW natural gas diffusion flame using finite-rate chemistry schemes
International Nuclear Information System (INIS)
Mueller, Christian; Kremer, Hans; Brink, Anders; Kilpinen, Pia; Hupa, Mikko
1999-01-01
The Eddy-Dissipation Combustion Model combined with three different reaction mechanisms is applied to simulate a fuel-rich 400 kW natural gas diffusion flame. The chemical schemes include a global 2-step and a global 4-step approach as well as a reduced 4-step mechanism systematically derived from an elementary scheme. The species and temperature distributions resulting from the different schemes are studied in detail and compared to each other and to experiments. Furthermore the method of implementing finite-rate chemistry to the Eddy-Dissipation Combustion Model is discussed. (author)
International Nuclear Information System (INIS)
Coelho, Pedro J.
2014-01-01
Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. - Highlights: • We survey recent advances in the discrete ordinates and finite volume methods. • Developments in spatial and angular discretization schemes are described. • Progress in solution algorithms and parallelization methods is reviewed. • Advances in the transient solution of the radiative transfer equation are appraised. • Non-gray media and variable refractive index media are briefly addressed
International Nuclear Information System (INIS)
Xi Li-Ying; Chen Huan-Ming; Zheng Fu; Gao Hua; Tong Yang; Ma Zhi
2015-01-01
Three-dimensional simulations of ferroelectric hysteresis and butterfly loops are carried out based on solving the time dependent Ginzburg–Landau equations using a finite volume method. The influence of externally mechanical loadings with a tensile strain and a compressive strain on the hysteresis and butterfly loops is studied numerically. Different from the traditional finite element and finite difference methods, the finite volume method is applicable to simulate the ferroelectric phase transitions and properties of ferroelectric materials even for more realistic and physical problems. (paper)
De Hon, B. P.; Arnold, J. M.
2016-01-01
Time-domain 3-D lattice Green's function (LGF) sequences can be evaluated using a single-lattice point recurrence scheme, and play an important role in finite-difference Green's function diakoptics. Asymptotically, at large distances, the LGFs in three dimensions can be described in terms of six
Finite elements volumes methods: applications to the Navier-Stokes equations and convergence results
International Nuclear Information System (INIS)
Emonot, P.
1992-01-01
In the first chapter are described the equations modeling incompressible fluid flow and a quick presentation of finite volumes method. The second chapter is an introduction to the finite elements volumes method. The box model is described and a method adapted to Navier-Stokes problems is proposed. The third chapter shows a fault analysis of the finite elements volumes method for the Laplacian problem and some examples in one, two, three dimensional calculations. The fourth chapter is an extension of the error analysis of the method for the Navier-Stokes problem
Simulations of viscous and compressible gas-gas flows using high-order finite difference schemes
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.
International Nuclear Information System (INIS)
Tan, Sirui; Huang, Lianjie
2014-01-01
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 a 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
Czech Academy of Sciences Publication Activity Database
Berezovski, A.; Kolman, Radek; Blažek, Jiří; Kopačka, Ján; Gabriel, Dušan; Plešek, Jiří
2014-01-01
Roč. 19, č. 12 (2014) ISSN 1435-4934. [European Conference on Non-Destructive Testing (ECNDT 2014) /11./. Praha, 06.10.2014-10.10.2014] R&D Projects: GA ČR(CZ) GAP101/11/0288; GA ČR(CZ) GAP101/12/2315 Institutional support: RVO:61388998 Keywords : elastic wave propagation * finite element method * isogeometric analysis * finite volume method * stress discontinuities * spurious oscillations Subject RIV: JR - Other Machinery http://www.ndt.net/events/ECNDT2014/app/content/Paper/25_Berezovski_Rev1.pdf
An enhanced matrix-free edge-based finite volume approach to model structures
CSIR Research Space (South Africa)
Suliman, Ridhwaan
2010-01-01
Full Text Available application to a number of test-cases. As will be demonstrated, the finite volume approach exhibits distinct advantages over the Q4 finite element formulation. This provides an alternative approach to the analysis of solid mechanics and allows...
A finite volume procedure for fluid flow, heat transfer and solid-body stress analysis
Jagad, P. I.; Puranik, B. P.; Date, A. W.
2018-01-01
A unified cell-centered unstructured mesh finite volume procedure is presented for fluid flow, heat transfer and solid-body stress analysis. An in-house procedure (A. W. Date, Solution of Transport Equations on Unstructured Meshes with Cell
Volume changes in hydrogels subjected to finite deformations
DEFF Research Database (Denmark)
Drozdov, Aleksey; Christiansen, Jesper de Claville
2013-01-01
Constitutive equations are derived for the elastic response of hydrogels under an arbitrary deformationwith finite strains. An expression is proposed for the free energy density of a hydrogel based on the Floryconcept of a network of flexible chains with constrained junctions whose reference conf...
Al Jarro, Ahmed; Salem, Mohamed; Bagci, Hakan; Benson, Trevor; Sewell, Phillip D.; Vuković, Ana
2012-01-01
An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.
Al Jarro, Ahmed
2012-11-01
An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.
Modified pause schemes and working days for more volume flexibility in manufactering
Rhijn, G.; Looze, M. de; Bosch, T.
2005-01-01
The effects of two measures to increase the volume flexibility, namely the introduction of an alternating pause scheme and the elongation of the working day, were evaluated in two manufacturing companies. Both measures led to an increase in volume output of about 16% at relatively low costs. The
Glazyrina, O. V.; Pavlova, M. F.
2016-11-01
We consider the parabolic inequality with monotone with respect to a gradient space operator, which is depended on integral with respect to space variables solution characteristic. We construct a two-layer differential scheme for this problem with use of penalty method, semidiscretization with respect to time variable method and the finite element method (FEM) with respect to space variables. We proved a convergence of constructed mothod.
International Nuclear Information System (INIS)
Amaziane, Brahim; Bourgeois, Marc; El Fatini, Mohamed
2014-01-01
In this paper, we consider adaptive numerical simulation of miscible displacement problems in porous media, which are modeled by single phase flow equations. A vertex-centred finite volume method is employed to discretize the coupled system: the Darcy flow equation and the diffusion-convection concentration equation. The convection term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion-dispersion term is discretized by piecewise linear conforming finite elements. We introduce two kinds of indicators, both of them of residual type. The first one is related to time discretization and is local with respect to the time discretization: thus, at each time, it provides an appropriate information for the choice of the next time step. The second is related to space discretization and is local with respect to both the time and space variable and the idea is that at each time it is an efficient tool for mesh adaptivity. An error estimation procedure evaluates where additional refinement is needed and grid generation procedures dynamically create or remove fine-grid patches as resolution requirements change. The method was implemented in the software MELODIE, developed by the French Institute for Radiological Protection and Nuclear Safety (IRSN, Institut de Radioprotection et de Surete Nucleaire). The algorithm is then used to simulate the evolution of radionuclide migration from the waste packages through a heterogeneous disposal, demonstrating its capability to capture complex behavior of the resulting flow. (authors)
Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid
Moatssime, H. Al; Esselaoui, D.; Hakim, A.; Raghay, S.
2001-08-01
This paper reports on a numerical algorithm for the steady flow of viscoelastic fluid. The conservative and constitutive equations are solved using the finite volume method (FVM) with a hybrid scheme for the velocities and first-order upwind approximation for the viscoelastic stress. A non-uniform staggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebraic equations over the flow domain are solved iteratively by the symmetrical coupled Gauss-Seidel (SCGS) method. In both, the full approximation storage (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contraction at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid refinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright
Large parallel volumes of finite and compact sets in d-dimensional Euclidean space
DEFF Research Database (Denmark)
Kampf, Jürgen; Kiderlen, Markus
The r-parallel volume V (Cr) of a compact subset C in d-dimensional Euclidean space is the volume of the set Cr of all points of Euclidean distance at most r > 0 from C. According to Steiner’s formula, V (Cr) is a polynomial in r when C is convex. For finite sets C satisfying a certain geometric...
The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment
Energy Technology Data Exchange (ETDEWEB)
Long, Wen; Yang, Zhaoqing; Copping, Andrea E.; Jung, Ki Won; Deng, Zhiqun
2015-10-28
: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3D sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.
Finite volume effects on the electric polarizability of neutral hadrons in lattice QCD
Lujan, M.; Alexandru, A.; Freeman, W.; Lee, F. X.
2016-10-01
We study the finite volume effects on the electric polarizability for the neutron, neutral pion, and neutral kaon using eight dynamically generated two-flavor nHYP-clover ensembles at two different pion masses: 306(1) and 227(2) MeV. An infinite volume extrapolation is performed for each hadron at both pion masses. For the neutral kaon, finite volume effects are relatively mild. The dependence on the quark mass is also mild, and a reliable chiral extrapolation can be performed along with the infinite volume extrapolation. Our result is αK0 phys=0.356 (74 )(46 )×10-4 fm3 . In contrast, for neutron, the electric polarizability depends strongly on the volume. After removing the finite volume corrections, our neutron polarizability results are in good agreement with chiral perturbation theory. For the connected part of the neutral pion polarizability, the negative trend persists, and it is not due to finite volume effects but likely sea quark charging effects.
A simple finite-difference scheme for handling topography with the first-order wave equation
Mulder, W.A.; Huiskes, M.J.
2017-01-01
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
A simple finite-difference scheme for handling topography with the second-order wave equation
Mulder, W.A.
2017-01-01
The presence of topography poses a challenge for seismic modeling with finite-difference codes. The representation of topography by means of an air layer or vacuum often leads to a substantial loss of numerical accuracy. A suitable modification of the finite-difference weights near the free
Finite-volume spectra of the Lee-Yang model
Energy Technology Data Exchange (ETDEWEB)
Bajnok, Zoltan [MTA Lendület Holographic QFT Group, Wigner Research Centre for Physics,H-1525 Budapest 114, P.O.B. 49 (Hungary); Deeb, Omar el [MTA Lendület Holographic QFT Group, Wigner Research Centre for Physics,H-1525 Budapest 114, P.O.B. 49 (Hungary); Physics Department, Faculty of Science, Beirut Arab University (BAU),Beirut (Lebanon); Pearce, Paul A. [School of Mathematics and Statistics, University of Melbourne,Parkville, Victoria 3010 (Australia)
2015-04-15
We consider the non-unitary Lee-Yang minimal model M(2,5) in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels (r,s)=(1,1),(1,2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ{sub 1,3} integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ{sub 1,3} integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A{sub 4} RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of (m,n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.
Syrakos, Alexandros; Varchanis, Stylianos; Dimakopoulos, Yannis; Goulas, Apostolos; Tsamopoulos, John
2017-12-01
Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM.
Kim, Jae Wook
2013-05-01
This paper proposes a novel systematic approach for the parallelization of pentadiagonal compact finite-difference schemes and filters based on domain decomposition. The proposed approach allows a pentadiagonal banded matrix system to be split into quasi-disjoint subsystems by using a linear-algebraic transformation technique. As a result the inversion of pentadiagonal matrices can be implemented within each subdomain in an independent manner subject to a conventional halo-exchange process. The proposed matrix transformation leads to new subdomain boundary (SB) compact schemes and filters that require three halo terms to exchange with neighboring subdomains. The internode communication overhead in the present approach is equivalent to that of standard explicit schemes and filters based on seven-point discretization stencils. The new SB compact schemes and filters demand additional arithmetic operations compared to the original serial ones. However, it is shown that the additional cost becomes sufficiently low by choosing optimal sizes of their discretization stencils. Compared to earlier published results, the proposed SB compact schemes and filters successfully reduce parallelization artifacts arising from subdomain boundaries to a level sufficiently negligible for sophisticated aeroacoustic simulations without degrading parallel efficiency. The overall performance and parallel efficiency of the proposed approach are demonstrated by stringent benchmark tests.
A finite volume method for cylindrical heat conduction problems based on local analytical solution
Li, Wang
2012-10-01
A new finite volume method for cylindrical heat conduction problems based on local analytical solution is proposed in this paper with detailed derivation. The calculation results of this new method are compared with the traditional second-order finite volume method. The newly proposed method is more accurate than conventional ones, even though the discretized expression of this proposed method is slightly more complex than the second-order central finite volume method, making it cost more calculation time on the same grids. Numerical result shows that the total CPU time of the new method is significantly less than conventional methods for achieving the same level of accuracy. © 2012 Elsevier Ltd. All rights reserved.
A finite volume method for cylindrical heat conduction problems based on local analytical solution
Li, Wang; Yu, Bo; Wang, Xinran; Wang, Peng; Sun, Shuyu
2012-01-01
A new finite volume method for cylindrical heat conduction problems based on local analytical solution is proposed in this paper with detailed derivation. The calculation results of this new method are compared with the traditional second-order finite volume method. The newly proposed method is more accurate than conventional ones, even though the discretized expression of this proposed method is slightly more complex than the second-order central finite volume method, making it cost more calculation time on the same grids. Numerical result shows that the total CPU time of the new method is significantly less than conventional methods for achieving the same level of accuracy. © 2012 Elsevier Ltd. All rights reserved.
A General Finite Element Scheme for Limit State Analysis and Optimization
DEFF Research Database (Denmark)
Damkilde, Lars
1999-01-01
Limit State analysis which is based on a perfect material behaviour is used in many different applications primarily within Structural Engineering and Geotechnics. The calculation methods have not reached the same level of automation such as Finite Element Analysis for elastic structures....... The computer based systems are more ad hoc based and are typically not well-integrated with pre- and postprocessors well-known from commercial Finite Element codes.A finite element based formulation of limit state analysis is presented which allows an easy integration with standard Finite Element codes...... for elastic analysis. In this way the user is able to perform a limit state analysis on the same model used for elastic analysis only adding data for the yield surface.The method is based on the lower-bound theorem and uses stress-based elements with a linearized yield surface. The mathematical problem...
Mickens, Ronald E.
1989-01-01
A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.
Simulation of pore pressure accumulation under cyclic loading using Finite Volume Method
DEFF Research Database (Denmark)
Tang, Tian; Hededal, Ole
2014-01-01
This paper presents a finite volume implementation of a porous, nonlinear soil model capable of simulating pore pressure accumulation under cyclic loading. The mathematical formulations are based on modified Biot’s coupled theory by substituting the original elastic constitutive model...... with an advanced elastoplastic model suitable for describing monotonic as well as cyclic loading conditions. The finite volume method is applied to discretize these formulations. The resulting set of coupled nonlinear algebraic equations are then solved by a ’segregated’ solution procedure. An efficient return...
Hybrid Finite Element and Volume Integral Methods for Scattering Using Parametric Geometry
DEFF Research Database (Denmark)
Volakis, John L.; Sertel, Kubilay; Jørgensen, Erik
2004-01-01
n this paper we address several topics relating to the development and implementation of volume integral and hybrid finite element methods for electromagnetic modeling. Comparisons of volume integral equation formulations with the finite element-boundary integral method are given in terms of accu...... of vanishing divergence within the element but non-zero curl. In addition, a new domain decomposition is introduced for solving array problems involving several million degrees of freedom. Three orders of magnitude CPU reduction is demonstrated for such applications....
On a Stable and Consistent Finite Difference Scheme for a Time ...
African Journals Online (AJOL)
NJABS
established time independent Schrodinger Wave Equation (SWE). To develop the stability criterion .... the rate at which signals in the numerical scheme travel will be faster than their real world counterparts and this unrealistic expectation leads ...
Rezki, Zouheir
2011-06-01
In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secret multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secret diversity gain estimates of ZF are derived. Through asymptotic analysis, we show that the upper bound underestimates the secret diversity gain, whereas the lower bound is tight at high-SNR, and thus its related diversity gain estimate is equal to the actual asymptotic secret diversity gain of the Multiple-Input Multiple-Output (MIMO) wiretap channel. © 2011 IEEE.
International Nuclear Information System (INIS)
Galán, J; Verleysen, P; Lebensohn, R A
2014-01-01
A new algorithm for the solution of the deformation of a polycrystalline material using a self-consistent scheme, and its integration as part of the finite element software Abaqus/Standard are presented. The method is based on the original VPSC formulation by Lebensohn and Tomé and its integration with Abaqus/Standard by Segurado et al. The new algorithm has been implemented as a set of Fortran 90 modules, to be used either from a standalone program or from Abaqus subroutines. The new implementation yields the same results as VPSC7, but with a significantly better performance, especially when used in multicore computers. (paper)
A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene
International Nuclear Information System (INIS)
Brinkman, D.; Heitzinger, C.; Markowich, P.A.
2014-01-01
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 convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene
Brinkman, Daniel; Heitzinger, Clemens Heitzinger; Markowich, Peter A.
2014-01-01
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. © 2013 Elsevier Inc.
Daude, F.; Galon, P.
2018-06-01
A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.
Sensitivity analyses on natural convection in an 8:1 tall enclosure using finite-volume methods
International Nuclear Information System (INIS)
Ambrosini, Walter; Forgione, N.; Ferreri, Juan C.
2004-01-01
Full text: The results herein presented are an extension of those obtained in previous work by the Authors in a benchmark problem dealing with flow driven by buoyancy in an 8:1 tall enclosure. A simple finite-volume model purposely set up for this application has provided the preliminary results reported. The adopted modeling technique was a direct extension of the one previously adopted by the Authors to deal with single-phase natural convection and boiling channel instabilities. This extension to two-dimensional flow is based on a finite-volume scheme using first order approximation in time and space. Despite its simplicity, results were reasonably good and detected the flow instabilities due to proper selection of cell Courant number and a semi-implicit solution algorithm. In this paper, results using the same code with different discretisations are presented in a more detailed way and are further discussed. They show proper capture of all the main characteristics of the flow, also reported by other authors and considered as 'converged' solutions. Results show that, as expected, first order explicit or semi-implicit methods can be considered reliable tools when dealing with stability problems, if properly used. Some initial results obtained using a second order upwind method are also presented for the purpose of comparison. Additionally, results obtained using a commercial code (FLUENT) are also reported. (author)
A novel 2.5D finite difference scheme for simulations of resistivity logging in anisotropic media
Zeng, Shubin; Chen, Fangzhou; Li, Dawei; Chen, Ji; Chen, Jiefu
2018-03-01
The objective of this study is to develop a method to model 3D resistivity well logging problems in 2D formation with anisotropy, known as 2.5D modeling. The traditional 1D forward modeling extensively used in practice lacks the capability of modeling 2D formation. A 2.5D finite difference method (FDM) solving all the electric and magnetic field components simultaneously is proposed. Compared to other previous 2.5D FDM schemes, this method is more straightforward in modeling fully anisotropic media and easy to be implemented. Fourier transform is essential to this FDM scheme, and by employing Gauss-Legendre (GL) quadrature rule the computational time of this step can be greatly reduced. In the numerical examples, we first demonstrate the validity of the FDM scheme with GL rule by comparing with 1D forward modeling for layered anisotropic problems, and then we model a complicated 2D formation case and find that the proposed 2.5D FD scheme is much more efficient than 3D numerical methods.
Secure diversity-multiplexing tradeoff of zero-forcing transmit scheme at finite-SNR
Rezki, Zouheir; Alouini, Mohamed-Slim
2012-01-01
information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secrecy multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under
Investigation of the factorization scheme dependence of finite order perturbative QCD calculations
Czech Academy of Sciences Publication Activity Database
Kolář, Karel
-, č. 11 (2011), 005/1-005/44 ISSN 1126-6708 R&D Projects: GA MŠk LC527 Institutional research plan: CEZ:AV0Z10100502 Keywords : QCD * parton distribution functions * factorization schemes * NLO Monte Carlo event generators Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 5.831, year: 2011
Finite-volume effects due to spatially non-local operators arXiv
Briceño, Raúl A.; Hansen, Maxwell T.; Monahan, Christopher J.
Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. To quote credible estimates of the systematic uncertainties in these calculations, one must understand, among other things, the size of the finite-volume effects when such matrix elements are extracted from numerical lattice calculations. In this work, we estimate finite-volume effects for matrix elements of non-local operators, composed of two currents displaced in a spatial direction by a distance $\\xi$. We find that the finite-volume corrections depend on the details of the matrix element. If the external state is the lightest degree of freedom in the theory, e.g.~the pion in QCD, then the volume corrections scale as $ e^{-m_\\pi (L- \\xi)} $, where $m_\\pi$ is the mass of the light state. For heavier external states the usual $e^{- m_\\pi L}$ form is recovered, but with a polynomial prefactor of the form $L^m/|L - \\xi|^n$ that can lead to enhanced volume effects. These ...
Energy Technology Data Exchange (ETDEWEB)
Karlsen, Kenneth Hvistendal; Risebro, Nils Henrik
2000-09-01
We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a ''rough'' coefficient function k(x). we show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, k' is in BV, thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion equations as well as new convergence results for their finite difference approximations. In the inviscid case, we also provide a rate of convergence. Our convergence proofs are based on deriving a series of a priori estimates and using a general L{sup p} compactness criterion. (author)
Directory of Open Access Journals (Sweden)
Litesh N. Sulbhewar
Full Text Available The convergence characteristic of the conventional two-noded Euler-Bernoulli piezoelectric beam finite element depends on the configuration of the beam cross-section. The element shows slower convergence for the asymmetric material distribution in the beam cross-section due to 'material-locking' caused by extension-bending coupling. Hence, the use of conventional Euler-Bernoulli beam finite element to analyze piezoelectric beams which are generally made of the host layer with asymmetrically surface bonded piezoelectric layers/patches, leads to increased computational effort to yield converged results. Here, an efficient coupled polynomial interpolation scheme is proposed to improve the convergence of the Euler-Bernoulli piezoelectric beam finite elements, by eliminating ill-effects of material-locking. The equilibrium equations, derived using a variational formulation, are used to establish relationships between field variables. These relations are used to find a coupled quadratic polynomial for axial displacement, having contributions from an assumed cubic polynomial for transverse displacement and assumed linear polynomials for layerwise electric potentials. A set of coupled shape functions derived using these polynomials efficiently handles extension-bending and electromechanical couplings at the field interpolation level itself in a variationally consistent manner, without increasing the number of nodal degrees of freedom. The comparison of results obtained from numerical simulation of test problems shows that the convergence characteristic of the proposed element is insensitive to the material configuration of the beam cross-section.
A simple finite-difference scheme for handling topography with the first-order wave equation
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.
International Nuclear Information System (INIS)
Hees, Hendrik van; Knoll, Joern
2002-01-01
The theoretical concepts for the renormalization of self-consistent Dyson resummations, devised in the first paper of this series, are applied to first example cases of φ 4 theory. In addition to the tadpole (Hartree) approximation, as a novel part the numerical solutions are presented, which include the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or the two-particle irreducible effective action concept
International Nuclear Information System (INIS)
Hees, H. van; Knoll, J.
2001-01-01
The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the φ 4 -theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or 2PI effective action concept. (orig.)
Extrusion Process by Finite Volume Method Using OpenFoam Software
International Nuclear Information System (INIS)
Matos Martins, Marcelo; Tonini Button, Sergio; Divo Bressan, Jose; Ivankovic, Alojz
2011-01-01
The computational codes are very important tools to solve engineering problems. In the analysis of metal forming process, such as extrusion, this is not different because the computational codes allow analyzing the process with reduced cost. Traditionally, the Finite Element Method is used to solve solid mechanic problems, however, the Finite Volume Method (FVM) have been gaining force in this field of applications. This paper presents the velocity field and friction coefficient variation results, obtained by numerical simulation using the OpenFoam Software and the FVM to solve an aluminum direct cold extrusion process.
International Nuclear Information System (INIS)
Gazdallah, Moncef; Feldheim, Véronique; Claramunt, Kilian; Hirsch, Charles
2012-01-01
This paper presents the implementation of the finite volume method to solve the radiative transfer equation in a commercial code. The particularity of this work is that the method applied on unstructured hexahedral meshes does not need a pre-processing step establishing a particular marching order to visit all the control volumes. The solver simply visits the faces of the control volumes as numbered in the hexahedral unstructured mesh. A cell centred mesh and a spatial differencing step scheme to relate facial radiative intensities to nodal intensities is used. The developed computer code based on FVM has been integrated in the CFD solver FINE/Open from NUMECA Int. Radiative heat transfer can be evaluated within systems containing uniform, grey, emitting, absorbing and/or isotropically or linear anisotropically scattering medium bounded by diffuse grey walls. This code has been validated for three test cases. The first one is a three dimensional rectangular enclosure filled with emitting, absorbing and anisotropically scattering media. The second is the differentially heated cubic cavity. The third one is the L-shaped enclosure. For these three test cases a good agreement has been observed when temperature and heat fluxes predictions are compared with references taken, from literature.
Homogenization of Periodic Masonry Using Self-Consistent Scheme and Finite Element Method
Kumar, Nitin; Lambadi, Harish; Pandey, Manoj; Rajagopal, Amirtham
2016-01-01
Masonry is a heterogeneous anisotropic continuum, made up of the brick and mortar arranged in a periodic manner. Obtaining the effective elastic stiffness of the masonry structures has been a challenging task. In this study, the homogenization theory for periodic media is implemented in a very generic manner to derive the anisotropic global behavior of the masonry, through rigorous application of the homogenization theory in one step and through a full three-dimensional behavior. We have considered the periodic Eshelby self-consistent method and the finite element method. Two representative unit cells that represent the microstructure of the masonry wall exactly are considered for calibration and numerical application of the theory.
Lattice study of finite volume effect in HVP for muon g-2
Directory of Open Access Journals (Sweden)
Izubuchi Taku
2018-01-01
Full Text Available We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp,in lattice QCD by comparison with two different volumes, L4 = (5.44 and (8.14 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a−1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.
Lattice study of finite volume effect in HVP for muon g-2
Izubuchi, Taku; Kuramashi, Yoshinobu; Lehner, Christoph; Shintani, Eigo
2018-03-01
We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp, in lattice QCD by comparison with two different volumes, L4 = (5.4)4 and (8.1)4 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a-1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.
Directory of Open Access Journals (Sweden)
Huawei Zhou
2016-10-01
Full Text Available Achieving an effective combination of various temperature control measures is critical for temperature control and crack prevention of concrete dams. This paper presents a procedure for optimizing the temperature control scheme of roller compacted concrete (RCC dams that couples the finite element method (FEM with a sensitivity analysis method. In this study, seven temperature control schemes are defined according to variations in three temperature control measures: concrete placement temperature, water-pipe cooling time, and thermal insulation layer thickness. FEM is employed to simulate the equivalent temperature field and temperature stress field obtained under each of the seven designed temperature control schemes for a typical overflow dam monolith based on the actual characteristics of a RCC dam located in southwestern China. A sensitivity analysis is subsequently conducted to investigate the degree of influence each of the three temperature control measures has on the temperature field and temperature tensile stress field of the dam. Results show that the placement temperature has a substantial influence on the maximum temperature and tensile stress of the dam, and that the placement temperature cannot exceed 15 °C. The water-pipe cooling time and thermal insulation layer thickness have little influence on the maximum temperature, but both demonstrate a substantial influence on the maximum tensile stress of the dam. The thermal insulation thickness is significant for reducing the probability of cracking as a result of high thermal stress, and the maximum tensile stress can be controlled under the specification limit with a thermal insulation layer thickness of 10 cm. Finally, an optimized temperature control scheme for crack prevention is obtained based on the analysis results.
International Nuclear Information System (INIS)
Saha Ray, S.; Patra, A.
2012-01-01
Highlights: ► In this paper fractional neutron point kinetic equation has been analyzed. ► The numerical solution for fractional neutron point kinetic equation is obtained. ► Explicit Finite Difference Method has been applied. ► Supercritical reactivity, critical reactivity and subcritical reactivity analyzed. ► Comparison between fractional and classical neutron density is presented. - Abstract: In the present article, a numerical procedure to efficiently calculate the solution for fractional point kinetics equation in nuclear reactor dynamics is investigated. The Explicit Finite Difference Method is applied to solve the fractional neutron point kinetic equation with the Grunwald–Letnikov (GL) definition (). Fractional Neutron Point Kinetic Model has been analyzed for the dynamic behavior of the neutron motion in which the relaxation time associated with a variation in the neutron flux involves a fractional order acting as exponent of the relaxation time, to obtain the best operation of a nuclear reactor dynamics. Results for neutron dynamic behavior for subcritical reactivity, supercritical reactivity and critical reactivity and also for different values of fractional order have been presented and compared with the classical neutron point kinetic (NPK) equation as well as the results obtained by the learned researchers .
Directory of Open Access Journals (Sweden)
Mohammad Iranmanesh
2014-12-01
Full Text Available Many standard brands sell products under the volume discount scheme (VDS as more and more consumers are fond of purchasing products under this scheme. Despite volume discount being commonly practiced, there is a dearth of research, both conceptual and empirical, focusing on purchase characteristics factors and consumer internal evaluation concerning the purchase of products under VDS. To attempt to fill this void, this article develops a conceptual model on VDS with the intention of delineating the influence of the purchase characteristics factors on the consumer intention to purchase products under VDS and provides an explanation of their effects through consumer internal evaluation. Finally, the authors discuss the managerial implications of their research and offer guidelines for future empirical research.
Energy Technology Data Exchange (ETDEWEB)
Delcourte, S
2007-09-15
We aim to develop a finite volume method which applies to a greater class of meshes than other finite volume methods, restricted by orthogonality constraints. We build discrete differential operators over the three staggered tessellations needed for the construction of the method. These operators verify some analogous properties to those of the continuous operators. At first, the method is applied to the Div-Curl problem, which can be viewed as a building block of the Stokes problem. Then, the Stokes problem is dealt with with various boundary conditions. It is well known that when the computational domain is polygonal and non-convex, the order of convergence of numerical methods is deteriorated. Consequently, we have studied how an appropriate local refinement is able to restore the optimal order of convergence for the Laplacian problem. At last, we have discretized the non-linear Navier-Stokes problem, using the rotational formulation of the convection term, associated to the Bernoulli pressure. With an iterative algorithm, we are led to solve a saddle-point problem at each iteration. We give a particular interest to this linear problem by testing some pre-conditioners issued from finite elements, which we adapt to our method. Each problem is illustrated by numerical results on arbitrary meshes, such as strongly non-conforming meshes. (author)
Directory of Open Access Journals (Sweden)
Andranik Tsakanian
2012-05-01
Full Text Available In particle accelerators a preferred direction, the direction of motion, is well defined. If in a numerical calculation the (numerical dispersion in this direction is suppressed, a quite coarse mesh and moderate computational resources can be used to reach accurate results even for extremely short electron bunches. Several approaches have been proposed in the past decades to reduce the accumulated dispersion error in wakefield calculations for perfectly conducting structures. In this paper we extend the TE/TM splitting algorithm to a new hybrid scheme that allows for wakefield calculations in structures with walls of finite conductivity. The conductive boundary is modeled by one-dimensional wires connected to each boundary cell. A good agreement of the numerical simulations with analytical results and other numerical approaches is obtained.
International Nuclear Information System (INIS)
Akeju, T.A.I.; Kelly, D.W.; Zienkiewicz, O.C.; Kanaka Raju, K.
1981-01-01
The eigenvalue equations governing the free vibration of axisymmetric solids are derived by means of a semi-analytical finite element scheme. In particular we investigated the use of an 8-node solid element in structures which exhibit a 'shell-like' behaviour. Bathe-Wilson subspace iteration algorithm is employed for the solution of the equations. The element is shown to give good results for beam and shell vibration problems. It is also utilised to solve a complex solid in the form of an internal component of a modern jet engine. This particular application is of considerable practical importance as the dynamics of such components form a dominant design constraint. (orig./HP)
Czech Academy of Sciences Publication Activity Database
Marcinkowski, L.; Rahman, T.; Loneland, A.; Valdman, Jan
2016-01-01
Roč. 56, č. 3 (2016), s. 967-993 ISSN 0006-3835 R&D Projects: GA ČR GA13-18652S Institutional support: RVO:67985556 Keywords : Domain decomposition * Additive Schwarz method * Finite volume element * GMRES Subject RIV: BA - General Mathematics Impact factor: 1.670, year: 2016 http://library.utia.cas.cz/separaty/2015/MTR/valdman-0447835.pdf
Application of the finite volume method in the simulation of saturated flows of binary mixtures
International Nuclear Information System (INIS)
Murad, M.A.; Gama, R.M.S. da; Sampaio, R.
1989-12-01
This work presents the simulation of saturated flows of an incompressible Newtonian fluid through a rigid, homogeneous and isotropic porous medium. The employed mathematical model is derived from the Continuum Theory of Mixtures and generalizes the classical one which is based on Darcy's Law form of the momentum equation. In this approach fluid and porous matrix are regarded as continuous constituents of a binary mixture. The finite volume method is employed in the simulation. (author) [pt
New finite volume methods for approximating partial differential equations on arbitrary meshes
International Nuclear Information System (INIS)
Hermeline, F.
2008-12-01
This dissertation presents some new methods of finite volume type for approximating partial differential equations on arbitrary meshes. The main idea lies in solving twice the problem to be dealt with. One addresses the elliptic equations with variable (anisotropic, antisymmetric, discontinuous) coefficients, the parabolic linear or non linear equations (heat equation, radiative diffusion, magnetic diffusion with Hall effect), the wave type equations (Maxwell, acoustics), the elasticity and Stokes'equations. Numerous numerical experiments show the good behaviour of this type of method. (author)
Energy Technology Data Exchange (ETDEWEB)
Ju, Lili; Tian, Li; Wang, Desheng
2008-10-31
In this paper, we present a residual-based a posteriori error estimate for the finite volume discretization of steady convection– diffusion–reaction equations defined on surfaces in R3, which are often implicitly represented as level sets of smooth functions. Reliability and efficiency of the proposed a posteriori error estimator are rigorously proved. Numerical experiments are also conducted to verify the theoretical results and demonstrate the robustness of the error estimator.
A spatial discretization of the MHD equations based on the finite volume - spectral method
International Nuclear Information System (INIS)
Miyoshi, Takahiro
2000-05-01
Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA φ , is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)
An efficicient data structure for three-dimensional vertex based finite volume method
Akkurt, Semih; Sahin, Mehmet
2017-11-01
A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.
Kiessling, Jonas
2014-05-06
Option prices in exponential Lévy models solve certain partial integro-differential equations. This work focuses on developing novel, computable error approximations for a finite difference scheme that is suitable for solving such PIDEs. The scheme was introduced in (Cont and Voltchkova, SIAM J. Numer. Anal. 43(4):1596-1626, 2005). The main results of this work are new estimates of the dominating error terms, namely the time and space discretisation errors. In addition, the leading order terms of the error estimates are determined in a form that is more amenable to computations. The payoff is only assumed to satisfy an exponential growth condition, it is not assumed to be Lipschitz continuous as in previous works. If the underlying Lévy process has infinite jump activity, then the jumps smaller than some (Formula presented.) are approximated by diffusion. The resulting diffusion approximation error is also estimated, with leading order term in computable form, as well as the dependence of the time and space discretisation errors on this approximation. Consequently, it is possible to determine how to jointly choose the space and time grid sizes and the cut off parameter (Formula presented.). © 2014 Springer Science+Business Media Dordrecht.
An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation
Zhan, Ge
2013-02-19
The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward-backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. © 2013 Sinopec Geophysical Research Institute.
An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation
International Nuclear Information System (INIS)
Zhan, Ge; Pestana, Reynam C; Stoffa, Paul L
2013-01-01
The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward–backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. (paper)
The low-energy effective theory of QCD at small quark masses in a finite volume
Energy Technology Data Exchange (ETDEWEB)
Lehner, Christoph
2010-01-15
At low energies the theory of quantum chromodynamics (QCD) can be described effectively in terms of the lightest particles of the theory, the pions. This approximation is valid for temperatures well below the mass difference of the pions to the next heavier particles. We study the low-energy effective theory at very small quark masses in a finite volume V. The corresponding perturbative expansion in 1/{radical}(V) is called {epsilon} expansion. At each order of this expansion a finite number of low-energy constants completely determine the effective theory. These low-energy constants are of great phenomenological importance. In the leading order of the {epsilon} expansion, called {epsilon} regime, the theory becomes zero-dimensional and is therefore described by random matrix theory (RMT). The dimensionless quantities of RMT are mapped to dimensionful quantities of the low-energy effective theory using the leading-order lowenergy constants {sigma} and F. In this way {sigma} and F can be obtained from lattice QCD simulations in the '' regime by a fit to RMT predictions. For typical volumes of state-of-the-art lattice QCD simulations, finite-volume corrections to the RMT prediction cannot be neglected. These corrections can be calculated in higher orders of the {epsilon} expansion. We calculate the finite-volume corrections to {sigma} and F at next-to-next-to-leading order in the {epsilon} expansion. We also discuss non-universal modifications of the theory due to the finite volume. These results are then applied to lattice QCD simulations, and we extract {sigma} and F from eigenvalue correlation functions of the Dirac operator. As a side result, we provide a proof of equivalence between the parametrization of the partially quenched low-energy effective theory without singlet particle and that of the super-Riemannian manifold used earlier in the literature. Furthermore, we calculate a special version of the massless sunset diagram at finite volume without
Test Functions for Three-Dimensional Control-Volume Mixed Finite-Element Methods on Irregular Grids
National Research Council Canada - National Science Library
Naff, R. L; Russell, T. F; Wilson, J. D
2000-01-01
.... For control-volume mixed finite-element methods, vector shape functions are used to approximate the distribution of velocities across cells and vector test functions are used to minimize the error...
Solution of the square lid-driven cavity flow of a Bingham plastic using the finite volume method
Syrakos, Alexandros; Georgiou, Georgios C.; Alexandrou, Andreas N.
2016-01-01
We investigate the performance of the finite volume method in solving viscoplastic flows. The creeping square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by Papanastasiou [J. Rheol. 31 (1987) 385-404]. It is shown that the convergence rate of the standard SIMPLE pressure-correction algorithm, which is used to solve the algebraic equation system that is produced by the finite volume discretisation, severely det...
Finite spatial-volume effect for π-N sigma term in lattice QCD
International Nuclear Information System (INIS)
Fukushima, M.; Chiba, S.; Tanigawa, T.
2003-01-01
We report on a finite spatial-volume effect for the pion-nucleon sigma term σ πN for quenched Wilson fermion on 8 3 x 20 and 16 3 x 20 lattices at β = 5.7 with the spatial lattice size of La∼1.12fm and La∼2.24fm, respectively. It is found that the spatial size dependence of the connected part of σ πN con is significant small. We observed the magnitude of finite size effect for the disconnected part of σ πN dis is much larger than for to connected one and an almost drastic decrease of σ πN dis amounting to 50% between La∼2.24fm to the smaller lattice size of La∼1.12fm. (author)
Analysis of the neutron flux in an annular pulsed reactor by using finite volume method
Energy Technology Data Exchange (ETDEWEB)
Silva, Mário A.B. da; Narain, Rajendra; Bezerra, Jair de L., E-mail: mabs500@gmail.com, E-mail: narain@ufpe.br, E-mail: jairbezerra@gmail.com [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Centro de Tecnologia e Geociências. Departamento de Energia Nuclear
2017-07-01
Production of very intense neutron sources is important for basic nuclear physics and for material testing and isotope production. Nuclear reactors have been used as sources of intense neutron fluxes, although the achievement of such levels is limited by the inability to remove fission heat. Periodic pulsed reactors provide very intense fluxes by a rotating modulator near a subcritical core. A concept for the production of very intense neutron fluxes that combines features of periodic pulsed reactors and steady state reactors was proposed by Narain (1997). Such a concept is known as Very Intense Continuous High Flux Pulsed Reactor (VICHFPR) and was analyzed by using diffusion equation with moving boundary conditions and Finite Difference Method with Crank-Nicolson formalism. This research aims to analyze the flux distribution in the Very Intense Continuous Flux High Pulsed Reactor (VICHFPR) by using the Finite Volume Method and compares its results with those obtained by the previous computational method. (author)
Analysis of the neutron flux in an annular pulsed reactor by using finite volume method
International Nuclear Information System (INIS)
Silva, Mário A.B. da; Narain, Rajendra; Bezerra, Jair de L.
2017-01-01
Production of very intense neutron sources is important for basic nuclear physics and for material testing and isotope production. Nuclear reactors have been used as sources of intense neutron fluxes, although the achievement of such levels is limited by the inability to remove fission heat. Periodic pulsed reactors provide very intense fluxes by a rotating modulator near a subcritical core. A concept for the production of very intense neutron fluxes that combines features of periodic pulsed reactors and steady state reactors was proposed by Narain (1997). Such a concept is known as Very Intense Continuous High Flux Pulsed Reactor (VICHFPR) and was analyzed by using diffusion equation with moving boundary conditions and Finite Difference Method with Crank-Nicolson formalism. This research aims to analyze the flux distribution in the Very Intense Continuous Flux High Pulsed Reactor (VICHFPR) by using the Finite Volume Method and compares its results with those obtained by the previous computational method. (author)
Directory of Open Access Journals (Sweden)
W.R. Azzam
2015-08-01
Full Text Available This paper reports the application of using a skirted foundation system to study the behavior of foundations with structural skirts adjacent to a sand slope and subjected to earthquake loading. The effect of the adopted skirts to safeguard foundation and slope from collapse is studied. The skirts effect on controlling horizontal soil movement and decreasing pore water pressure beneath foundations and beside the slopes during earthquake is investigated. This technique is investigated numerically using finite element analysis. A four story reinforced concrete building that rests on a raft foundation is idealized as a two-dimensional model with and without skirts. A two dimensional plain strain program PLAXIS, (dynamic version is adopted. A series of models for the problem under investigation were run under different skirt depths and lactation from the slope crest. The effect of subgrade relative density and skirts thickness is also discussed. Nodal displacement and element strains were analyzed for the foundation with and without skirts and at different studied parameters. The research results showed a great effectiveness in increasing the overall stability of the slope and foundation. The confined soil footing system by such skirts reduced the foundation acceleration therefore it can be tended to damping element and relieved the transmitted disturbance to the adjacent slope. This technique can be considered as a good method to control the slope deformation and decrease the slope acceleration during earthquakes.
Finite-volume and partial quenching effects in the magnetic polarizability of the neutron
Hall, J. M. M.; Leinweber, D. B.; Young, R. D.
2014-03-01
There has been much progress in the experimental measurement of the electric and magnetic polarizabilities of the nucleon. Similarly, lattice QCD simulations have recently produced dynamical QCD results for the magnetic polarizability of the neutron approaching the chiral regime. In order to compare the lattice simulations with experiment, calculation of partial quenching and finite-volume effects is required prior to an extrapolation in quark mass to the physical point. These dependencies are described using chiral effective field theory. Corrections to the partial quenching effects associated with the sea-quark-loop electric charges are estimated by modeling corrections to the pion cloud. These are compared to the uncorrected lattice results. In addition, the behavior of the finite-volume corrections as a function of pion mass is explored. Box sizes of approximately 7 fm are required to achieve a result within 5% of the infinite-volume result at the physical pion mass. A variety of extrapolations are shown at different box sizes, providing a benchmark to guide future lattice QCD calculations of the magnetic polarizabilities. A relatively precise value for the physical magnetic polarizability of the neutron is presented, βn=1.93(11)stat(11)sys×10-4 fm3, which is in agreement with current experimental results.
Flow simulation of a Pelton bucket using finite volume particle method
International Nuclear Information System (INIS)
Vessaz, C; Jahanbakhsh, E; Avellan, F
2014-01-01
The objective of the present paper is to perform an accurate numerical simulation of the high-speed water jet impinging on a Pelton bucket. To reach this goal, the Finite Volume Particle Method (FVPM) is used to discretize the governing equations. FVPM is an arbitrary Lagrangian-Eulerian method, which combines attractive features of Smoothed Particle Hydrodynamics and conventional mesh-based Finite Volume Method. This method is able to satisfy free surface and no-slip wall boundary conditions precisely. The fluid flow is assumed weakly compressible and the wall boundary is represented by one layer of particles located on the bucket surface. In the present study, the simulations of the flow in a stationary bucket are investigated for three different impinging angles: 72°, 90° and 108°. The particles resolution is first validated by a convergence study. Then, the FVPM results are validated with available experimental data and conventional grid-based Volume Of Fluid simulations. It is shown that the wall pressure field is in good agreement with the experimental and numerical data. Finally, the torque evolution and water sheet location are presented for a simulation of five rotating Pelton buckets
International Nuclear Information System (INIS)
Cambon, S.; Lacoste, P.
2011-01-01
We propose a finite element method to solve the axisymmetric scattering problem posed on a regular bounded domain. Here we shall show how to reduce the initial 3D problem into a truncated sum of 2D independent problems posed into a meridian plane of the object. Each of these problem results in the coupling of a partial differential equation into the interior domain and an integral equation on the surface simulating the free space. Then variational volume and boundary integral formulations of Maxwell's equation on regular surfaces are derived. We introduce some general finite element adapted to cylindrical coordinates and constructed from nodal and mixed finite element both for the interior (volume) and for the integral equation (surface). (authors)
3D Finite Volume Modeling of ENDE Using Electromagnetic T-Formulation
Directory of Open Access Journals (Sweden)
Yue Li
2012-01-01
Full Text Available An improved method which can analyze the eddy current density in conductor materials using finite volume method is proposed on the basis of Maxwell equations and T-formulation. The algorithm is applied to solve 3D electromagnetic nondestructive evaluation (E’NDE benchmark problems. The computing code is applied to study an Inconel 600 work piece with holes or cracks. The impedance change due to the presence of the crack is evaluated and compared with the experimental data of benchmark problems No. 1 and No. 2. The results show a good agreement between both calculated and measured data.
A finite volume method for density driven flows in porous media
Directory of Open Access Journals (Sweden)
Hilhorst Danielle
2013-01-01
Full Text Available In this paper, we apply a semi-implicit finite volume method for the numerical simulation of density driven flows in porous media; this amounts to solving a nonlinear convection-diffusion parabolic equation for the concentration coupled with an elliptic equation for the pressure. We compute the solutions for two specific problems: a problem involving a rotating interface between salt and fresh water and the classical but difficult Henry’s problem. All solutions are compared to results obtained by running FEflow, a commercial software package for the simulation of groundwater flow, mass and heat transfer in porous media.
Accurate B-spline-based 3-D interpolation scheme for digital volume correlation
Ren, Maodong; Liang, Jin; Wei, Bin
2016-12-01
An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.
Exact finite volume expectation values of local operators in excited states
Energy Technology Data Exchange (ETDEWEB)
Pozsgay, B. [MTA-BME “Momentum” Statistical Field Theory Research Group,Budafoki út 8, 1111 Budapest (Hungary); Szécsényi, I.M. [Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE (United Kingdom); Institute of Theoretical Physics, Eötvös Loránd University,Pázmány Péter sétány 1/A, 1117 Budapest (Hungary); Takács, G. [MTA-BME “Momentum” Statistical Field Theory Research Group,Budafoki út 8, 1111 Budapest (Hungary); Department of Theoretical Physics, Budapest University of Technology and Economics,Budafoki út 8, 1111 Budapest (Hungary)
2015-04-07
We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.
Exact finite volume expectation values of local operators in excited states
International Nuclear Information System (INIS)
Pozsgay, B.; Szécsényi, I.M.; Takács, G.
2015-01-01
We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.
International Nuclear Information System (INIS)
Sulbhewar, Litesh N; Raveendranath, P
2014-01-01
An efficient piezoelectric smart beam finite element based on Reddy’s third-order displacement field and layerwise linear potential is presented here. The present formulation is based on the coupled polynomial field interpolation of variables, unlike conventional piezoelectric beam formulations that use independent polynomials. Governing equations derived using a variational formulation are used to establish the relationship between field variables. The resulting expressions are used to formulate coupled shape functions. Starting with an assumed cubic polynomial for transverse displacement (w) and a linear polynomial for electric potential (φ), coupled polynomials for axial displacement (u) and section rotation (θ) are found. This leads to a coupled quadratic polynomial representation for axial displacement (u) and section rotation (θ). The formulation allows accommodation of extension–bending, shear–bending and electromechanical couplings at the interpolation level itself, in a variationally consistent manner. The proposed interpolation scheme is shown to eliminate the locking effects exhibited by conventional independent polynomial field interpolations and improve the convergence characteristics of HSDT based piezoelectric beam elements. Also, the present coupled formulation uses only three mechanical degrees of freedom per node, one less than the conventional formulations. Results from numerical test problems prove the accuracy and efficiency of the present formulation. (paper)
International Nuclear Information System (INIS)
Hua Jinsong; Lin Ping; Liu Chun; Wang Qi
2011-01-01
Highlights: → We study phase-field models for multi-phase flow computation. → We develop an energy-law preserving C0 FEM. → We show that the energy-law preserving method work better. → We overcome unphysical oscillation associated with the Cahn-Hilliard model. - Abstract: We use the idea in to develop the energy law preserving method and compute the diffusive interface (phase-field) models of Allen-Cahn and Cahn-Hilliard type, respectively, governing the motion of two-phase incompressible flows. We discretize these two models using a C 0 finite element in space and a modified midpoint scheme in time. To increase the stability in the pressure variable we treat the divergence free condition by a penalty formulation, under which the discrete energy law can still be derived for these diffusive interface models. Through an example we demonstrate that the energy law preserving method is beneficial for computing these multi-phase flow models. We also demonstrate that when applying the energy law preserving method to the model of Cahn-Hilliard type, un-physical interfacial oscillations may occur. We examine the source of such oscillations and a remedy is presented to eliminate the oscillations. A few two-phase incompressible flow examples are computed to show the good performance of our method.
Flux schemes based finite volume method for internal transonic flow with condensation
Czech Academy of Sciences Publication Activity Database
Halama, Jan; Benkhaldoun, F.; Fořt, J.
2011-01-01
Roč. 65, č. 8 (2011), s. 953-968 ISSN 0271-2091 Institutional research plan: CEZ:AV0Z20760514 Keywords : VFFC flux * SRNH flux * two-phase homogeneous flow * fractional step method * condensation Subject RIV: BK - Fluid Dynamics Impact factor: 1.176, year: 2011
International Nuclear Information System (INIS)
Nagai, Katsuaki; Ushijima, Satoru
2010-01-01
A numerical prediction method has been proposed to predict Bingham plastic fluids with free-surface in a two-dimensional container. Since the linear relationships between stress tensors and strain rate tensors are not assumed for non-Newtonian fluids, the liquid motions are described with Cauchy momentum equations rather than Navier-Stokes equations. The profile of a liquid surface is represented with the two-dimensional curvilinear coordinates which are represented in each computational step on the basis of the arbitrary Lagrangian-Eulerian (ALE) method. Since the volumes of the fluid cells are transiently changed in the physical space, the geometric conservation law is applied to the finite volume discretizations. As a result, it has been shown that the present method enables us to predict reasonably the Bingham plastic fluids with free-surface in a container.
Nagai, Katsuaki; Ushijima, Satoru
2010-06-01
A numerical prediction method has been proposed to predict Bingham plastic fluids with free-surface in a two-dimensional container. Since the linear relationships between stress tensors and strain rate tensors are not assumed for non-Newtonian fluids, the liquid motions are described with Cauchy momentum equations rather than Navier-Stokes equations. The profile of a liquid surface is represented with the two-dimensional curvilinear coordinates which are represented in each computational step on the basis of the arbitrary Lagrangian-Eulerian (ALE) method. Since the volumes of the fluid cells are transiently changed in the physical space, the geometric conservation law is applied to the finite volume discretizations. As a result, it has been shown that the present method enables us to predict reasonably the Bingham plastic fluids with free-surface in a container.
Beckstein, Pascal; Galindo, Vladimir; Vukčević, Vuko
2017-09-01
Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution of such problems in the finite volume framework of foam-extend, an extended version of the very popular OpenFOAM software. The numerical procedure involves a semi-coupled multi-mesh approach to solve Maxwell's equations for non-magnetic materials by means of the Coulomb gauged magnetic vector potential A and the electric scalar potential ϕ. The concept is further extended on the basis of the impressed and reduced magnetic vector potential and its usage in accordance with Biot-Savart's law to achieve a very efficient overall modelling even for complex three-dimensional geometries. Moreover, we present a special discretisation scheme to account for possible discontinuities in the electrical conductivity. To complement our numerical method, an extensive validation is completing the paper, which provides insight into the behaviour and the potential of our approach.
Energy Technology Data Exchange (ETDEWEB)
Ahmadi, M. [Heriot Watt Univ., Edinburgh (United Kingdom)
2008-10-15
This paper described a project in which a higher order up-winding scheme was used to solve mass/energy conservation equations for simulating steam flood processes in an oil reservoir. Thermal recovery processes are among the most complex because they require a detailed accounting of thermal energy and chemical reaction kinetics. The numerical simulation of thermal recovery processes involves localized phenomena such as saturation and temperatures fronts due to hyperbolic features of governing conservation laws. A second order accurate FV method that was improved by a moving mesh strategy was used to adjust for moving coordinates on a finely gridded domain. The Finite volume method was used and the problem of steam injection was then tested using derived solution frameworks on both mixed and moving coordinates. The benefits of using a higher-order Godunov solver instead of lower-order ones were qualified. This second order correction resulted in better resolution on moving features. Preferences of higher-order solvers over lower-order ones in terms of shock capturing is under further investigation. It was concluded that although this simulation study was limited to steam flooding processes, the newly presented approach may be suitable to other enhanced oil recovery processes such as VAPEX, SAGD and in situ combustion processes. 23 refs., 28 figs.
International Nuclear Information System (INIS)
Amor, H.; Bourgeois, M.
2012-01-01
Document available in extended abstract form only. The disposal of high level, long lived waste in deep underground clay formations is investigated by several countries including France. In the safety assessment of such geological repositories, a thoughtful consideration must be given to the mechanisms and possible pathways of migration of radionuclides released from waste packages. However, when modelling the transfer of radionuclides throughout the disposal facilities and geological formations, the numerical simulations must take into consideration, in addition to long durations of concern, the variety in the properties as well as in geometrical scales of the different components of the overall disposal, including the host formation. This task presents significant computational challenges. Numerical methods used in the MELODIE software The MELODIE software is developed by IRSN, and constantly upgraded, with the aim to assess the long-term containment capabilities of underground and surface radioactive waste repositories. The MELODIE software models water flow and the phenomena involved in the transport of radionuclides in saturated and unsaturated porous media in 2 and 3 dimensions; chemical processes are represented by a retardation factor and a solubility limit, for sorption and solubility respectively, integrated in the computational equations. These equations are discretized using a so-called Finite Volume Finite Element method (FVFE), which is based on a Galerkin method to discretize time and variables, together with a Finite Volume method using the Godunov scheme for the convection term. The FVFE method is used to convert partial differential equations into a finite number of algebraic equations that match the number of nodes in the mesh used to model the considered domain. It is also used to stabilise the numerical scheme. In order to manage the variety in properties and geometrical scales of underground disposal components, an a posteriori error estimator
Yang, Lei; Yan, Hongyong; Liu, Hong
2017-03-01
Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.
Simplicity of state and overlap structure in finite-volume realistic spin glasses
International Nuclear Information System (INIS)
Newman, C.M.; Stein, D.L.
1998-01-01
We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent boundary conditions, such as periodic, at most a pair of flip-related (or the appropriate number of symmetry-related in the non-Ising case) states appear, and the Parisi overlap distribution correspondingly exhibits at most a pair of δ functions at ±q EA . This rules out the nonstandard mean-field picture introduced by us earlier, and when combined with our previous elimination of more standard versions of the mean-field picture, argues against the possibility of even limited versions of mean-field ordering in realistic spin glasses. If broken spin-flip symmetry should occur, this leaves open two main possibilities for ordering in the spin glass phase: the droplet-scaling two-state picture, and the chaotic pairs many-state picture introduced by us earlier. We present scaling arguments which provide a possible physical basis for the latter picture, and discuss possible reasons behind numerical observations of more complicated overlap structures in finite volumes. copyright 1998 The American Physical Society
Charged hadrons in local finite-volume QED+QCD with C* boundary conditions
Lucini, Biagio; Ramos, Alberto; Tantalo, Nazario
2016-01-01
In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C* boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C* boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in this setup in a fully consistent fashion, without relying on gauge fixing. We argue that this class of states covers most of the interesting phenomenological applications in the framework of numerical simulations. We also calculate finite-volume corrections to the mass of stable charg...
Modelling of Evaporator in Waste Heat Recovery System using Finite Volume Method and Fuzzy Technique
Directory of Open Access Journals (Sweden)
Jahedul Islam Chowdhury
2015-12-01
Full Text Available The evaporator is an important component in the Organic Rankine Cycle (ORC-based Waste Heat Recovery (WHR system since the effective heat transfer of this device reflects on the efficiency of the system. When the WHR system operates under supercritical conditions, the heat transfer mechanism in the evaporator is unpredictable due to the change of thermo-physical properties of the fluid with temperature. Although the conventional finite volume model can successfully capture those changes in the evaporator of the WHR process, the computation time for this method is high. To reduce the computation time, this paper develops a new fuzzy based evaporator model and compares its performance with the finite volume method. The results show that the fuzzy technique can be applied to predict the output of the supercritical evaporator in the waste heat recovery system and can significantly reduce the required computation time. The proposed model, therefore, has the potential to be used in real time control applications.
Fracture criterion for brittle materials based on statistical cells of finite volume
International Nuclear Information System (INIS)
Cords, H.; Kleist, G.; Zimmermann, R.
1986-06-01
An analytical consideration of the Weibull Statistical Analysis of brittle materials established the necessity of including one additional material constant for a more comprehensive description of the failure behaviour. The Weibull analysis is restricted to infinitesimal volume elements in consequence of the differential calculus applied. It was found that infinitesimally small elements are in conflict with the basic statistical assumption and that the differential calculus is not needed in fact since nowadays most of the stress analyses are based on finite element calculations, and these are most suitable for a subsequent statistical analysis of strength. The size of a finite statistical cell has been introduced as the third material parameter. It should represent the minimum volume containing all statistical features of the material such as distribution of pores, flaws and grains. The new approach also contains a unique treatment of failure under multiaxial stresses. The quantity responsible for failure under multiaxial stresses is introduced as a modified strain energy. Sixteen different tensile specimens including CT-specimens have been investigated experimentally and analyzed with the probabilistic fracture criterion. As a result it can be stated that the failure rates of all types of specimens made from three different grades of graphite are predictable. The accuracy of the prediction is one standard deviation. (orig.) [de
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.
Wang, Hua; Tao, Guo; Shang, Xue-Feng; Fang, Xin-Ding; Burns, Daniel R.
2013-12-01
In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ˜27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d 0. The optimal parameter space for the maximum value of the linear frequency-shifted factor ( α 0) and the scaling factor ( β 0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1
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J. Thuburn
2014-05-01
Full Text Available A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV. The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.
Finite difference techniques for nonlinear hyperbolic conservation laws
International Nuclear Information System (INIS)
Sanders, R.
1985-01-01
The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references
El-Amin, Mohamed
2011-05-14
In this paper, a finite difference scheme is developed to solve the unsteady problem of combined heat and mass transfer from an isothermal curved surface to a porous medium saturated by a non-Newtonian fluid. The curved surface is kept at constant temperature and the power-law model is used to model the non-Newtonian fluid. The explicit finite difference method is used to solve simultaneously the equations of momentum, energy and concentration. The consistency of the explicit scheme is examined and the stability conditions are determined for each equation. Boundary layer and Boussinesq approximations have been incorporated. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles are shown graphically. It is found that as time approaches infinity, the values of wall shear, heat transfer coefficient and concentration gradient at the wall, which are entered in tables, approach the steady state values.
Lonsdale, R. D.; Webster, R.
This paper demonstrates the application of a simple finite volume approach to a finite element mesh, combining the economy of the former with the geometrical flexibility of the latter. The procedure is used to model a three-dimensional flow on a mesh of linear eight-node brick (hexahedra). Simulations are performed for a wide range of flow problems, some in excess of 94,000 nodes. The resulting computer code ASTEC that incorporates these procedures is described.
A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows
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.
Directory of Open Access Journals (Sweden)
Ye. S. Sherina
2014-01-01
Full Text Available This research has been aimed to carry out a study of peculiarities that arise in a numerical simulation of the electrical impedance tomography (EIT problem. Static EIT image reconstruction is sensitive to a measurement noise and approximation error. A special consideration has been given to reducing of the approximation error, which originates from numerical implementation drawbacks. This paper presents in detail two numerical approaches for solving EIT forward problem. The finite volume method (FVM on unstructured triangular mesh is introduced. In order to compare this approach, the finite element (FEM based forward solver was implemented, which has gained the most popularity among researchers. The calculated potential distribution with the assumed initial conductivity distribution has been compared to the analytical solution of a test Neumann boundary problem and to the results of problem simulation by means of ANSYS FLUENT commercial software. Two approaches to linearized EIT image reconstruction are discussed. Reconstruction of the conductivity distribution is an ill-posed problem, typically requiring a large amount of computation and resolved by minimization techniques. The objective function to be minimized is constructed of measured voltage and calculated boundary voltage on the electrodes. A classical modified Newton type iterative method and the stochastic differential evolution method are employed. A software package has been developed for the problem under investigation. Numerical tests were conducted on simulated data. The obtained results could be helpful to researches tackling the hardware and software issues for medical applications of EIT.
Modelling the Hydraulic Behaviour of Growing Media with the Explicit Finite Volume Solution
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Marco Carbone
2015-02-01
Full Text Available The increasing imperviousness of urban areas reduces the infiltration and evapotranspiration capacity of urban catchments and results in increased runoff. In the last few decades, several solutions and techniques have been proposed to prevent such impacts by restoring the hydrological cycle. A limiting factor in spreading the use of such systems is the lack of proper modelling tools for design, especially for the infiltration processes in a growing medium. In this research, a physically-based model, employing the explicit Finite Volume Method (FVM, is proposed for modelling infiltration into growing media. The model solves a modified version of the Richards equation using a formulation which takes into account the main characteristics of green infrastructure substrates. The proposed model was verified against the HYDRUS-1D software and the comparison of results confirmed the suitability of the proposed model for correctly describing the hydraulic behaviour of soil substrates.
Ramses-GPU: Second order MUSCL-Handcock finite volume fluid solver
Kestener, Pierre
2017-10-01
RamsesGPU is a reimplementation of RAMSES (ascl:1011.007) which drops the adaptive mesh refinement (AMR) features to optimize 3D uniform grid algorithms for modern graphics processor units (GPU) to provide an efficient software package for astrophysics applications that do not need AMR features but do require a very large number of integration time steps. RamsesGPU provides an very efficient C++/CUDA/MPI software implementation of a second order MUSCL-Handcock finite volume fluid solver for compressible hydrodynamics as a magnetohydrodynamics solver based on the constraint transport technique. Other useful modules includes static gravity, dissipative terms (viscosity, resistivity), and forcing source term for turbulence studies, and special care was taken to enhance parallel input/output performance by using state-of-the-art libraries such as HDF5 and parallel-netcdf.
An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry
International Nuclear Information System (INIS)
Bernard-Champmartin, Aude; Ghidaglia, Jean-Michel; Braeunig, Jean-Philippe
2013-01-01
In this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z axis (i.e. all the functions do not depend explicitly on the angular variable h), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific up-winding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity uh. (authors)
A finite volume procedure for fluid flow, heat transfer and solid-body stress analysis
Jagad, P. I.
2018-04-12
A unified cell-centered unstructured mesh finite volume procedure is presented for fluid flow, heat transfer and solid-body stress analysis. An in-house procedure (A. W. Date, Solution of Transport Equations on Unstructured Meshes with Cell-Centered Colocated Variables. Part I: Discretization, International Journal of Heat and Mass Transfer, vol. 48 (6), 1117-1127, 2005) is extended to include the solid-body stress analysis. The transport terms for a cell-face are evaluated in a structured grid-like manner. The Cartesian gradients at the center of each cell-face are evaluated using the coordinate transformation relations. The accuracy of the procedure is demonstrated by solving several benchmark problems involving different boundary conditions, source terms, and types of loading.
Finite-volume Atmospheric Model of the IAP/LASG (FAMIL)
Bao, Q.
2015-12-01
The Finite-volume Atmospheric Model of the IAP/LASG (FAMIL) is introduced in this work. FAMIL have the flexible horizontal and vertical resolutions up to 25km and 1Pa respectively, which currently running on the "Tianhe 1A&2" supercomputers. FAMIL is the atmospheric component of the third-generation Flexible Global Ocean-Atmosphere-Land climate System model (FGOALS3) which will participate in the Coupled Model Intercomparison Project Phase 6 (CMIP6). In addition to describing the dynamical core and physical parameterizations of FAMIL, this talk describes the simulated characteristics of energy and water balances, precipitation, Asian Summer Monsoon and stratospheric circulation, and compares them with observational/reanalysis data. Finally, the model biases as well as possible solutions are discussed.
International Nuclear Information System (INIS)
Lu, Y Charles; Kurapati, Siva N V R K; Yang Fuqian
2008-01-01
The cylindrical indentation is analysed, using the finite element method, for determining the plastic properties of elastic-plastic materials and the effect of strain hardening. The results are compared with those obtained from spherical indentation, the commonly used technique for measuring plastic properties of materials in small volumes. The analysis shows that the deformation under a cylindrical indenter quickly reaches a fully plastic state and that the size (diameter) of the plastic zone remains constant during further indentation. The indentation load is proportional to the indentation depth at large indentation depth, from which the indentation pressure P m at the onset of yielding can be readily extrapolated. The analysis of cylindrical indentation suggests that it does not need parameters such as impression radius (a) and contact stiffness (S) for determining the plastic behaviour of materials. Thus, the cylindrical indentation can suppress the uncertainties in measuring material properties
Barajas-Solano, D. A.; Tartakovsky, A. M.
2017-12-01
We present a multiresolution method for the numerical simulation of flow and reactive transport in porous, heterogeneous media, based on the hybrid Multiscale Finite Volume (h-MsFV) algorithm. The h-MsFV algorithm allows us to couple high-resolution (fine scale) flow and transport models with lower resolution (coarse) models to locally refine both spatial resolution and transport models. The fine scale problem is decomposed into various "local'' problems solved independently in parallel and coordinated via a "global'' problem. This global problem is then coupled with the coarse model to strictly ensure domain-wide coarse-scale mass conservation. The proposed method provides an alternative to adaptive mesh refinement (AMR), due to its capacity to rapidly refine spatial resolution beyond what's possible with state-of-the-art AMR techniques, and the capability to locally swap transport models. We illustrate our method by applying it to groundwater flow and reactive transport of multiple species.
Schallhorn, Paul; Majumdar, Alok
2012-01-01
This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.
A solution of two-dimensional magnetohydrodynamic flow using the finite volume method
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Naceur Sonia
2014-01-01
Full Text Available This paper presents the two dimensional numerical modeling of the coupling electromagnetic-hydrodynamic phenomena in a conduction MHD pump using the Finite volume Method. Magnetohydrodynamic problems are, thus, interdisciplinary and coupled, since the effect of the velocity field appears in the magnetic transport equations, and the interaction between the electric current and the magnetic field appears in the momentum transport equations. The resolution of the Maxwell's and Navier Stokes equations is obtained by introducing the magnetic vector potential A, the vorticity z and the stream function y. The flux density, the electromagnetic force, and the velocity are graphically presented. Also, the simulation results agree with those obtained by Ansys Workbench Fluent software.
A finite volume alternate direction implicit approach to modeling selective laser melting
DEFF Research Database (Denmark)
Hattel, Jesper Henri; Mohanty, Sankhya
2013-01-01
Over the last decade, several studies have attempted to develop thermal models for analyzing the selective laser melting process with a vision to predict thermal stresses, microstructures and resulting mechanical properties of manufactured products. While a holistic model addressing all involved...... to accurately simulate the process, are constrained by either the size or scale of the model domain. A second challenging aspect involves the inclusion of non-linear material behavior into the 3D implicit FE models. An alternating direction implicit (ADI) method based on a finite volume (FV) formulation...... is proposed for modeling single-layer and few-layers selective laser melting processes. The ADI technique is implemented and applied for two cases involving constant material properties and non-linear material behavior. The ADI FV method consume less time while having comparable accuracy with respect to 3D...
A Finite-Volume computational mechanics framework for multi-physics coupled fluid-stress problems
International Nuclear Information System (INIS)
Bailey, C; Cross, M.; Pericleous, K.
1998-01-01
Where there is a strong interaction between fluid flow, heat transfer and stress induced deformation, it may not be sufficient to solve each problem separately (i.e. fluid vs. stress, using different techniques or even different computer codes). This may be acceptable where the interaction is static, but less so, if it is dynamic. It is desirable for this reason to develop software that can accommodate both requirements (i.e. that of fluid flow and that of solid mechanics) in a seamless environment. This is accomplished in the University of Greenwich code PHYSICA, which solves both the fluid flow problem and the stress-strain equations in a unified Finite-Volume environment, using an unstructured computational mesh that can deform dynamically. Example applications are given of the work of the group in the metals casting process (where thermal stresses cause elasto- visco-plastic distortion)
FINITE VOLUME METHOD FOR SOLVING THREE-DIMENSIONAL ELECTRIC FIELD DISTRIBUTION
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Paţiuc V.I.
2011-04-01
Full Text Available The paper examines a new approach to finite volume method which is used to calculate the electric field spatially homogeneous three-dimensional environment. It is formulated the problem Dirihle with building of the computational grid on base of space partition, which is known as Delone triangulation with the use of Voronoi cells. It is proposed numerical algorithm for calculating the potential and electric field strength in the space formed by a cylinder placed in the air. It is developed algorithm and software which were for the case, when the potential on the inner surface of the cylinder has been assigned and on the outer surface and the bottom of cylinder it was assigned zero potential. There are presented results of calculations of distribution in the potential space and electric field strength.
Kou, Jisheng; Sun, Shuyu
2017-01-01
In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated
Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step
Energy Technology Data Exchange (ETDEWEB)
Jayakumar, J S; Kumar, Inder [Bhabha Atomic Research Center, Mumbai (India); Eswaran, V, E-mail: jsjayan@gmail.com, E-mail: inderk@barc.gov.in, E-mail: eswar@iitk.ac.in [Indian Institute of Technology, Kanpur (India)
2010-12-15
Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-{omega}. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.
Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step
Jayakumar, J. S.; Kumar, Inder; Eswaran, V.
2010-12-01
Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-ω. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.
Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step
International Nuclear Information System (INIS)
Jayakumar, J S; Kumar, Inder; Eswaran, V
2010-01-01
Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-ω. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.
Energy Technology Data Exchange (ETDEWEB)
Marcondes, Francisco [Federal University of Ceara, Fortaleza (Brazil). Dept. of Metallurgical Engineering and Material Science], e-mail: marcondes@ufc.br; Varavei, Abdoljalil; Sepehrnoori, Kamy [The University of Texas at Austin (United States). Petroleum and Geosystems Engineering Dept.], e-mails: varavei@mail.utexas.edu, kamys@mail.utexas.edu
2010-07-01
An element-based finite-volume approach in conjunction with unstructured grids for naturally fractured compositional reservoir simulation is presented. In this approach, both the discrete fracture and the matrix mass balances are taken into account without any additional models to couple the matrix and discrete fractures. The mesh, for two dimensional domains, can be built of triangles, quadrilaterals, or a mix of these elements. However, due to the available mesh generator to handle both matrix and discrete fractures, only results using triangular elements will be presented. The discrete fractures are located along the edges of each element. To obtain the approximated matrix equation, each element is divided into three sub-elements and then the mass balance equations for each component are integrated along each interface of the sub-elements. The finite-volume conservation equations are assembled from the contribution of all the elements that share a vertex, creating a cell vertex approach. The discrete fracture equations are discretized only along the edges of each element and then summed up with the matrix equations in order to obtain a conservative equation for both matrix and discrete fractures. In order to mimic real field simulations, the capillary pressure is included in both matrix and discrete fracture media. In the implemented model, the saturation field in the matrix and discrete fractures can be different, but the potential of each phase in the matrix and discrete fracture interface needs to be the same. The results for several naturally fractured reservoirs are presented to demonstrate the applicability of the method. (author)
Settle, Sean O.
2013-01-01
The primary aim of this paper is to answer the question, What are the highest-order five- or nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the one- and two-dimensional Poisson equation on uniform, quasi-uniform, and nonuniform face-to-face hyperrectangular grids and directly prove the existence or nonexistence of their highest-order local accuracies. Our derivations are unique in that we do not make any initial assumptions on stencil symmetries or weights. For the one-dimensional problem, the derivation using the three-point stencil on both uniform and nonuniform grids yields a scheme with arbitrarily high-order local accuracy. However, for the two-dimensional problem, the derivation using the corresponding five-point stencil on uniform and quasi-uniform grids yields a scheme with at most second-order local accuracy, and on nonuniform grids yields at most first-order local accuracy. When expanding the five-point stencil to the nine-point stencil, the derivation using the nine-point stencil on uniform grids yields at most sixth-order local accuracy, but on quasi- and nonuniform grids yields at most fourth- and third-order local accuracy, respectively. © 2013 Society for Industrial and Applied Mathematics.
Multi-channel 1-to-2 transition amplitudes in a finite volume
Energy Technology Data Exchange (ETDEWEB)
Briceno, Raul [JLAB; Hansen, Maxwell [Helmholtz Institute Mainz; Walker-Loud, Andre P [W& M. JLAB
2015-04-01
We derive a model-independent expression for finite-volume matrix elements. Specifically, we present a relativistic, non-perturbative analysis of the matrix element of an external current between a one-scalar in-state and a two-scalar out-state. Our result, which is valid for energies below higher-particle inelastic thresholds, generalizes the Lellouch-Luscher formula in two ways: we allow the external current to inject arbitrary momentum into the system and we allow for the final state to be composed an arbitrary number of strongly coupled two-particle states with arbitrary partial waves (including partial-wave mixing induced by the volume). We also illustrate how our general result can be applied to some key examples, such as heavy meson decays and meson photo production. Finally, we point out complications that arise involving unstable resonance states, such as B to K*+l+l when staggered or mixed-action/partially-quenched calculations are performed.
Energy Technology Data Exchange (ETDEWEB)
Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G., E-mail: ansar.calloo@cea.fr, E-mail: jean-francois.vidal@cea.fr, E-mail: romain.le-tellier@cea.fr, E-mail: gerald.rimpault@cea.fr [CEA, DEN, DER/SPRC/LEPh, Saint-Paul-lez-Durance (France)
2011-07-01
This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S{sub n} method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)
International Nuclear Information System (INIS)
Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G.
2011-01-01
This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S_n method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)
Simulation of Jetting in Injection Molding Using a Finite Volume Method
Directory of Open Access Journals (Sweden)
Shaozhen Hua
2016-05-01
Full Text Available In order to predict the jetting and the subsequent buckling flow more accurately, a three dimensional melt flow model was established on a viscous, incompressible, and non-isothermal fluid, and a control volume-based finite volume method was employed to discretize the governing equations. A two-fold iterative method was proposed to decouple the dependence among pressure, velocity, and temperature so as to reduce the computation and improve the numerical stability. Based on the proposed theoretical model and numerical method, a program code was developed to simulate melt front progress and flow fields. The numerical simulations for different injection speeds, melt temperatures, and gate locations were carried out to explore the jetting mechanism. The results indicate the filling pattern depends on the competition between inertial and viscous forces. When inertial force exceeds the viscous force jetting occurs, then it changes to a buckling flow as the viscous force competes over the inertial force. Once the melt contacts with the mold wall, the melt filling switches to conventional sequential filling mode. Numerical results also indicate jetting length increases with injection speed but changes little with melt temperature. The reasonable agreements between simulated and experimental jetting length and buckling frequency imply the proposed method is valid for jetting simulation.
Comparison of Moving Boundary and Finite-Volume Heat Exchanger Models in the Modelica Language
Directory of Open Access Journals (Sweden)
Adriano Desideri
2016-05-01
Full Text Available When modeling low capacity energy systems, such as a small size (5–150 kWel organic Rankine cycle unit, the governing dynamics are mainly concentrated in the heat exchangers. As a consequence, the accuracy and simulation speed of the higher level system model mainly depend on the heat exchanger model formulation. In particular, the modeling of thermo-flow systems characterized by evaporation or condensation requires heat exchanger models capable of handling phase transitions. To this aim, the finite volume (FV and the moving boundary (MB approaches are the most widely used. The two models are developed and included in the open-source ThermoCycle Modelica library. In this contribution, a comparison between the two approaches is presented. An integrity and accuracy test is designed to evaluate the performance of the FV and MB models during transient conditions. In order to analyze how the two modeling approaches perform when integrated at a system level, two organic Rankine cycle (ORC system models are built using the FV and the MB evaporator model, and their responses are compared against experimental data collected on an 11 kWel ORC power unit. Additionally, the effect of the void fraction value in the MB evaporator model and of the number of control volumes (CVs in the FV one is investigated. The results allow drawing general guidelines for the development of heat exchanger dynamic models involving two-phase flows.
On fully multidimensional and high order non oscillatory finite volume methods, I
International Nuclear Information System (INIS)
Lafon, F.
1992-11-01
A fully multidimensional flux formulation for solving nonlinear conservation laws of hyperbolic type is introduced to perform calculations on unstructured grids made of triangular or quadrangular cells. Fluxes are computed across dual median cells with a multidimensional 2D Riemann Solver (R2D Solver) whose intermediate states depend on either a three (on triangle R2DT solver) of four (on quadrangle, R2DQ solver) state solutions prescribed on the three or four sides of a gravity cell. Approximate Riemann solutions are computed via a linearization process of Roe's type involving multidimensional effects. Moreover, a monotonous scheme using stencil and central Lax-Friedrichs corrections on sonic curves are built in. Finally, high order accurate ENO-like (Essentially Non Oscillatory) reconstructions using plane and higher degree polynomial limitations are defined in the set up of finite element Lagrange spaces P k and Q k for k≥0, on triangles and quadrangles, respectively. Numerical experiments involving both linear and nonlinear conservation laws to be solved on unstructured grids indicate the ability of our techniques when dealing with strong multidimensional effects. An application to Euler's equations for the Mach three step problem illustrates the robustness and usefulness of our techniques using triangular and quadrangular grids. (Author). 33 refs., 13 figs
International Nuclear Information System (INIS)
Barber, R.W.; Fonty, A.
2003-01-01
This paper describes a novel vortex element method for simulating incompressible laminar flow over a two-dimensional backward-facing step. The model employs an operator-splitting technique to compute the evolution of the vorticity field downstream of abrupt changes in flow geometry. During the advective stage of the computation, a semi-Lagrangian scheme is used to update the positions of the vortex elements, whilst an analytical diffusion algorithm employing Oseen vortices is implemented during the diffusive time step. Redistributing the vorticity analytically instead of using the more traditional random-walk method enables the numerical model to simulate steady flows directly and avoids the need to filter the results to remove the oscillations created by the random-walk procedure. Model validation has been achieved by comparing the length of the recirculating eddy behind a confined backward-facing step against data from experimental and alternative numerical investigations. In addition, results from the vortex element method are compared against predictions obtained using the commercial finite-volume computational fluid dynamics code, CFD-ACE+. The results show that the vortex element scheme marginally overpredicts the length of the downstream recirculating eddy, implying that the method may be associated with an artificial reduction in the vorticity diffusion rate. Nevertheless the results demonstrate that the proposed vortex redistribution scheme provides a practical alternative to traditional random-walk discrete vortex algorithms. (author)
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.
Directory of Open Access Journals (Sweden)
Qian Zhang
2014-01-01
Full Text Available The paper presents a framework for the construction of Monte Carlo finite volume element method (MCFVEM for the convection-diffusion equation with a random diffusion coefficient, which is described as a random field. We first approximate the continuous stochastic field by a finite number of random variables via the Karhunen-Loève expansion and transform the initial stochastic problem into a deterministic one with a parameter in high dimensions. Then we generate independent identically distributed approximations of the solution by sampling the coefficient of the equation and employing finite volume element variational formulation. Finally the Monte Carlo (MC method is used to compute corresponding sample averages. Statistic error is estimated analytically and experimentally. A quasi-Monte Carlo (QMC technique with Sobol sequences is also used to accelerate convergence, and experiments indicate that it can improve the efficiency of the Monte Carlo method.
DEFF Research Database (Denmark)
Troldborg, Niels; Sørensen, Niels N.; Réthoré, Pierre-Elouan
2015-01-01
This paper describes a consistent algorithm for eliminating the numerical wiggles appearing when solving the finite volume discretized Navier-Stokes equations with discrete body forces in a collocated grid arrangement. The proposed method is a modification of the Rhie-Chow algorithm where the for...
Energy Technology Data Exchange (ETDEWEB)
Munz, C D; Schneider, R; Stein, E; Voss, U [Forschungszentrum Karlsruhe (Germany). Institut fuer Neutronenphysik und Reaktortechnik; Westermann, T [FH Karlsruhe (Germany). Fachbereich Naturwissenschaften; Krauss, M [Forschungszentrum Karlsruhe (Germany). Hauptabteilung Informations- und Kommunikationstechik
1997-12-31
The numerical concept realized in the the Karlsruhe Diode Code KADI2D is briefly reviewed. Several new aspects concerning the Maxwell field solver based on high resolution finite-volume methods are presented. A new approach maintaining charge conservation numerically for the Maxwell-Lorentz equations is shortly summarized. (author). 2 figs., 12 refs.
DEFF Research Database (Denmark)
Morningstar, Colin; Bulava, John; Singha, Bijit
2017-01-01
An implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the L\\"uscher formalism and involving a Hermitian matrix known as the "box matrix" is described. The method includes higher partial waves and multiple decay channels. Two fitting procedures for estimating...
International Nuclear Information System (INIS)
Munz, C.D.; Schneider, R.; Stein, E.; Voss, U.; Westermann, T.; Krauss, M.
1996-01-01
The numerical concept realized in the the Karlsruhe Diode Code KADI2D is briefly reviewed. Several new aspects concerning the Maxwell field solver based on high resolution finite-volume methods are presented. A new approach maintaining charge conservation numerically for the Maxwell-Lorentz equations is shortly summarized. (author). 2 figs., 12 refs
Recent advances in marching-on-in-time schemes for solving time domain volume integral equations
Sayed, Sadeed Bin; Ulku, Huseyin Arda; Bagci, Hakan
2015-01-01
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are constructed by setting the summation of the incident and scattered field intensities to the total field intensity on the volumetric support of the scatterer. The unknown can be the field intensity or flux/current density. Representing the total field intensity in terms of the unknown using the relevant constitutive relation and the scattered field intensity in terms of the spatiotemporal convolution of the unknown with the Green function yield the final form of the TDVIE. The unknown is expanded in terms of local spatial and temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation at discrete times yield a system of equations that is solved by the marching on-in-time (MOT) scheme. At each time step, a smaller system of equations, termed MOT system is solved for the coefficients of the expansion. The right-hand side of this system consists of the tested incident field and discretized spatio-temporal convolution of the unknown samples computed at the previous time steps with the Green function.
Recent advances in marching-on-in-time schemes for solving time domain volume integral equations
Sayed, Sadeed Bin
2015-05-16
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are constructed by setting the summation of the incident and scattered field intensities to the total field intensity on the volumetric support of the scatterer. The unknown can be the field intensity or flux/current density. Representing the total field intensity in terms of the unknown using the relevant constitutive relation and the scattered field intensity in terms of the spatiotemporal convolution of the unknown with the Green function yield the final form of the TDVIE. The unknown is expanded in terms of local spatial and temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation at discrete times yield a system of equations that is solved by the marching on-in-time (MOT) scheme. At each time step, a smaller system of equations, termed MOT system is solved for the coefficients of the expansion. The right-hand side of this system consists of the tested incident field and discretized spatio-temporal convolution of the unknown samples computed at the previous time steps with the Green function.
Kirk, Benjamin S.; Bova, Stephen W.; Bond, Ryan B.
2011-01-01
Presentation topics include background and motivation; physical modeling including governing equations and thermochemistry; finite element formulation; results of inviscid thermal nonequilibrium chemically reacting flow and viscous thermal equilibrium chemical reacting flow; and near-term effort.
Kumari, Komal; Donzis, Diego
2017-11-01
Highly resolved computational simulations on massively parallel machines are critical in understanding the physics of a vast number of complex phenomena in nature governed by partial differential equations. Simulations at extreme levels of parallelism present many challenges with communication between processing elements (PEs) being a major bottleneck. In order to fully exploit the computational power of exascale machines one needs to devise numerical schemes that relax global synchronizations across PEs. This asynchronous computations, however, have a degrading effect on the accuracy of standard numerical schemes.We have developed asynchrony-tolerant (AT) schemes that maintain order of accuracy despite relaxed communications. We show, analytically and numerically, that these schemes retain their numerical properties with multi-step higher order temporal Runge-Kutta schemes. We also show that for a range of optimized parameters,the computation time and error for AT schemes is less than their synchronous counterpart. Stability of the AT schemes which depends upon history and random nature of delays, are also discussed. Support from NSF is gratefully acknowledged.
Effect of restoration volume on stresses in a mandibular molar: a finite element study.
Wayne, Jennifer S; Chande, Ruchi; Porter, H Christian; Janus, Charles
2014-10-01
There can be significant disagreement among dentists when planning treatment for a tooth with a failing medium-to-large--sized restoration. The clinician must determine whether the restoration should be replaced or treated with a crown, which covers and protects the remaining weakened tooth structure during function. The purpose of this study was to evaluate the stresses generated in different sized amalgam restorations via a computational modeling approach and reveal whether a predictable pattern emerges. A computer tomography scan was performed of an extracted mandibular first molar, and the resulting images were imported into a medical imaging software package for tissue segmentation. The software was used to separate the enamel, dentin, and pulp cavity through density thresholding and surface rendering. These tissue structures then were imported into 3-dimensional computer-aided design software in which material properties appropriate to the tissues in the model were assigned. A static finite element analysis was conducted to investigate the stresses that result from normal occlusal forces. Five models were analyzed, 1 with no restoration and 4 with increasingly larger restoration volume proportions: a normal-sized tooth, a small-sized restoration, 2 medium-sized restorations, and 1 large restoration as determined from bitewing radiographs and occlusal surface digital photographs. The resulting von Mises stresses for dentin-enamel of the loaded portion of the tooth grew progressively greater as the size of the restoration increased. The average stress in the normal, unrestored tooth was 4.13 MPa, whereas the smallest restoration size increased this stress to 5.52 MPa. The largest restoration had a dentin-enamel stress of 6.47 MPa. A linear correlation existed between restoration size and dentin-enamel stress, with an R(2) of 0.97. A larger restoration volume proportion resulted in higher dentin-enamel stresses under static loading. A comparison of the von Mises
Energy Technology Data Exchange (ETDEWEB)
Bijnens, Johan; Rössler, Thomas [Department of Astronomy and Theoretical Physics, Lund University,Sölvegatan 14A, SE 223-62 Lund (Sweden)
2015-11-16
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. Partial analytical results can be found in the appendices. Some examples of cases relevant to lattice QCD are studied numerically. Numerical programs for all results are available as part of the CHIRON package.
International Nuclear Information System (INIS)
Bijnens, Johan; Rössler, Thomas
2015-01-01
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. Partial analytical results can be found in the appendices. Some examples of cases relevant to lattice QCD are studied numerically. Numerical programs for all results are available as part of the CHIRON package.
Directory of Open Access Journals (Sweden)
Marcin Krzeszowiec
2015-03-01
Full Text Available Computer simulations of physical phenomena are at the moment common both in science and industry. The possibility of finding approximate solutions for complicated systems of differential equations, mathematically describing issues in the fields of mechanics, physics or chemistry, allows for shorten design and research time, often significantly reducing the need for expensive experimental studies or costly production of prototypes. However, the mentioned prevalence of these methods, particularly the Finite Element Method, resulted in analysis outcomes to be often in advance regarded as accurate ones. The purpose of the article is to showcase, on a simple stress analysis problem, how parameters such as the density of the finite element mesh, finite element formulation or integration scheme significantly influence on the simulation results and how easy it is to end up with the results that do not hold any physical sense, despite the fact that all the basic assumptions of correct analysis (suitable boundary conditions, total system energy stored etc. have been met. The results of this study can serve as a warning against premature conclusion drawing from calculations carried out by means of FEM simulation.[b]Keywords[/b]: computational mechanics, finite element method, shell elements, numerical integration
International Nuclear Information System (INIS)
Moiseenko, Vitali; Battista, Jerry; Van Dyk, Jake
2000-01-01
Purpose: To evaluate the impact of dose-volume histogram (DVH) reduction schemes and models of normal tissue complication probability (NTCP) on ranking of radiation treatment plans. Methods and Materials: Data for liver complications in humans and for spinal cord in rats were used to derive input parameters of four different NTCP models. DVH reduction was performed using two schemes: 'effective volume' and 'preferred Lyman'. DVHs for competing treatment plans were derived from a sample DVH by varying dose uniformity in a high dose region so that the obtained cumulative DVHs intersected. Treatment plans were ranked according to the calculated NTCP values. Results: Whenever the preferred Lyman scheme was used to reduce the DVH, competing plans were indistinguishable as long as the mean dose was constant. The effective volume DVH reduction scheme did allow us to distinguish between these competing treatment plans. However, plan ranking depended on the radiobiological model used and its input parameters. Conclusions: Dose escalation will be a significant part of radiation treatment planning using new technologies, such as 3-D conformal radiotherapy and tomotherapy. Such dose escalation will depend on how the dose distributions in organs at risk are interpreted in terms of expected complication probabilities. The present study indicates considerable variability in predicted NTCP values because of the methods used for DVH reduction and radiobiological models and their input parameters. Animal studies and collection of standardized clinical data are needed to ascertain the effects of non-uniform dose distributions and to test the validity of the models currently in use
Two-dimensional transient thermal analysis of a fuel rod by finite volume method
Energy Technology Data Exchange (ETDEWEB)
Costa, Rhayanne Yalle Negreiros; Silva, Mário Augusto Bezerra da; Lira, Carlos Alberto de Oliveira, E-mail: ryncosta@gmail.com, E-mail: mabs500@gmail.com, E-mail: cabol@ufpe.br [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Departamento de Energia Nuclear
2017-07-01
One of the greatest concerns when studying a nuclear reactor is the warranty of safe temperature limits all over the system at all time. The preservation of core structure along with the constraint of radioactive material into a controlled system are the main focus during the operation of a reactor. The purpose of this paper is to present the temperature distribution for a nominal channel of the AP1000 reactor developed by Westinghouse Co. during steady-state and transient operations. In the analysis, the system was subjected to normal operation conditions and then to blockages of the coolant flow. The time necessary to achieve a new safe stationary stage (when it was possible) was presented. The methodology applied in this analysis was based on a two-dimensional survey accomplished by the application of Finite Volume Method (FVM). A steady solution is obtained and compared with an analytical analysis that disregard axial heat transport to determine its relevance. The results show the importance of axial heat transport consideration in this type of study. A transient analysis shows the behavior of the system when submitted to coolant blockage at channel's entrance. Three blockages were simulated (10%, 20% and 30%) and the results show that, for a nominal channel, the system can still be considerate safe (there's no bubble formation until that point). (author)
Directory of Open Access Journals (Sweden)
C Silva
2016-09-01
Full Text Available The main objective of this research was to study the pressure waves propagation generated by a sudden closure of a valve in a straight pipe. The physical model consisted of a head tank that can be pressurized with air, and a copper pipe with a fast-closing ball valve on the downstream end of the line. The cavitation and fluid-structure interaction phenomena were integrated analytically into the one-dimensional continuity and momentum equations, by assuming that the fluid density and the flow area vary with pressure. These equations were solved through a high resolution finite volume method, in combination with others numerical methods such as Taylor series expansion, Newton method, Simpson's Rule and quadratic interpolation. Due to the complexity of the solution procedure, a computational code in FORTRAN 95 language was developed in order to obtain numerical solutions. Several discretizations of the computational grid were achieved to assess their impact on the solution. The model was validated with experimental data and analytic results obtained by other researchers. Several pressure values, in different points of pipe, were compared, and an excellent agreement was found for both cases.
On finite volume effects in the chiral extrapolation of baryon masses
Lutz, M F M; Kobdaj, C; Schwarz, K
2014-01-01
We perform an analysis of the QCD lattice data on the baryon octet and decuplet masses based on the relativistic chiral Lagrangian. The baryon self energies are computed in a finite volume at next-to-next-to-next-to leading order (N^3LO), where the dependence on the physical meson and baryon masses is kept. The number of free parameters is reduced significantly down to 12 by relying on large-N_c sum rules. Altogether we describe accurately more than 220 data points from six different lattice groups, BMW, PACS-CS, HSC, LHPC, QCDSF-UKQCD and NPLQCD. Precise values for all counter terms relevant at N^3LO are predicted. In particular we extract a pion-nucleon sigma term of (39 +- 1) MeV and a strangeness sigma term of the nucleon of sigma_{sN} simeq (4 +- 1) MeV. The flavour SU(3) chiral limit of the baryon octet and decuplet masses is determined with ( 802 +- 4 ) MeV and (1103 +- 6) MeV. Detailed predictions for the baryon masses as currently evaluated by the ETM lattice QCD group are made.
Harijishnu, R.; Jayakumar, J. S.
2017-09-01
The main objective of this paper is to study the heat transfer rate of thermal radiation in participating media. For that, a generated collimated beam has been passed through a two dimensional slab model of flint glass with a refractive index 2. Both Polar and azimuthal angle have been varied to generate such a beam. The Temperature of the slab and Snells law has been validated by Radiation Transfer Equation (RTE) in OpenFOAM (Open Field Operation and Manipulation), a CFD software which is the major computational tool used in Industry and research applications where the source code is modified in which radiation heat transfer equation is added to the case and different radiation heat transfer models are utilized. This work concentrates on the numerical strategies involving both transparent and participating media. Since Radiation Transfer Equation (RTE) is difficult to solve, the purpose of this paper is to use existing solver buoyantSimlpeFoam to solve radiation model in the participating media by compiling the source code to obtain the heat transfer rate inside the slab by varying the Intensity of radiation. The Finite Volume Method (FVM) is applied to solve the Radiation Transfer Equation (RTE) governing the above said physical phenomena.
Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers
Directory of Open Access Journals (Sweden)
K. Yapici
2013-12-01
Full Text Available In this work, computer simulation results of steady incompressible flow in a 2-D square lid-driven cavity up to Reynolds number (Re 65000 are presented and compared with those of earlier studies. The governing flow equations are solved by using the finite volume approach. Quadratic upstream interpolation for convective kinematics (QUICK is used for the approximation of the convective terms in the flow equations. In the implementation of QUICK, the deferred correction technique is adopted. A non-uniform staggered grid arrangement of 768x768 is employed to discretize the flow geometry. Algebraic forms of the coupled flow equations are then solved through the iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation algorithm. The outlined computational methodology allows one to meet the main objective of this work, which is to address the computational convergence and wiggled flow problems encountered at high Reynolds and Peclet (Pe numbers. Furthermore, after Re > 25000 additional vortexes appear at the bottom left and right corners that have not been observed in earlier studies.
International Nuclear Information System (INIS)
Aruchunan, E.
2015-01-01
In this paper, we have examined the effectiveness of the quarter-sweep iteration concept on conjugate gradient normal residual (CGNR) iterative method by using composite Simpson's (CS) and finite difference (FD) discretization schemes in solving Fredholm integro-differential equations. For comparison purposes, Gauss- Seidel (GS) and the standard or full- and half-sweep CGNR methods namely FSCGNR and HSCGNR are also presented. To validate the efficacy of the proposed method, several analyses were carried out such as computational complexity and percentage reduction on the proposed and existing methods. (author)
Recovery Act: Finite Volume Based Computer Program for Ground Source Heat Pump Systems
Energy Technology Data Exchange (ETDEWEB)
James A Menart, Professor
2013-02-22
This report is a compilation of the work that has been done on the grant DE-EE0002805 entitled Finite Volume Based Computer Program for Ground Source Heat Pump Systems. The goal of this project was to develop a detailed computer simulation tool for GSHP (ground source heat pump) heating and cooling systems. Two such tools were developed as part of this DOE (Department of Energy) grant; the first is a two-dimensional computer program called GEO2D and the second is a three-dimensional computer program called GEO3D. Both of these simulation tools provide an extensive array of results to the user. A unique aspect of both these simulation tools is the complete temperature profile information calculated and presented. Complete temperature profiles throughout the ground, casing, tube wall, and fluid are provided as a function of time. The fluid temperatures from and to the heat pump, as a function of time, are also provided. In addition to temperature information, detailed heat rate information at several locations as a function of time is determined. Heat rates between the heat pump and the building indoor environment, between the working fluid and the heat pump, and between the working fluid and the ground are computed. The heat rates between the ground and the working fluid are calculated as a function time and position along the ground loop. The heating and cooling loads of the building being fitted with a GSHP are determined with the computer program developed by DOE called ENERGYPLUS. Lastly COP (coefficient of performance) results as a function of time are provided. Both the two-dimensional and three-dimensional computer programs developed as part of this work are based upon a detailed finite volume solution of the energy equation for the ground and ground loop. Real heat pump characteristics are entered into the program and used to model the heat pump performance. Thus these computer tools simulate the coupled performance of the ground loop and the heat pump. The
Finite Volume Based Computer Program for Ground Source Heat Pump System
Energy Technology Data Exchange (ETDEWEB)
Menart, James A. [Wright State University
2013-02-22
This report is a compilation of the work that has been done on the grant DE-EE0002805 entitled ?Finite Volume Based Computer Program for Ground Source Heat Pump Systems.? The goal of this project was to develop a detailed computer simulation tool for GSHP (ground source heat pump) heating and cooling systems. Two such tools were developed as part of this DOE (Department of Energy) grant; the first is a two-dimensional computer program called GEO2D and the second is a three-dimensional computer program called GEO3D. Both of these simulation tools provide an extensive array of results to the user. A unique aspect of both these simulation tools is the complete temperature profile information calculated and presented. Complete temperature profiles throughout the ground, casing, tube wall, and fluid are provided as a function of time. The fluid temperatures from and to the heat pump, as a function of time, are also provided. In addition to temperature information, detailed heat rate information at several locations as a function of time is determined. Heat rates between the heat pump and the building indoor environment, between the working fluid and the heat pump, and between the working fluid and the ground are computed. The heat rates between the ground and the working fluid are calculated as a function time and position along the ground loop. The heating and cooling loads of the building being fitted with a GSHP are determined with the computer program developed by DOE called ENERGYPLUS. Lastly COP (coefficient of performance) results as a function of time are provided. Both the two-dimensional and three-dimensional computer programs developed as part of this work are based upon a detailed finite volume solution of the energy equation for the ground and ground loop. Real heat pump characteristics are entered into the program and used to model the heat pump performance. Thus these computer tools simulate the coupled performance of the ground loop and the heat pump
Directory of Open Access Journals (Sweden)
Alina BOGOI
2016-12-01
Full Text Available Supersonic/hypersonic flows with strong shocks need special treatment in Computational Fluid Dynamics (CFD in order to accurately capture the discontinuity location and his magnitude. To avoid numerical instabilities in the presence of discontinuities, the numerical schemes must generate low dissipation and low dispersion error. Consequently, the algorithms used to calculate the time and space-derivatives, should exhibit a low amplitude and phase error. This paper focuses on the comparison of the numerical results obtained by simulations with some high resolution numerical schemes applied on linear and non-linear one-dimensional conservation low. The analytical solutions are provided for all benchmark tests considering smooth periodical conditions. All the schemes converge to the proper weak solution for linear flux and smooth initial conditions. However, when the flux is non-linear, the discontinuities may develop from smooth initial conditions and the shock must be correctly captured. All the schemes accurately identify the shock position, with the price of the numerical oscillation in the vicinity of the sudden variation. We believe that the identification of this pure numerical behavior, without physical relevance, in 1D case is extremely useful to avoid problems related to the stability and convergence of the solution in the general 3D case.
von Boetticher, Albrecht; Turowski, Jens M.; McArdell, Brian; Rickenmann, Dieter
2016-04-01
Debris flows are frequent natural hazards that cause massive damage. A wide range of debris flow models try to cover the complex flow behavior that arises from the inhomogeneous material mixture of water with clay, silt, sand, and gravel. The energy dissipation between moving grains depends on grain collisions and tangential friction, and the viscosity of the interstitial fine material suspension depends on the shear gradient. Thus a rheology description needs to be sensitive to the local pressure and shear rate, making the three-dimensional flow structure a key issue for flows in complex terrain. Furthermore, the momentum exchange between the granular and fluid phases should account for the presence of larger particles. We model the fine material suspension with a Herschel-Bulkley rheology law, and represent the gravel with the Coulomb-viscoplastic rheology of Domnik & Pudasaini (Domnik et al. 2013). Both composites are described by two phases that can mix; a third phase accounting for the air is kept separate to account for the free surface. The fluid dynamics are solved in three dimensions using the finite volume open-source code OpenFOAM. Computational costs are kept reasonable by using the Volume of Fluid method to solve only one phase-averaged system of Navier-Stokes equations. The Herschel-Bulkley parameters are modeled as a function of water content, volumetric solid concentration of the mixture, clay content and its mineral composition (Coussot et al. 1989, Yu et al. 2013). The gravel phase properties needed for the Coulomb-viscoplastic rheology are defined by the angle of repose of the gravel. In addition to this basic setup, larger grains and the corresponding grain collisions can be introduced by a coupled Lagrangian particle simulation. Based on the local Savage number a diffusive term in the gravel phase can activate phase separation. The resulting model can reproduce the sensitivity of the debris flow to water content and channel bed roughness, as
Computing with high-resolution upwind schemes for hyperbolic equations
International Nuclear Information System (INIS)
Chakravarthy, S.R.; Osher, S.; California Univ., Los Angeles)
1985-01-01
Computational aspects of modern high-resolution upwind finite-difference schemes for hyperbolic systems of conservation laws are examined. An operational unification is demonstrated for constructing a wide class of flux-difference-split and flux-split schemes based on the design principles underlying total variation diminishing (TVD) schemes. Consideration is also given to TVD scheme design by preprocessing, the extension of preprocessing and postprocessing approaches to general control volumes, the removal of expansion shocks and glitches, relaxation methods for implicit TVD schemes, and a new family of high-accuracy TVD schemes. 21 references
International Nuclear Information System (INIS)
Núñez, Jóse; Ramos, Eduardo; Lopez, Juan M
2012-01-01
We describe a hybrid method based on the combined use of the Fourier Galerkin and finite-volume techniques to solve the fluid dynamics equations in cylindrical geometries. A Fourier expansion is used in the angular direction, partially translating the problem to the Fourier space and then solving the resulting equations using a finite-volume technique. We also describe an algorithm required to solve the coupled mass and momentum conservation equations similar to a pressure-correction SIMPLE method that is adapted for the present formulation. Using the Fourier–Galerkin method for the azimuthal direction has two advantages. Firstly, it has a high-order approximation of the partial derivatives in the angular direction, and secondly, it naturally satisfies the azimuthal periodic boundary conditions. Also, using the finite-volume method in the r and z directions allows one to handle boundary conditions with discontinuities in those directions. It is important to remark that with this method, the resulting linear system of equations are band-diagonal, leading to fast and efficient solvers. The benefits of the mixed method are illustrated with example problems. (paper)
'Finite' non-Gaussianities and tensor-scalar ratio in large volume Swiss-cheese compactifications
International Nuclear Information System (INIS)
Misra, Aalok; Shukla, Pramod
2009-01-01
Developing on the ideas of (Section 4 of) [A. Misra, P. Shukla, Moduli stabilization, large-volume dS minimum without anti-D3-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi-Yau's, Nucl. Phys. B 799 (2008) 165-198, (arXiv: 0707.0105)] and [A. Misra, P. Shukla, Large volume axionic Swiss-cheese inflation, Nucl. Phys. B 800 (2008) 384-400, (arXiv: 0712.1260 [hep-th])] and using the formalisms of [S. Yokoyama, T. Suyama, T. Tanaka, Primordial non-Gaussianity in multi-scalar slow-roll inflation, (arXiv: 0705.3178 [astro-ph]); S. Yokoyama, T. Suyama, T. Tanaka, Primordial non-Gaussianity in multi-scalar inflation, Phys. Rev. D 77 (2008) 083511, (arXiv: 0711.2920 [astro-ph])], after inclusion of perturbative and non-perturbative α' corrections to the Kaehler potential and (D1- and D3-)instanton generated superpotential, we show the possibility of getting finite values for the non-linear parameter f NL while looking for non-Gaussianities in type IIB compactifications on orientifolds of the Swiss cheese Calabi-Yau WCP 4 [1,1,1,6,9] in the L(arge) V(olume) S(cenarios) limit. We show the same in two contexts. First is multi-field slow-roll inflation with D3-instanton contribution coming from a large number of multiple wrappings of a single (Euclidean) D3-brane around the 'small' divisor yielding f NL ∼O(1). The second is when the slow-roll conditions are violated and for the number of the aforementioned D3-instanton wrappings being of O(1) but more than one, yielding f NL ∼O(1). Based on general arguments not specific to our (string-theory) set-up, we argue that requiring curvature perturbations not to grow at horizon crossing and at super-horizon scales, automatically picks out hybrid inflationary scenarios which in our set up can yield f NL ∼O(1) and tensor-scalar ratio of O(10 -2 ). For all our calculations, the world-sheet instanton contributions to the Kaehler potential coming from the non-perturbative α ' corrections
Error estimates for the finite volume discretization for the porous medium equation
Pop, I.S.; Sepúlveda, M.; Radu, F.A.; Vera Villagrán, O.P.
2010-01-01
We analyze the convergence of a numerical scheme for a class of degenerate parabolic problems modelling reactions in porous media, and involving a nonlinear, possibly vanishing diffusion. The scheme involves the Kirchhoff transformation of the regularized nonlinearity, as well as an Euler implicit
Steger, J. L.; Dougherty, F. C.; Benek, J. A.
1983-01-01
A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.
International Nuclear Information System (INIS)
Mechitoua, N.; Boucker, M.; Lavieville, J.; Pigny, S.; Serre, G.
2003-01-01
Based on experience gained at EDF and Cea, a more general and robust 3-dimensional (3D) multiphase flow solver has been being currently developed for over three years. This solver, based on an elliptic oriented fractional step approach, is able to simulate multicomponent/multiphase flows. Discretization follows a 3D full unstructured finite volume approach, with a collocated arrangement of all variables. The non linear behaviour between pressure and volume fractions and a symmetric treatment of all fields are taken into account in the iterative procedure, within the time step. It greatly enforces the realizability of volume fractions (i.e 0 < α < 1), without artificial numerical needs. Applications to widespread test cases as static sedimentation, water hammer and phase separation are shown to assess the accuracy and the robustness of the flow solver in different flow conditions, encountered in nuclear reactors pipes. (authors)
Renteria Marquez, I A; Bolborici, V
2017-05-01
This manuscript presents a method to model in detail the piezoelectric traveling wave rotary ultrasonic motor (PTRUSM) stator response under the action of DC and AC voltages. The stator is modeled with a discrete two dimensional system of equations using the finite volume method (FVM). In order to obtain accurate results, a model of the stator bridge is included into the stator model. The model of the stator under the action of DC voltage is presented first, and the results of the model are compared versus a similar model using the commercial finite element software COMSOL Multiphysics. One can observe that there is a difference of less than 5% between the displacements of the stator using the proposed model and the one with COMSOL Multiphysics. After that, the model of the stator under the action of AC voltages is presented. The time domain analysis shows the generation of the traveling wave in the stator surface. One can use this model to accurately calculate the stator surface velocities, elliptical motion of the stator surface and the amplitude and shape of the stator traveling wave. A system of equations discretized with the finite volume method can easily be transformed into electrical circuits, because of that, FVM may be a better choice to develop a model-based control strategy for the PTRUSM. Copyright © 2017 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
A. R. Appadu
2013-01-01
for which the Reynolds number is 2 or 4. Some errors are computed, namely, the error rate with respect to the L1 norm, dispersion, and dissipation errors. We have both dissipative and dispersive errors, and this indicates that the methods generate artificial dispersion, though the partial differential considered is not dispersive. It is seen that the Lax-Wendroff and NSFD are quite good methods to approximate the 1D advection-diffusion equation at some values of k and h. Two optimisation techniques are then implemented to find the optimal values of k when h=0.02 for the Lax-Wendroff and NSFD schemes, and this is validated by numerical experiments.
Xu, Wenying; Wang, Zidong; Ho, Daniel W C
2018-05-01
This paper is concerned with the finite-horizon consensus problem for a class of discrete time-varying multiagent systems with external disturbances and missing measurements. To improve the communication reliability, redundant channels are introduced and the corresponding protocol is constructed for the information transmission over redundant channels. An event-triggered scheme is adopted to determine whether the information of agents should be transmitted to their neighbors. Subsequently, an observer-type event-triggered control protocol is proposed based on the latest received neighbors' information. The purpose of the addressed problem is to design a time-varying controller based on the observed information to achieve the consensus performance in a finite horizon. By utilizing a constrained recursive Riccati difference equation approach, some sufficient conditions are obtained to guarantee the consensus performance, and the controller parameters are also designed. Finally, a numerical example is provided to demonstrate the desired reliability of redundant channels and the effectiveness of the event-triggered control protocol.
International Nuclear Information System (INIS)
Niemierko, Andrzej; Goitein, Michael
1991-01-01
The authors investigate a model of normal tissue complication probability for tissues that may be represented by a critical element architecture. They derive formulas for complication probability that apply to both a partial volume irradiation and to an arbitrary inhomogeneous dose distribution. The dose-volume isoeffect relationship which is a consequence of a critical element architecture is discussed and compared to the empirical power law relationship. A dose-volume histogram reduction scheme for a 'pure' critical element model is derived. In addition, a point-based algorithm which does not require precomputation of a dose-volume histogram is derived. The existing published dose-volume histogram reduction algorithms are analyzed. The authors show that the existing algorithms, developed empirically without an explicit biophysical model, have a close relationship to the critical element model at low levels of complication probability. However, it is also showed that they have aspects which are not compatible with a critical element model and the authors propose a modification to one of them to circumvent its restriction to low complication probabilities. (author). 26 refs.; 7 figs
International Nuclear Information System (INIS)
Lee, Y. M.; Hwang, Y. S.; Kim, S. G.; Kang, C. H.
2002-01-01
Using a three-dimensional numerical code, B3R developed for nuclide transport of an arbitrary length of decay chain in the buffer between the canister and adjacent rock in a high-level radioactive waste repository by adopting a finite difference method utilizing the control-volume scheme, some illustrative calculations have been done. A linear sorption isotherm, nuclide transport due to diffusion in the buffer and the rock matrix, and advection and dispersion along thin rigid parallel fractures existing in a saturated porous rock matrix as well as diffusion through the fracture wall into the matrix is assumed. In such kind of repository, buffer and rock matrix are known to be important physico-chemical barriers in nuclide retardation. To show effects of buffer and rock matrix on nuclide transport in HLW repository and also to demonstrate usefulness of B3R, several cases of breakthrough curves as well as three-dimensional plots of concentration isopleths associated with these two barriers are introduced for a typical case of decay chain of 234 U→ 230 Th→ 226 Ra, which is the most important chain as far as the human environment is concerned
Kumar, A.; Rudy, D. H.; Drummond, J. P.; Harris, J. E.
1982-01-01
Several two- and three-dimensional external and internal flow problems solved on the STAR-100 and CYBER-203 vector processing computers are described. The flow field was described by the full Navier-Stokes equations which were then solved by explicit finite-difference algorithms. Problem results and computer system requirements are presented. Program organization and data base structure for three-dimensional computer codes which will eliminate or improve on page faulting, are discussed. Storage requirements for three-dimensional codes are reduced by calculating transformation metric data in each step. As a result, in-core grid points were increased in number by 50% to 150,000, with a 10% execution time increase. An assessment of current and future machine requirements shows that even on the CYBER-205 computer only a few problems can be solved realistically. Estimates reveal that the present situation is more storage limited than compute rate limited, but advancements in both storage and speed are essential to realistically calculate three-dimensional flow.
Banks, H T; Birch, Malcolm J; Brewin, Mark P; Greenwald, Stephen E; Hu, Shuhua; Kenz, Zackary R; Kruse, Carola; Maischak, Matthias; Shaw, Simon; Whiteman, John R
2014-04-13
We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685-6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension ( r + 1) D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over [Formula: see text] for r ⩽ 100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin-Voigt and Maxwell-Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
Very Large Data Volumes Analysis of Collaborative Systems with Finite Number of States
Ivan, Ion; Ciurea, Cristian; Pavel, Sorin
2010-01-01
The collaborative system with finite number of states is defined. A very large database is structured. Operations on large databases are identified. Repetitive procedures for collaborative systems operations are derived. The efficiency of such procedures is analyzed. (Contains 6 tables, 5 footnotes and 3 figures.)
Hybrid finite-volume-ROM approach to non-linear aerospace fluid-structure interaction modelling
CSIR Research Space (South Africa)
Mowat, AGB
2011-06-01
Full Text Available ). Approximate riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics, 43(2), 357?372. [31] van Leer, B. (1979). Toward the ultimate conservative scheme v: A second order sequel to godunov?s method. Journal... of Computational Physics, 32, 101?136. [32] van Albada, G. D., van Leer, B., and Roberts, W. W. (1982). A comparative study of computational methods in cosmic gas dynamics. Astronomy and Astrophysics, 108(1), 76?84. [33] Dohrmann, C. R. and Segalman, D. J...
J.K. Hoogland (Jiri); C.D.D. Neumann
2000-01-01
textabstractIn this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing
Directory of Open Access Journals (Sweden)
Grönemeyer Dietrich HW
2006-05-01
investigations. The finite volume analysis calculates the time developing temperature maps for the model of a broken linear metallic wire embedded in tissue. Half of the total hot spot power loss is assumed to diffuse into both wire parts at the location of a defect. The energy is distributed from there by heat conduction. Additionally the effect of blood perfusion and blood flow is respected in some simulations because the simultaneous appearance of all worst case conditions, especially the absence of blood perfusion and blood flow near the hot spot, is very unlikely for vessel implants. Results The analytical solution as worst case scenario as well as the finite volume analysis for near worst case situations show not negligible volumes with critical temperature increases for part of the modeled hot spot situations. MR investigations with a high rf-pulse density lasting below a minute can establish volumes of several cubic millimeters with temperature increases high enough to start cell destruction. Longer exposure times can involve volumes larger than 100 mm3. Even temperature increases in the range of thermal ablation are reached for substantial volumes. MR sequence exposure time and hot spot power loss are the primary factors influencing the volume with critical temperature increases. Wire radius, wire material as well as the physiological parameters blood perfusion and blood flow inside larger vessels reduce the volume with critical temperature increases, but do not exclude a volume with critical tissue heating for resonators with a large product of resonator volume and quality factor. Conclusion The worst case scenario assumes thermal equilibrium for a hot spot embedded in homogeneous tissue without any cooling due to blood perfusion or flow. The finite volume analysis can calculate the results for near and not close to worst case conditions. For both cases a substantial volume can reach a critical temperature increase in a short time. The analytical solution, as absolute
Asynchronous discrete event schemes for PDEs
Stone, D.; Geiger, S.; Lord, G. J.
2017-08-01
A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.
Batty, Christopher
2017-02-01
This paper introduces a two-dimensional cell-centred finite volume discretization of the Poisson problem on adaptive Cartesian quadtree grids which exhibits second order accuracy in both the solution and its gradients, and requires no grading condition between adjacent cells. At T-junction configurations, which occur wherever resolution differs between neighboring cells, use of the standard centred difference gradient stencil requires that ghost values be constructed by interpolation. To properly recover second order accuracy in the resulting numerical gradients, prior work addressing block-structured grids and graded trees has shown that quadratic, rather than linear, interpolation is required; the gradients otherwise exhibit only first order convergence, which limits potential applications such as fluid flow. However, previous schemes fail or lose accuracy in the presence of the more complex T-junction geometries arising in the case of general non-graded quadtrees, which place no restrictions on the resolution of neighboring cells. We therefore propose novel quadratic interpolant constructions for this case that enable second order convergence by relying on stencils oriented diagonally and applied recursively as needed. The method handles complex tree topologies and large resolution jumps between neighboring cells, even along the domain boundary, and both Dirichlet and Neumann boundary conditions are supported. Numerical experiments confirm the overall second order accuracy of the method in the L∞ norm.
Directory of Open Access Journals (Sweden)
Krvavica Nino
2017-03-01
Full Text Available A finite volume model for two-layer shallow water flow in microtidal salt-wedge estuaries is presented in this work. The governing equations are a coupled system of shallow water equations with source terms accounting for irregular channel geometry and shear stress at the bed and interface between the layers. To solve this system we applied the Q-scheme of Roe with suitable treatment of source terms, coupling terms, and wet-dry fronts. The proposed numerical model is explicit in time, shock-capturing and it satisfies the extended conservation property for water at rest. The model was validated by comparing the steady-state solutions against a known arrested salt-wedge model and by comparing both steady-state and time-dependant solutions against field observations in Rječina Estuary in Croatia. When the interfacial friction factor λi was chosen correctly, the agreement between numerical results and field observations was satisfactory.
PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual
Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.
1977-01-01
The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.
Multiphase volume-preserving interface motions via localized signed distance vector scheme
Czech Academy of Sciences Publication Activity Database
Muhammad, R. Z.; Švadlenka, Karel
2015-01-01
Roč. 8, č. 5 (2015), s. 969-988 ISSN 1937-1632 Institutional support: RVO:67985840 Keywords : multiphase mean curvature flow * vector-valued signed distance * volume preservation Subject RIV: BA - General Mathematics Impact factor: 0.737, year: 2015 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11386
Finite volume spectrum of 2D field theories from Hirota dynamics
International Nuclear Information System (INIS)
Gromov, Nikolay; Kazakov, Vladimir; Vieira, Pedro; Univ. do Porto
2008-12-01
We propose, using the example of the O(4) sigma model, a general method for solving integrable two dimensional relativistic sigma models in a finite size periodic box. Our starting point is the so-called Y-system, which is equivalent to the thermodynamic Bethe ansatz equations of Yang and Yang. It is derived from the Zamolodchikov scattering theory in the cross channel, for virtual particles along the non-compact direction of the space-time cylinder. The method is based on the integrable Hirota dynamics that follows from the Y-system. The outcome is a nonlinear integral equation for a single complex function, valid for an arbitrary quantum state and accompanied by the finite size analogue of Bethe equations. It is close in spirit to the Destri-deVega (DdV) equation. We present the numerical data for the energy of various states as a function of the size, and derive the general Luescher-type formulas for the finite size corrections. We also re-derive by our method the DdV equation for the SU(2) chiral Gross-Neveu model. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Chen, Li; He, Ya-Ling [Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China); Kang, Qinjun [Computational Earth Science Group (EES-16), Los Alamos National Laboratory, Los Alamos, NM (United States); Tao, Wen-Quan, E-mail: wqtao@mail.xjtu.edu.cn [Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)
2013-12-15
A coupled (hybrid) simulation strategy spatially combining the finite volume method (FVM) and the lattice Boltzmann method (LBM), called CFVLBM, is developed to simulate coupled multi-scale multi-physicochemical processes. In the CFVLBM, computational domain of multi-scale problems is divided into two sub-domains, i.e., an open, free fluid region and a region filled with porous materials. The FVM and LBM are used for these two regions, respectively, with information exchanged at the interface between the two sub-domains. A general reconstruction operator (RO) is proposed to derive the distribution functions in the LBM from the corresponding macro scalar, the governing equation of which obeys the convection–diffusion equation. The CFVLBM and the RO are validated in several typical physicochemical problems and then are applied to simulate complex multi-scale coupled fluid flow, heat transfer, mass transport, and chemical reaction in a wall-coated micro reactor. The maximum ratio of the grid size between the FVM and LBM regions is explored and discussed. -- Highlights: •A coupled simulation strategy for simulating multi-scale phenomena is developed. •Finite volume method and lattice Boltzmann method are coupled. •A reconstruction operator is derived to transfer information at the sub-domains interface. •Coupled multi-scale multiple physicochemical processes in micro reactor are simulated. •Techniques to save computational resources and improve the efficiency are discussed.
Directory of Open Access Journals (Sweden)
Hassan Badreddine
2017-01-01
Full Text Available The current work focuses on the development and application of a new finite volume immersed boundary method (IBM to simulate three-dimensional fluid flows and heat transfer around complex geometries. First, the discretization of the governing equations based on the second-order finite volume method on Cartesian, structured, staggered grid is outlined, followed by the description of modifications which have to be applied to the discretized system once a body is immersed into the grid. To validate the new approach, the heat conduction equation with a source term is solved inside a cavity with an immersed body. The approach is then tested for a natural convection flow in a square cavity with and without circular cylinder for different Rayleigh numbers. The results computed with the present approach compare very well with the benchmark solutions. As a next step in the validation procedure, the method is tested for Direct Numerical Simulation (DNS of a turbulent flow around a surface-mounted matrix of cubes. The results computed with the present method compare very well with Laser Doppler Anemometry (LDA measurements of the same case, showing that the method can be used for scale-resolving simulations of turbulence as well.
Coupling of a 3-D vortex particle-mesh method with a finite volume near-wall solver
Marichal, Y.; Lonfils, T.; Duponcheel, M.; Chatelain, P.; Winckelmans, G.
2011-11-01
This coupling aims at improving the computational efficiency of high Reynolds number bluff body flow simulations by using two complementary methods and exploiting their respective advantages in distinct parts of the domain. Vortex particle methods are particularly well suited for free vortical flows such as wakes or jets (the computational domain -with non zero vorticity- is then compact and dispersion errors are negligible). Finite volume methods, however, can handle boundary layers much more easily due to anisotropic mesh refinement. In the present approach, the vortex method is used in the whole domain (overlapping domain technique) but its solution is highly underresolved in the vicinity of the wall. It thus has to be corrected by the near-wall finite volume solution at each time step. Conversely, the vortex method provides the outer boundary conditions for the near-wall solver. A parallel multi-resolution vortex particle-mesh approach is used here along with an Immersed Boundary method in order to take the walls into account. The near-wall flow is solved by OpenFOAM® using the PISO algorithm. We validate the methodology on the flow past a sphere at a moderate Reynolds number. F.R.S. - FNRS Research Fellow.
Moukalled, F; Darwish, M
2016-01-01
This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programm...
Schemes for aggregating preferential tariffs in agriculture,export volume effects and African LDCs
DEFF Research Database (Denmark)
Yu, Wusheng
Trade-weighted aggregated tariffs (TWPT) are often used in analyzing the issues of erosion of non-reciprocal preferences. This paper argues that commonly used TWPTs under-estimate the true protection on imports originated from preference-receiving countries, including LDCs. When used in numerical...... simulations of preference erosion and expansion scenarios, the TWPTs tend to incorrectly downplay preference erosion effect of MFN tariff cuts, and understate the export promotion effect of expanding preferences. In light of these claims, an alternative aggregation scheme is developed to calculate aggregated...... preferential tariffs imposed by a number of developed countries on African LDCs. These are shown to be higher than the TWPTs aggregated from the same disaggregated tariff data set. Numerical simulations conducted with the two sets of aggregated tariffs confirm the two claims and suggest that TWPTs may lead...
Energy Technology Data Exchange (ETDEWEB)
Bernard, Claude [Department of Physics, Washington University,One Brookings Drive, Saint Louis (United States); Bijnens, Johan [Department of Astronomy and Theoretical Physics, Lund University,Sölvegatan 14A, SE 223-62 Lund (Sweden); Gámiz, Elvira [CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada,Campus de Fuente Nueva, E-18002 Granada (Spain); Relefors, Johan [Department of Astronomy and Theoretical Physics, Lund University,Sölvegatan 14A, SE 223-62 Lund (Sweden)
2017-03-23
The determination of |V{sub us}| from kaon semileptonic decays requires the value of the form factor f{sub +}(q{sup 2}=0) which can be calculated precisely on the lattice. We provide the one-loop partially quenched chiral perturbation theory expressions both with and without including the effects of staggered quarks for all form factors at finite volume and with partially twisted boundary conditions for both the vector current and scalar density matrix elements at all q{sup 2}. We point out that at finite volume there are more form factors than just f{sub +} and f{sub −} for the vector current matrix element but that the Ward identity is fully satisfied. The size of the finite-volume corrections at present lattice sizes is small. This will help improve the lattice determination of f{sub +}(q{sup 2}=0) since the finite-volume error is the dominant error source for some calculations. The size of the finite-volume corrections may be estimated on a single lattice ensemble by comparing results for various twist choices.
Zaghi, S.
2014-07-01
OFF, an open source (free software) code for performing fluid dynamics simulations, is presented. The aim of OFF is to solve, numerically, the unsteady (and steady) compressible Navier-Stokes equations of fluid dynamics by means of finite volume techniques: the research background is mainly focused on high-order (WENO) schemes for multi-fluids, multi-phase flows over complex geometries. To this purpose a highly modular, object-oriented application program interface (API) has been developed. In particular, the concepts of data encapsulation and inheritance available within Fortran language (from standard 2003) have been stressed in order to represent each fluid dynamics "entity" (e.g. the conservative variables of a finite volume, its geometry, etc…) by a single object so that a large variety of computational libraries can be easily (and efficiently) developed upon these objects. The main features of OFF can be summarized as follows: Programming LanguageOFF is written in standard (compliant) Fortran 2003; its design is highly modular in order to enhance simplicity of use and maintenance without compromising the efficiency; Parallel Frameworks Supported the development of OFF has been also targeted to maximize the computational efficiency: the code is designed to run on shared-memory multi-cores workstations and distributed-memory clusters of shared-memory nodes (supercomputers); the code's parallelization is based on Open Multiprocessing (OpenMP) and Message Passing Interface (MPI) paradigms; Usability, Maintenance and Enhancement in order to improve the usability, maintenance and enhancement of the code also the documentation has been carefully taken into account; the documentation is built upon comprehensive comments placed directly into the source files (no external documentation files needed): these comments are parsed by means of doxygen free software producing high quality html and latex documentation pages; the distributed versioning system referred as git
Brinkman, Daniel
2013-05-01
We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction-diffusion equation for the excitons/polaron pairs and Poisson\\'s equation for the self-consistent electrostatic potential. The material difference (i.e. the HOMO/LUMO gap) of the two organic substrates forming the bilayer device is included as a work-function potential. Firstly, we perform an asymptotic analysis of the scaled one-dimensional stationary state system: (i) with focus on the dynamics on the interface and (ii) with the goal of simplifying the bulk dynamics away from the interface. Secondly, we present a two-dimensional hybrid discontinuous Galerkin finite element numerical scheme which is very well suited to resolve: (i) the material changes, (ii) the resulting strong variation over the interface, and (iii) the necessary upwinding in the discretization of drift-diffusion equations. Finally, we compare the numerical results with the approximating asymptotics. © 2013 World Scientific Publishing Company.
Directory of Open Access Journals (Sweden)
Schnorr Jörg
2005-04-01
Full Text Available Abstract Background Active Magnetic Resonance Imaging implants are constructed as resonators tuned to the Larmor frequency of a magnetic resonance system with a specific field strength. The resonating circuit may be embedded into or added to the normal metallic implant structure. The resonators build inductively coupled wireless transmit and receive coils and can amplify the signal, normally decreased by eddy currents, inside metallic structures without affecting the rest of the spin ensemble. During magnetic resonance imaging the resonators generate heat, which is additional to the usual one described by the specific absorption rate. This induces temperature increases of the tissue around the circuit paths and inside the lumen of an active implant and may negatively influence patient safety. Methods This investigation provides an overview of the supplementary power absorbed by active implants with a cylindrical geometry, corresponding to vessel implants such as stents, stent grafts or vena cava filters. The knowledge of the overall absorbed power is used in a finite volume analysis to estimate temperature maps around different implant structures inside homogeneous tissue under worst-case assumptions. The "worst-case scenario" assumes thermal heat conduction without blood perfusion inside the tissue around the implant and mostly without any cooling due to blood flow inside vessels. Results The additional power loss of a resonator is proportional to the volume and the quality factor, as well as the field strength of the MRI system and the specific absorption rate of the applied sequence. For properly working devices the finite volume analysis showed only tolerable heating during MRI investigations in most cases. Only resonators transforming a few hundred mW into heat may reach temperature increases over 5 K. This requires resonators with volumes of several ten cubic centimeters, short inductor circuit paths with only a few 10 cm and a quality
Busch, Martin H J; Vollmann, Wolfgang; Schnorr, Jörg; Grönemeyer, Dietrich H W
2005-04-08
Active Magnetic Resonance Imaging implants are constructed as resonators tuned to the Larmor frequency of a magnetic resonance system with a specific field strength. The resonating circuit may be embedded into or added to the normal metallic implant structure. The resonators build inductively coupled wireless transmit and receive coils and can amplify the signal, normally decreased by eddy currents, inside metallic structures without affecting the rest of the spin ensemble. During magnetic resonance imaging the resonators generate heat, which is additional to the usual one described by the specific absorption rate. This induces temperature increases of the tissue around the circuit paths and inside the lumen of an active implant and may negatively influence patient safety. This investigation provides an overview of the supplementary power absorbed by active implants with a cylindrical geometry, corresponding to vessel implants such as stents, stent grafts or vena cava filters. The knowledge of the overall absorbed power is used in a finite volume analysis to estimate temperature maps around different implant structures inside homogeneous tissue under worst-case assumptions. The "worst-case scenario" assumes thermal heat conduction without blood perfusion inside the tissue around the implant and mostly without any cooling due to blood flow inside vessels. The additional power loss of a resonator is proportional to the volume and the quality factor, as well as the field strength of the MRI system and the specific absorption rate of the applied sequence. For properly working devices the finite volume analysis showed only tolerable heating during MRI investigations in most cases. Only resonators transforming a few hundred mW into heat may reach temperature increases over 5 K. This requires resonators with volumes of several ten cubic centimeters, short inductor circuit paths with only a few 10 cm and a quality factor above ten. Using MR sequences, for which the MRI
Energy Technology Data Exchange (ETDEWEB)
Touma, Rony [Department of Computer Science & Mathematics, Lebanese American University, Beirut (Lebanon); Zeidan, Dia [School of Basic Sciences and Humanities, German Jordanian University, Amman (Jordan)
2016-06-08
In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential of the proposed scheme.
DEFF Research Database (Denmark)
Hattel, Jesper; Hansen, Preben
1995-01-01
This paper presents a novel control volume based FD method for solving the equilibrium equations in terms of displacements, i.e. the generalized Navier equations. The method is based on the widely used cv-FDM solution of heat conduction and fluid flow problems involving a staggered grid formulati....... The resulting linear algebraic equations are solved by line-Gauss-Seidel....
Trauma of the Frontal Region Is Influenced by the Volume of Frontal Sinuses. A Finite Element Study
Directory of Open Access Journals (Sweden)
Srbislav S. Pajic
2017-07-01
Full Text Available Anatomy of frontal sinuses varies individually, from differences in volume and shape to a rare case when the sinuses are absent. However, there are scarce data related to influence of these variations on impact generated fracture pattern. Therefore, the aim of this study was to analyse the influence of frontal sinus volume on the stress distribution and fracture pattern in the frontal region. The study included four representative Finite Element models of the skull. Reference model was built on the basis of computed tomography scans of a human head with normally developed frontal sinuses. By modifying the reference model, three additional models were generated: a model without sinuses, with hypoplasic, and with hyperplasic sinuses. A 7.7 kN force was applied perpendicularly to the forehead of each model, in order to simulate a frontal impact. The results demonstrated that the distribution of impact stress in frontal region depends on the frontal sinus volume. The anterior sinus wall showed the highest fragility in case with hyperplasic sinuses, whereas posterior wall/inner plate showed more fragility in cases with hypoplasic and undeveloped sinuses. Well-developed frontal sinuses might, through absorption of the impact energy by anterior wall, protect the posterior wall and intracranial contents.
An accelerated, fully-coupled, parallel 3D hybrid finite-volume fluid–structure interaction scheme
CSIR Research Space (South Africa)
Malan, AG
2012-09-01
Full Text Available -elemental strain procedure is employed for the solid in the interest of accuracy. For the incompressible fluid, a split-step algorithm is presented which allows the entire fluid-solid system to be solved in a fully-implicit yet matrix-free manner. The algorithm...
ABAQUS-EPGEN: a general-purpose finite-element code. Volume 1. User's manual
International Nuclear Information System (INIS)
Hibbitt, H.D.; Karlsson, B.I.; Sorensen, E.P.
1982-10-01
This document is the User's Manual for ABAQUS/EPGEN, a general purpose finite element computer program, designed specifically to serve advanced structural analysis needs. The program contains very general libraries of elements, materials and analysis procedures, and is highly modular, so that complex combinations of features can be put together to model physical problems. The program is aimed at production analysis needs, and for this purpose aspects such as ease-of-use, reliability, flexibility and efficiency have received maximum attention. The input language is designed to make it straightforward to describe complicated models; the analysis procedures are highly automated with the program choosing time or load increments based on user supplied tolerances and controls; and the program offers a wide range of post-processing options for display of the analysis results
Hegedűs, Árpád
2018-03-01
In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator \\overline{Ψ}Ψ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator \\overline{Ψ}Ψ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.
Pressure correction schemes for compressible flows
International Nuclear Information System (INIS)
Kheriji, W.
2011-01-01
This thesis is concerned with the development of semi-implicit fractional step schemes, for the compressible Navier-Stokes equations; these schemes are part of the class of the pressure correction methods. The chosen spatial discretization is staggered: non conforming mixed finite elements (Crouzeix-Raviart or Rannacher-Turek) or the classic MA C scheme. An upwind finite volume discretization of the mass balance guarantees the positivity of the density. The positivity of the internal energy is obtained by discretizing the internal energy balance by an upwind finite volume scheme and b y coupling the discrete internal energy balance with the pressure correction step. A special finite volume discretization on dual cells is performed for the convection term in the momentum balance equation, and a renormalisation step for the pressure is added to the algorithm; this ensures the control in time of the integral of the total energy over the domain. All these a priori estimates imply the existence of a discrete solution by a topological degree argument. The application of this scheme to Euler equations raises an additional difficulty. Indeed, obtaining correct shocks requires the scheme to be consistent with the total energy balance, property which we obtain as follows. First of all, a local discrete kinetic energy balance is established; it contains source terms winch we somehow compensate in the internal energy balance. The kinetic and internal energy equations are associated with the dual and primal meshes respectively, and thus cannot be added to obtain a total energy balance; its continuous counterpart is however recovered at the limit: if we suppose that a sequence of discrete solutions converges when the space and time steps tend to 0, we indeed show, in 1D at least, that the limit satisfies a weak form of the equation. These theoretical results are comforted by numerical tests. Similar results are obtained for the baro-tropic Navier-Stokes equations. (author)
Directory of Open Access Journals (Sweden)
Colin Morningstar
2017-11-01
Full Text Available An implementation of estimating the two-to-two K-matrix from finite-volume energies based on the Lüscher formalism and involving a Hermitian matrix known as the “box matrix” is described. The method includes higher partial waves and multiple decay channels. Two fitting procedures for estimating the K-matrix parameters, which properly incorporate all statistical covariances, are discussed. Formulas and software for handling total spins up to S=2 and orbital angular momenta up to L=6 are obtained for total momenta in several directions. First tests involving ρ-meson decay to two pions include the L=3 and L=5 partial waves, and the contributions from these higher waves are found to be negligible in the elastic energy range.
Bolborici, V; Dawson, F P; Pugh, M C
2014-03-01
Piezoelectric traveling wave rotary ultrasonic motors are motors that generate torque by using the friction force between a piezoelectric composite ring (or disk-shaped stator) and a metallic ring (or disk-shaped rotor) when a traveling wave is excited in the stator. The motor speed is proportional to the amplitude of the traveling wave and, in order to obtain large amplitudes, the stator is excited at frequencies close to its resonance frequency. This paper presents a non-empirical partial differential equations model for the stator, which is discretized using the finite volume method. The fundamental frequency of the discretized model is computed and compared to the experimentally-measured operating frequency of the stator of Shinsei USR60 piezoelectric motor. Copyright © 2013 Elsevier B.V. All rights reserved.
Lv, X.; Zhao, Y.; Huang, X. Y.; Xia, G. H.; Su, X. H.
2007-07-01
A new three-dimensional (3D) matrix-free implicit unstructured multigrid finite volume (FV) solver for structural dynamics is presented in this paper. The solver is first validated using classical 2D and 3D cantilever problems. It is shown that very accurate predictions of the fundamental natural frequencies of the problems can be obtained by the solver with fast convergence rates. This method has been integrated into our existing FV compressible solver [X. Lv, Y. Zhao, et al., An efficient parallel/unstructured-multigrid preconditioned implicit method for simulating 3d unsteady compressible flows with moving objects, Journal of Computational Physics 215(2) (2006) 661-690] based on the immersed membrane method (IMM) [X. Lv, Y. Zhao, et al., as mentioned above]. Results for the interaction between the fluid and an immersed fixed-free cantilever are also presented to demonstrate the potential of this integrated fluid-structure interaction approach.
ABAQUS-EPGEN: a general-purpose finite element code. Volume 3. Example problems manual
International Nuclear Information System (INIS)
Hibbitt, H.D.; Karlsson, B.I.; Sorensen, E.P.
1983-03-01
This volume is the Example and Verification Problems Manual for ABAQUS/EPGEN. Companion volumes are the User's, Theory and Systems Manuals. This volume contains two major parts. The bulk of the manual (Sections 1-8) contains worked examples that are discussed in detail, while Appendix A documents a large set of basic verification cases that provide the fundamental check of the elements in the code. The examples in Sections 1-8 illustrate and verify significant aspects of the program's capability. Most of these problems provide verification, but they have also been chosen to allow discussion of modeling and analysis techniques. Appendix A contains basic verification cases. Each of these cases verifies one element in the program's library. The verification consists of applying all possible load or flux types (including thermal loading of stress elements), and all possible foundation or film/radiation conditions, and checking the resulting force and stress solutions or flux and temperature results. This manual provides program verification. All of the problems described in the manual are run and the results checked, for each release of the program, and these verification results are made available
International Nuclear Information System (INIS)
Bernal, A.; Roman, J.E.; Miró, R.; Verdú, G.
2016-01-01
Highlights: • A method is proposed to solve the eigenvalue problem of the Neutron Diffusion Equation in BWR. • The Neutron Diffusion Equation is discretized with the Finite Volume Method. • The currents are calculated by using a polynomial expansion of the neutron flux. • The current continuity and boundary conditions are defined implicitly to reduce the size of the matrices. • Different structured and unstructured meshes were used to discretize the BWR. - Abstract: The neutron flux spatial distribution in Boiling Water Reactors (BWRs) can be calculated by means of the Neutron Diffusion Equation (NDE), which is a space- and time-dependent differential equation. In steady state conditions, the time derivative terms are zero and this equation is rewritten as an eigenvalue problem. In addition, the spatial partial derivatives terms are transformed into algebraic terms by discretizing the geometry and using numerical methods. As regards the geometrical discretization, BWRs are complex systems containing different components of different geometries and materials, but they are usually modelled as parallelepiped nodes each one containing only one homogenized material to simplify the solution of the NDE. There are several techniques to correct the homogenization in the node, but the most commonly used in BWRs is that based on Assembly Discontinuity Factors (ADFs). As regards numerical methods, the Finite Volume Method (FVM) is feasible and suitable to be applied to the NDE. In this paper, a FVM based on a polynomial expansion method has been used to obtain the matrices of the eigenvalue problem, assuring the accomplishment of the ADFs for a BWR. This eigenvalue problem has been solved by means of the SLEPc library.
High Resolution DNS of Turbulent Flows using an Adaptive, Finite Volume Method
Trebotich, David
2014-11-01
We present a new computational capability for high resolution simulation of incompressible viscous flows. Our approach is based on cut cell methods where an irregular geometry such as a bluff body is intersected with a rectangular Cartesian grid resulting in cut cells near the boundary. In the cut cells we use a conservative discretization based on a discrete form of the divergence theorem to approximate fluxes for elliptic and hyperbolic terms in the Navier-Stokes equations. Away from the boundary the method reduces to a finite difference method. The algorithm is implemented in the Chombo software framework which supports adaptive mesh refinement and massively parallel computations. The code is scalable to 200,000 + processor cores on DOE supercomputers, resulting in DNS studies at unprecedented scale and resolution. For flow past a cylinder in transition (Re = 300) we observe a number of secondary structures in the far wake in 2D where the wake is over 120 cylinder diameters in length. These are compared with the more regularized wake structures in 3D at the same scale. For flow past a sphere (Re = 600) we resolve an arrowhead structure in the velocity in the near wake. The effectiveness of AMR is further highlighted in a simulation of turbulent flow (Re = 6000) in the contraction of an oil well blowout preventer. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Contract Number DE-AC02-05-CH11231.
Numerical simulation of bubble deformation in magnetic fluids by finite volume method
International Nuclear Information System (INIS)
Yamasaki, Haruhiko; Yamaguchi, Hiroshi
2017-01-01
Bubble deformation in magnetic fluids under magnetic field is investigated numerically by an interface capturing method. The numerical method consists of a coupled level-set and VOF (Volume of Fluid) method, combined with conservation CIP (Constrained Interpolation Profile) method with the self-correcting procedure. In the present study considering actual physical properties of magnetic fluid, bubble deformation under given uniform magnetic field is analyzed for internal magnetic field passing through a magnetic gaseous and liquid phase interface. The numerical results explain the mechanism of bubble deformation under presence of given magnetic field. - Highlights: • A magnetic field analysis is developed to simulate the bubble dynamics in magnetic fluid with two-phase interface. • The elongation of bubble increased with increasing magnetic flux intensities due to strong magnetic normal force. • Proposed technique explains the bubble dynamics, taking into account of the continuity of the magnetic flux density.
ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics
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.
International Nuclear Information System (INIS)
Liang, Hongbo; Fan, Man; You, Shijun; Zheng, Wandong; Zhang, Huan; Ye, Tianzhen; Zheng, Xuejing
2017-01-01
Highlights: •Four optical models for parabolic trough solar collectors were compared in detail. •Characteristics of Monte Carlo Method and Finite Volume Method were discussed. •A novel method was presented combining advantages of different models. •The method was suited to optical analysis of collectors with different geometries. •A new kind of cavity receiver was simulated depending on the novel method. -- Abstract: The PTC (parabolic trough solar collector) is widely used for space heating, heat-driven refrigeration, solar power, etc. The concentrated solar radiation is the only energy source for a PTC, thus its optical performance significantly affects the collector efficiency. In this study, four different optical models were constructed, validated and compared in detail. On this basis, a novel coupled method was presented by combining advantages of these models, which was suited to carry out a mass of optical simulations of collectors with different geometrical parameters rapidly and accurately. Based on these simulation results, the optimal configuration of a collector with highest efficiency can be determined. Thus, this method was useful for collector optimization and design. In the four models, MCM (Monte Carlo Method) and FVM (Finite Volume Method) were used to initialize photons distribution, as well as CPEM (Change Photon Energy Method) and MCM were adopted to describe the process of reflecting, transmitting and absorbing. For simulating reflection, transmission and absorption, CPEM was more efficient than MCM, so it was utilized in the coupled method. For photons distribution initialization, FVM saved running time and computation effort, whereas it needed suitable grid configuration. MCM only required a total number of rays for simulation, whereas it needed higher computing cost and its results fluctuated in multiple runs. In the novel coupled method, the grid configuration for FVM was optimized according to the “true values” from MCM of
Institute of Scientific and Technical Information of China (English)
高夫征
2005-01-01
A finite volume element predictor-correetor method for a class of nonlinear parabolic system of equations is presented and analyzed. Suboptimal L2 error estimate for the finite volume element predictor-corrector method is derived. A numerical experiment shows that the numerical results are consistent with theoretical analysis.
Directory of Open Access Journals (Sweden)
Aoki Sinya
2018-01-01
Full Text Available The sanity check is to rule out certain classes of obviously false results, not to catch every possible error. After reviewing such a sanity check for NN bound states with the Lüscher’s finite volume formula [1–3], we give further evidences for the operator dependence of plateaux, a symptom of the fake plateau problem, against the claim [4]. We then present our critical comments on [5] by NPLQCD: (i Operator dependences of plateaux in NPL2013 [6, 7] exist with the P value of 4–5%. (ii The volume independence of plateaux in NPL2013 does not prove their correctness. (iii Effective range expansions (EREs in NPL2013 violate the physical pole condition. (iv Their comment is partly based on new data and analysis different from the original ones. (v Their new ERE does not satisfy the Lüscher’s finite volume formula.
Directory of Open Access Journals (Sweden)
yangchun chen
2017-01-01
Full Text Available Objective(s: In this study, we aimed to evaluate the efficacy of thyroid volume measurement using 99mTc pertechnetate single-photon emission computed tomography (SPECT images, acquired by the standardized uptake value (SUV-shape scheme designed by our expert team.Methods: A total of 18 consecutive patients with Graves’ disease (GD were subjected to both ultrasonographic and 99mTc pertechnetate SPECT examinations of thyroid within a five-day interval. The volume of thyroid lobes and isthmus was measured by ultrasonography (US according to the ellipsoid volume equation. The total thyroid volume, determined as the sum of the volume of both lobes and isthmus, was recorded as TV-US (i.e., thyroid volume measured by US and set as the reference. The thyroid volume was defined according to our SUV-shape scheme and was recorded as TV-SS (i.e., thyroid volume determined by the SUV-shape scheme. The data were analyzed using the Bland-Altman plot, linear regression analysis, Spearman’s rank correlation, and paired t-test, if necessary.Results: The values of TV-SS (40.2±29.4 mL and TV-US (43.0±34.7 mL were not significantly different (t=0.813; P=0.43. The linear regression equation of the two values was determined as TV-US= 1.072 × TV-SS − 0.29(r=0.906; P
Ishihara, Masamichi
2018-04-01
We studied the effects of nonextensivity on the phase transition for the system of finite volume V in the ϕ4 theory in the Tsallis nonextensive statistics of entropic parameter q and temperature T, when the deviation from the Boltzmann-Gibbs (BG) statistics, |q ‑ 1|, is small. We calculated the condensate and the effective mass to the order q ‑ 1 with the normalized q-expectation value under the free particle approximation with zero bare mass. The following facts were found. The condensate Φ divided by v, Φ/v, at q (v is the value of the condensate at T = 0) is smaller than that at q‧ for q > q‧ as a function of Tph/v which is the physical temperature Tph divided by v. The physical temperature Tph is related to the variation of the Tsallis entropy and the variation of the internal energies, and Tph at q = 1 coincides with T. The effective mass decreases, reaches minimum, and increases after that, as Tph increases. The effective mass at q > 1 is lighter than the effective mass at q = 1 at low physical temperature and heavier than the effective mass at q = 1 at high physical temperature. The effects of the nonextensivity on the physical quantity as a function of Tph become strong as |q ‑ 1| increases. The results indicate the significance of the definition of the expectation value, the definition of the physical temperature, and the constraints for the density operator, when the terms including the volume of the system are not negligible.
International Nuclear Information System (INIS)
Mishra, Subhash C.; Roy, Hillol K.
2007-01-01
The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The finite volume method (FVM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the FVM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 1-D planar and 2-D rectangular geometries were considered. In order to establish the suitability of the LBM, the energy equations of the two problems were also solved using the FVM of the computational fluid dynamics. The FVM used in the radiative heat transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FVM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the FVM for the radiative information, results were analyzed for the effects of various parameters such as the scattering albedo, the conduction-radiation parameter and the boundary emissivity. The results of the LBM-FVM combination were found to be in excellent agreement with the FVM-FVM combination. The number of iterations and CPU times in both the combinations were found comparable
A high-order finite-volume method for hyperbolic conservation laws on locally-refined grids
Energy Technology Data Exchange (ETDEWEB)
McCorquodale, Peter; Colella, Phillip
2011-01-28
We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on Cartesian grids with multiple levels of refinement. The underlying method is a generalization of that in [5] to nonlinear systems, and is based on using fourth-order accurate quadratures for computing fluxes on faces, combined with fourth-order accurate Runge?Kutta discretization in time. To interpolate boundary conditions at refinement boundaries, we interpolate in time in a manner consistent with the individual stages of the Runge-Kutta method, and interpolate in space by solving a least-squares problem over a neighborhood of each target cell for the coefficients of a cubic polynomial. The method also uses a variation on the extremum-preserving limiter in [8], as well as slope flattening and a fourth-order accurate artificial viscosity for strong shocks. We show that the resulting method is fourth-order accurate for smooth solutions, and is robust in the presence of complex combinations of shocks and smooth flows.
International Nuclear Information System (INIS)
Calise, Francesco; Palombo, Adolfo; Vanoli, Laura
2012-01-01
This paper presents a detailed finite-volume model of a concentrating photovoltaic/thermal (PVT) solar collector. The PVT solar collector consists in a parabolic trough concentrator and a linear triangular receiver. The bottom surfaces of the triangular receiver are equipped with triple-junction cells whereas the top surface is covered by an absorbing surface. The cooling fluid (water) flows inside a channel along the longitudinal direction of the PVT collector. The system was discretized along its axis and, for each slice of the discretized computational domain, mass and energy balances were considered. The model allows one to evaluate both thermodynamic and electrical parameters along the axis of the PVT collector. Then, for each slice of the computational domain, exergy balances were also considered in order to evaluate the corresponding exergy destruction rate and exergetic efficiency. Therefore, the model also calculates the magnitude of the irreversibilities inside the collector and it allows one to detect where these irreversibilities occur. A sensitivity analysis is also performed with the scope to evaluate the effect of the variation of the main design/environmental parameters on the energetic and exergetic performance of the PVT collector. -- Highlights: ► The paper investigates an innovative concentrating photovoltaic thermal solar collector. ► The collector is equipped with triple-junction photovoltaic layers. ► A local exergetic analysis is performed in order to detect sources of irreversibilities. ► Irreversibilities are mainly due to the heat transfer between sun and PVT collector.
Directory of Open Access Journals (Sweden)
Yuehua Lin
2014-03-01
Full Text Available The 3-D unstructured-grid, Finite-Volume Coastal Ocean Model (FVCOM was used to simulate the flows in Discovery Passage including the adjoining Lower Campbell River, British Columbia, Canada. Challenges in the studies include the strong tidal currents (e.g., up to 7.8 m/s in Seymour Narrows and tailrace discharges, small-scale topographic features and steep bottom slopes, and stratification affected by the Campbell River freshwater discharges. Two applications of high resolution 3-D FVCOM modeling were conducted. One is for the Lower Campbell River extending upstream as far as the John Hart Hydroelectric dam. The horizontal resolution varies from 0.27 m to 32 m in the unstructured triangular mesh to resolve the tailrace flow. The bottom elevation decreases ~14 m within the distance of ~1.4 km along the river. This pioneering FVCOM river modeling demonstrated a very good performance in simulating the river flow structures. The second application is to compute ocean currents immediately above the seabed along the present underwater electrical cable crossing routes across Discovery Passage. Higher resolution was used near the bottom with inter-layer spacing ranging from 0.125 to 0.0005 of total water depth. The model behaves very well in simulating the strong tidal currents in the area at high resolution in both the horizontal and vertical. One year maximum near bottom tidal current along the routes was then analyzed using the model results.
International Nuclear Information System (INIS)
Zhao, S.; Lardjane, N.; Fedioun, I.
2014-01-01
Improved WENO schemes, Z, M, and their combination MZ, originally designed to capture sharper discontinuities than the classical fifth order Jiang-Shu scheme does, are evaluated for the purpose of implicit large eddy simulation of free shear flows. 1D Fourier analysis of errors reveals the built-in filter and dissipative properties of the schemes, which are subsequently applied to the canonical Rayleigh-Taylor and Taylor-Green flows. Large eddy simulations of a transonic non-reacting and a supersonic reacting air/H2 jets are then performed at resolution 128 * 128 * 512, showing no significant difference in the flow statistics. However, the computational time varies from one scheme to the other, the Z scheme providing the smaller wall-time due to larger allowed time steps. (authors)
Rocklin, Gabriel J; Mobley, David L; Dill, Ken A; Hünenberger, Philippe H
2013-11-14
The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB
Energy Technology Data Exchange (ETDEWEB)
Rocklin, Gabriel J. [Department of Pharmaceutical Chemistry, University of California San Francisco, 1700 4th St., San Francisco, California 94143-2550, USA and Biophysics Graduate Program, University of California San Francisco, 1700 4th St., San Francisco, California 94143-2550 (United States); Mobley, David L. [Departments of Pharmaceutical Sciences and Chemistry, University of California Irvine, 147 Bison Modular, Building 515, Irvine, California 92697-0001, USA and Department of Chemistry, University of New Orleans, 2000 Lakeshore Drive, New Orleans, Louisiana 70148 (United States); Dill, Ken A. [Laufer Center for Physical and Quantitative Biology, 5252 Stony Brook University, Stony Brook, New York 11794-0001 (United States); Hünenberger, Philippe H., E-mail: phil@igc.phys.chem.ethz.ch [Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093 Zürich (Switzerland)
2013-11-14
The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges −5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol{sup −1}) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non
Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.
2013-11-01
The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol-1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB
ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and nn̅-oscillations
Directory of Open Access Journals (Sweden)
Bijnens Johan
2018-01-01
Full Text Available I present higher loop order results for several calculations in Chiral perturbation Theory. 1 Two-loop results at finite volume for hadronic vacuum polarization. 2 A three-loop calculation of the pion mass and decay constant in two-flavour ChPT. For the pion mass all needed auxiliary parameters can be determined from lattice calculations of ππ-scattering. 3 Chiral corrections to neutron-anti-neutron oscillations.
ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and nn̅-oscillations
Bijnens, Johan
2018-03-01
I present higher loop order results for several calculations in Chiral perturbation Theory. 1) Two-loop results at finite volume for hadronic vacuum polarization. 2) A three-loop calculation of the pion mass and decay constant in two-flavour ChPT. For the pion mass all needed auxiliary parameters can be determined from lattice calculations of ππ-scattering. 3) Chiral corrections to neutron-anti-neutron oscillations.
Sayed, Sadeed Bin
2015-05-05
A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert- Wilton-Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations can not be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.
Sayed, Sadeed Bin; Ulku, Huseyin; Bagci, Hakan
2015-01-01
A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert- Wilton-Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations can not be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.
Directory of Open Access Journals (Sweden)
Antonio J. Torregrosa
2017-05-01
Full Text Available Duct junctions play a major role in the operation and design of most piping systems. The objective of this paper is to establish the potential of a staggered mesh finite volume model as a way to improve the description of the effect of simple duct junctions on an otherwise one-dimensional flow system, such as the intake or exhaust of an internal combustion engine. Specific experiments have been performed in which different junctions have been characterized as a multi-port, and that have provided precise and reliable results on the propagation of pressure pulses across junctions. The results obtained have been compared to simulations performed with a staggered mesh finite volume method with different flux limiters and different meshes and, as a reference, have also been compared with the results of a more conventional pressure loss-based model. The results indicate that the staggered mesh finite volume model provides a closer description of wave dynamics, even if further work is needed to establish the optimal calculation settings.
Energy Technology Data Exchange (ETDEWEB)
Delfin L, A.; Alonso V, G. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico); Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: adl@nuclear.inin.mx
2003-07-01
In this work the development of a third order scheme of finite differences centered in mesh is presented and it is applied in the numerical solution of those diffusion equations in multi groups in stationary state and X Y geometry. Originally this scheme was developed by Hennart and del Valle for the monoenergetic diffusion equation with a well-known source and they show that the one scheme is of third order when comparing the numerical solution with the analytical solution of a model problem using several mesh refinements and boundary conditions. The scheme by them developed it also introduces the application of numeric quadratures to evaluate the rigidity matrices and of mass that its appear when making use of the finite elements method of Galerkin. One of the used quadratures is the open quadrature of 4 points, no-standard, of Newton-Cotes to evaluate in approximate form the elements of the rigidity matrices. The other quadrature is that of 3 points of Radau that it is used to evaluate the elements of all the mass matrices. One of the objectives of these quadratures are to eliminate the couplings among the Legendre moments 0 and 1 associated to the left and right faces as those associated to the inferior and superior faces of each cell of the discretization. The other objective is to satisfy the particles balance in weighed form in each cell. In this work it expands such development to multiplicative means considering several energy groups. There are described diverse details inherent to the technique, particularly those that refer to the simplification of the algebraic systems that appear due to the space discretization. Numerical results for several test problems are presented and are compared with those obtained with other nodal techniques. (Author)
International Nuclear Information System (INIS)
Capdevila, R.; Perez-Segarra, C.D.; Oliva, A.
2010-01-01
In the present work four different spatial numerical schemes have been developed with the aim of reducing the false-scattering of the numerical solutions obtained with the discrete ordinates (DOM) and the finite volume (FVM) methods. These schemes have been designed specifically for unstructured meshes by means of the extrapolation of nodal values of intensity on the studied radiative direction. The schemes have been tested and compared in several 3D benchmark test cases using both structured orthogonal and unstructured grids.
International Nuclear Information System (INIS)
Calise, F.; Ferruzzi, G.; Vanoli, L.
2009-01-01
This paper presents a very detailed local exergy analysis of a tubular Solid Oxide Fuel Cell (SOFC) stack. In particular, a complete parametric analysis has been carried out, in order to assess the effects of the synthesis/design parameters on the local irreversibilities in the components of the stack. A finite-volume axial-symmetric model of the tubular internal reforming Solid Oxide Fuel Cell stack under investigation has been used. The stack consists of: SOFC tubes, tube-in-tube pre-reformer and tube and shell catalytic burner. The model takes into account the effects of heat/mass transfer and chemical/electrochemical reactions. The model allows one to predict the performance of a SOFC stack once a series of design and operative parameters are fixed, but also to investigate the source and localization of inefficiency. To this scope, an exergy analysis was implemented. The SOFC tube, the pre-reformer and the catalytic burner are discretized along their longitudinal axes. Detailed models of the kinetics of the reforming, catalytic combustion and electrochemical reactions are implemented. Pressure drops, convection heat transfer and overvoltages are calculated on the basis of the work previously developed by the authors. The heat transfer model includes the contribution of thermal radiation, so improving the models previously used by the authors. Radiative heat transfer is calculated on the basis of the slice-to-slice configuration factors and corresponding radiosities. On the basis of this thermochemical model, an exergy analysis has been carried out, in order to localize the sources and the magnitude of irreversibilities along the components of the stack. In addition, the main synthesis/design variables were varied in order to assess their effect on the exergy destruction within the component to which the parameter directly refers ('endogenous' contribution) and on the exergy destruction of all remaining components ('exogenous' contribution). Then, this analysis
International Nuclear Information System (INIS)
Ediger, M.D.; Domingue, R.P.; Fayer, M.D.
1984-01-01
A detailed experimental and theoretical examination of electronic excited state transport in the finite volume system, octadecyl rhodamine B molecules in triton X-100 micelles, is presented. Picosecond fluorescence mixing and transient grating techniques were used to examine systems in which the average number of chromophores per micelle ranged from 0.1 to 11. Because of the clustering of chromophores in the small micelles, the energy transport observed is extremely efficient. A statistical mechanical theory, based on a density expansion with a Pade approximant, is developed for donor--donor transport on a spherical surface. This theory accurately accounts for the experimental data with only the micelle radius as an adjustable parameter. The radius obtained from this procedure is in good agreement with determinations by other methods. This demonstrates that quantitative information about the spatial extent of chromophore distributions in small volumes can be obtained when appropriate finite volume energy transport theories are employed. It is shown that theories developed for infinite volumes are not applicable to systems such as the ones considered here. Finally the partitioning of rhodamine B and octadecyl rhodamine B between aqueous and micellar phases is measured, and lifetimes and rotation times are reported
Aravena, J.; Dussaillant, A. R.
2006-12-01
Source control is the fundamental principle behind sustainable management of stormwater. Rain gardens are an infiltration practice that provides volume and water quality control, recharge, and multiple landscape, ecological and economic potential benefits. The fulfillment of these objectives requires understanding their behavior during events as well as long term, and tools for their design. We have developed a model based on Richards equation coupled to a surface water balance, solved with a 2D finite volume Fortran code which allows alternating upper boundary conditions, including ponding, which is not present in available 2D models. Also, it can simulate non homogeneous water input, heterogeneous soil (layered or more complex geometries), and surface irregularities -e.g. terracing-, so as to estimate infiltration and recharge. The algorithm is conservative; being an advantage compared to available finite difference and finite element methods. We will present performance comparisons to known models, to experimental data from a bioretention cell, which receives roof water to its surface depression planted with native species in an organic-rich root zone soil layer (underlain by a high conductivity lower layer that, while providing inter-event storage, percolates water readily), as well as long term simulations for different rain garden configurations. Recharge predictions for different climates show significant increases from natural recharge, and that the optimal area ratio (raingarden vs. contributing impervious area) reduces from 20% (humid) to 5% (dry).
Homogenization scheme for acoustic metamaterials
Yang, Min
2014-02-26
We present a homogenization scheme for acoustic metamaterials that is based on reproducing the lowest orders of scattering amplitudes from a finite volume of metamaterials. This approach is noted to differ significantly from that of coherent potential approximation, which is based on adjusting the effective-medium parameters to minimize scatterings in the long-wavelength limit. With the aid of metamaterials’ eigenstates, the effective parameters, such as mass density and elastic modulus can be obtained by matching the surface responses of a metamaterial\\'s structural unit cell with a piece of homogenized material. From the Green\\'s theorem applied to the exterior domain problem, matching the surface responses is noted to be the same as reproducing the scattering amplitudes. We verify our scheme by applying it to three different examples: a layered lattice, a two-dimensional hexagonal lattice, and a decorated-membrane system. It is shown that the predicted characteristics and wave fields agree almost exactly with numerical simulations and experiments and the scheme\\'s validity is constrained by the number of dominant surface multipoles instead of the usual long-wavelength assumption. In particular, the validity extends to the full band in one dimension and to regimes near the boundaries of the Brillouin zone in two dimensions.
Martin, Heiner; Guthoff, Rudolf; Schmitz, Klaus-Peter
2011-09-01
Polymer injection into the capsular bag after phakoemulsification is an interesting and promising approach to lens surgery. Safe clinical application of this technique will require an appropriate estimate of the effect of implantation variables on the lens power. This article details the results of finite element investigations into the effects of the injected polymer volume and capsular bag contraction on the resultant lens power and accommodation amplitude. An axisymmetric finite element model was created from literature sources. Polymer injection and the capsular contraction were simulated, and their effect on the lens power was calculated. The simulations show that overfilling during polymer injection leads to a refractive power increase of the lens. Capsular bag contraction also results in a power increase. The calculated accommodative amplitude of the lens is minimally affected by capsular bag contraction but decreases significantly with increased capsular bag stiffness as a result of fibrosis. © 2010 The Authors. Journal compilation © 2010 Acta Ophthalmol.
International Nuclear Information System (INIS)
Da Silva, R S; De Carvalho, D K E; Antunes, A R E; Lyra, P R M; Willmersdorf, R B
2010-01-01
In this paper a finite volume method with a 'Modified Implicit Pressure, Explicit Saturation' (MIMPES) approach is used to model the 3-D incompressible and immiscible two-phase flow of water and oil in heterogeneous and anisotropic porous media. A vertex centered finite volume method with an edge-based data structure is adopted to discretize both the elliptic pressure and the hyperbolic saturation equations using parallel computers with distributed memory. Due to the explicit solution of the saturation equation in the IMPES method, severe time step restrictions are imposed on the simulation. In order to circumvent this problem, an edge-based implementation of the MIMPES method was used. In this method, the pressure equation is solved and the velocity field is computed much less frequently than the saturation field. Following the work of Hurtado, a mean relative variation of the velocity field throughout the simulation is used to automatically control the updating process, allowing for much larger time-steps in a very simple way. In order to run large scale problems, we have developed a parallel implementation using clusters of PC's. The simulator uses open source parallel libraries like FMDB, ParMetis and PETSc. Results of speed-up and efficiency are presented to validate the performance of the parallel simulator.
Energy Technology Data Exchange (ETDEWEB)
Kawashima, H. [Ship Research Inst., Tokyo (Japan); Miyata, H. [The University of Tokyo, Tokyo (Japan). Faculty of Engineering
1996-12-31
With an objective to clarify possibility of application of time-advancing calculated fluid dynamic (CFD) simulation by using a finite volume method with moving grid system, a simulation was performed on motion of a ship with hydrofoils including the control system therein. The simulation consists of a method that couples a moving grid system technology, an equation of motion, and the control system. Complex interactions between wings and with free surface may be considered automatically by directly deriving fluid force from a flow field by using the CFD. In addition, two-dimensional flows around tandem hydrofoils were calculated to solve the motion problem within a vertical plane. As a result, the following results were obtained: a finite volume method using a dynamic moving grid system method was applied to problems in non-steady tandem hydrofoils to show its usefulness; a method that couples the CFD with the equation of motion was applied to the control problems in the tandem hydrofoils to show possibility of a new technology for simulating motions; and a simulation that considers such wing interference as wave creation, discharged vortices, and associated flows was shown useful to understand characteristics of the tandem hydrofoils. 13 refs., 14 figs.
Energy Technology Data Exchange (ETDEWEB)
Le Dez, V; Lallemand, M [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M; Charette, A [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees
1997-12-31
The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.
Energy Technology Data Exchange (ETDEWEB)
Le Dez, V.; Lallemand, M. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M.; Charette, A. [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees
1996-12-31
The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.
Cai, Xiaohui; Liu, Yang; Ren, Zhiming
2018-06-01
Reverse-time migration (RTM) is a powerful tool for imaging geologically complex structures such as steep-dip and subsalt. However, its implementation is quite computationally expensive. Recently, as a low-cost solution, the graphic processing unit (GPU) was introduced to improve the efficiency of RTM. In the paper, we develop three ameliorative strategies to implement RTM on GPU card. First, given the high accuracy and efficiency of the adaptive optimal finite-difference (FD) method based on least squares (LS) on central processing unit (CPU), we study the optimal LS-based FD method on GPU. Second, we develop the CPU-based hybrid absorbing boundary condition (ABC) to the GPU-based one by addressing two issues of the former when introduced to GPU card: time-consuming and chaotic threads. Third, for large-scale data, the combinatorial strategy for optimal checkpointing and efficient boundary storage is introduced for the trade-off between memory and recomputation. To save the time of communication between host and disk, the portable operating system interface (POSIX) thread is utilized to create the other CPU core at the checkpoints. Applications of the three strategies on GPU with the compute unified device architecture (CUDA) programming language in RTM demonstrate their efficiency and validity.
Energy Technology Data Exchange (ETDEWEB)
Sugano, Yasutaka [Graduate School of Health Sciences, Hokkaido University, Kita-12, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-0812 (Japan); Mizuta, Masahiro [Laboratory of Advanced Data Science, Information Initiative Center, Hokkaido University, Kita-11, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-0811 (Japan); Takao, Seishin; Shirato, Hiroki; Sutherland, Kenneth L. [Department of Radiation Medicine, Graduate School of Medicine, Hokkaido University, Kita-15, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-8638 (Japan); Date, Hiroyuki, E-mail: date@hs.hokudai.ac.jp [Faculty of Health Sciences, Hokkaido University, Kita-12, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-0812 (Japan)
2015-11-15
Purpose: Radiotherapy of solid tumors has been performed with various fractionation regimens such as multi- and hypofractionations. However, the ability to optimize the fractionation regimen considering the physical dose distribution remains insufficient. This study aims to optimize the fractionation regimen, in which the authors propose a graphical method for selecting the optimal number of fractions (n) and dose per fraction (d) based on dose–volume histograms for tumor and normal tissues of organs around the tumor. Methods: Modified linear-quadratic models were employed to estimate the radiation effects on the tumor and an organ at risk (OAR), where the repopulation of the tumor cells and the linearity of the dose-response curve in the high dose range of the surviving fraction were considered. The minimization problem for the damage effect on the OAR was solved under the constraint that the radiation effect on the tumor is fixed by a graphical method. Here, the damage effect on the OAR was estimated based on the dose–volume histogram. Results: It was found that the optimization of fractionation scheme incorporating the dose–volume histogram is possible by employing appropriate cell surviving models. The graphical method considering the repopulation of tumor cells and a rectilinear response in the high dose range enables them to derive the optimal number of fractions and dose per fraction. For example, in the treatment of prostate cancer, the optimal fractionation was suggested to lie in the range of 8–32 fractions with a daily dose of 2.2–6.3 Gy. Conclusions: It is possible to optimize the number of fractions and dose per fraction based on the physical dose distribution (i.e., dose–volume histogram) by the graphical method considering the effects on tumor and OARs around the tumor. This method may stipulate a new guideline to optimize the fractionation regimen for physics-guided fractionation.
A novel grain cluster-based homogenization scheme
International Nuclear Information System (INIS)
Tjahjanto, D D; Eisenlohr, P; Roters, F
2010-01-01
An efficient homogenization scheme, termed the relaxed grain cluster (RGC), for elasto-plastic deformations of polycrystals is presented. The scheme is based on a generalization of the grain cluster concept. A volume element consisting of eight (= 2 × 2 × 2) hexahedral grains is considered. The kinematics of the RGC scheme is formulated within a finite deformation framework, where the relaxation of the local deformation gradient of each individual grain is connected to the overall deformation gradient by the, so-called, interface relaxation vectors. The set of relaxation vectors is determined by the minimization of the constitutive energy (or work) density of the overall cluster. An additional energy density associated with the mismatch at the grain boundaries due to relaxations is incorporated as a penalty term into the energy minimization formulation. Effectively, this penalty term represents the kinematical condition of deformation compatibility at the grain boundaries. Simulations have been performed for a dual-phase grain cluster loaded in uniaxial tension. The results of the simulations are presented and discussed in terms of the effective stress–strain response and the overall deformation anisotropy as functions of the penalty energy parameters. In addition, the prediction of the RGC scheme is compared with predictions using other averaging schemes, as well as to the result of direct finite element (FE) simulation. The comparison indicates that the present RGC scheme is able to approximate FE simulation results of relatively fine discretization at about three orders of magnitude lower computational cost
International Nuclear Information System (INIS)
Kajzer, A; Pozorski, J; Szewc, K
2014-01-01
In the paper we present Large-eddy simulation (LES) results of 3D Taylor- Green vortex obtained by the three different computational approaches: Smoothed Particle Hydrodynamics (SPH), Lattice Boltzmann Method (LBM) and Finite Volume Method (FVM). The Smagorinsky model was chosen as a subgrid-scale closure in LES for all considered methods and a selection of spatial resolutions have been investigated. The SPH and LBM computations have been carried out with the use of the in-house codes executed on GPU and compared, for validation purposes, with the FVM results obtained using the open-source CFD software OpenFOAM. A comparative study in terms of one-point statistics and turbulent energy spectra shows a good agreement of LES results for all methods. An analysis of the GPU code efficiency and implementation difficulties has been made. It is shown that both SPH and LBM may offer a significant advantage over mesh-based CFD methods.
International Nuclear Information System (INIS)
Das, Ranjan; Mishra, Subhash C.; Ajith, M.; Uppaluri, R.
2008-01-01
This article deals with the simultaneous estimation of parameters in a 2-D transient conduction-radiation heat transfer problem. The homogeneous medium is assumed to be absorbing, emitting and scattering. The boundaries of the enclosure are diffuse gray. Three parameters, viz. the scattering albedo, the conduction-radiation parameter and the boundary emissivity, are simultaneously estimated by the inverse method involving the lattice Boltzmann method (LBM) and the finite volume method (FVM) in conjunction with the genetic algorithm (GA). In the direct method, the FVM is used for computing the radiative information while the LBM is used to solve the energy equation. The temperature field obtained in the direct method is used in the inverse method for simultaneous estimation of unknown parameters using the LBM-FVM and the GA. The LBM-FVM-GA combination has been found to accurately predict the unknown parameters
New advection schemes for free surface flows
International Nuclear Information System (INIS)
Pavan, Sara
2016-01-01
The purpose of this thesis is to build higher order and less diffusive schemes for pollutant transport in shallow water flows or 3D free surface flows. We want robust schemes which respect the main mathematical properties of the advection equation with relatively low numerical diffusion and apply them to environmental industrial applications. Two techniques are tested in this work: a classical finite volume method and a residual distribution technique combined with a finite element method. For both methods we propose a decoupled approach since it is the most advantageous in terms of accuracy and CPU time. Concerning the first technique, a vertex-centred finite volume method is used to solve the augmented shallow water system where the numerical flux is computed through an Harten-Lax-Van Leer-Contact Riemann solver. Starting from this solution, a decoupled approach is formulated and is preferred since it allows to compute with a larger time step the advection of a tracer. This idea was inspired by Audusse, E. and Bristeau, M.O. [13]. The Monotonic Upwind Scheme for Conservation Law, combined with the decoupled approach, is then used for the second order extension in space. The wetting and drying problem is also analysed and a possible solution is presented. In the second case, the shallow water system is entirely solved using the finite element technique and the residual distribution method is applied to the solution of the tracer equation, focusing on the case of time-dependent problems. However, for consistency reasons the resolution of the continuity equation must be considered in the numerical discretization of the tracer. In order to get second order schemes for unsteady cases a predictor-corrector scheme is used in this work. A first order but less diffusive version of the predictor-corrector scheme is also introduced. Moreover, we also present a new locally semi-implicit version of the residual distribution method which, in addition to good properties in
Space-Time Transformation in Flux-form Semi-Lagrangian Schemes
Directory of Open Access Journals (Sweden)
Peter C. Chu Chenwu Fan
2010-01-01
Full Text Available With a finite volume approach, a flux-form semi-Lagrangian (TFSL scheme with space-time transformation was developed to provide stable and accurate algorithm in solving the advection-diffusion equation. Different from the existing flux-form semi-Lagrangian schemes, the temporal integration of the flux from the present to the next time step is transformed into a spatial integration of the flux at the side of a grid cell (space for the present time step using the characteristic-line concept. The TFSL scheme not only keeps the good features of the semi-Lagrangian schemes (no Courant number limitation, but also has higher accuracy (of a second order in both time and space. The capability of the TFSL scheme is demonstrated by the simulation of the equatorial Rossby-soliton propagation. Computational stability and high accuracy makes this scheme useful in ocean modeling, computational fluid dynamics, and numerical weather prediction.
A well-balanced scheme for Ten-Moment Gaussian closure equations with source term
Meena, Asha Kumari; Kumar, Harish
2018-02-01
In this article, we consider the Ten-Moment equations with source term, which occurs in many applications related to plasma flows. We present a well-balanced second-order finite volume scheme. The scheme is well-balanced for general equation of state, provided we can write the hydrostatic solution as a function of the space variables. This is achieved by combining hydrostatic reconstruction with contact preserving, consistent numerical flux, and appropriate source discretization. Several numerical experiments are presented to demonstrate the well-balanced property and resulting accuracy of the proposed scheme.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 2. Electronic Commerce - Payment Schemes. V Rajaraman. Series Article Volume 6 Issue 2 February 2001 pp 6-13. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/02/0006-0013 ...
B. Koren (Barry); M.R. Lewis; E.H. van Brummelen (Harald); B. van Leer
2001-01-01
textabstractA finite-volume method is presented for the computation of compressible flows of two immiscible fluids at very different densities. The novel ingredient in the method is a two-fluid linearized Godunov scheme, allowing for flux computations in case of different fluids (e.g., water and
Finite size scaling and lattice gauge theory
International Nuclear Information System (INIS)
Berg, B.A.
1986-01-01
Finite size (Fisher) scaling is investigated for four dimensional SU(2) and SU(3) lattice gauge theories without quarks. It allows to disentangle violations of (asymptotic) scaling and finite volume corrections. Mass spectrum, string tension, deconfinement temperature and lattice β-function are considered. For appropriate volumes, Monte Carlo investigations seem to be able to control the finite volume continuum limit. Contact is made with Luescher's small volume expansion and possibly also with the asymptotic large volume behavior. 41 refs., 19 figs
Yuan, Chao; Chareyre, Bruno; Darve, Félix
2016-09-01
A pore-scale model is introduced for two-phase flow in dense packings of polydisperse spheres. The model is developed as a component of a more general hydromechanical coupling framework based on the discrete element method, which will be elaborated in future papers and will apply to various processes of interest in soil science, in geomechanics and in oil and gas production. Here the emphasis is on the generation of a network of pores mapping the void space between spherical grains, and the definition of local criteria governing the primary drainage process. The pore space is decomposed by Regular Triangulation, from which a set of pores connected by throats are identified. A local entry capillary pressure is evaluated for each throat, based on the balance of capillary pressure and surface tension at equilibrium. The model reflects the possible entrapment of disconnected patches of the receding wetting phase. It is validated by a comparison with drainage experiments. In the last part of the paper, a series of simulations are reported to illustrate size and boundary effects, key questions when studying small samples made of spherical particles be it in simulations or experiments. Repeated tests on samples of different sizes give evolution of water content which are not only scattered but also strongly biased for small sample sizes. More than 20,000 spheres are needed to reduce the bias on saturation below 0.02. Additional statistics are generated by subsampling a large sample of 64,000 spheres. They suggest that the minimal sampling volume for evaluating saturation is one hundred times greater that the sampling volume needed for measuring porosity with the same accuracy. This requirement in terms of sample size induces a need for efficient computer codes. The method described herein has a low algorithmic complexity in order to satisfy this requirement. It will be well suited to further developments toward coupled flow-deformation problems in which evolution of the
Salama, Amgad
2013-09-01
In this work the problem of flow in three-dimensional, axisymmetric, heterogeneous porous medium domain is investigated numerically. For this system, it is natural to use cylindrical coordinate system, which is useful in describing phenomena that have some rotational symmetry about the longitudinal axis. This can happen in porous media, for example, in the vicinity of production/injection wells. The basic feature of this system is the fact that the flux component (volume flow rate per unit area) in the radial direction is changing because of the continuous change of the area. In this case, variables change rapidly closer to the axis of symmetry and this requires the mesh to be denser. In this work, we generalize a methodology that allows coarser mesh to be used and yet yields accurate results. This method is based on constructing local analytical solution in each cell in the radial direction and moves the derivatives in the other directions to the source term. A new expression for the harmonic mean of the hydraulic conductivity in the radial direction is developed. Apparently, this approach conforms to the analytical solution for uni-directional flows in radial direction in homogeneous porous media. For the case when the porous medium is heterogeneous or the boundary conditions is more complex, comparing with the mesh-independent solution, this approach requires only coarser mesh to arrive at this solution while the traditional methods require more denser mesh. Comparisons for different hydraulic conductivity scenarios and boundary conditions have also been introduced. © 2013 Elsevier B.V.
Energy Technology Data Exchange (ETDEWEB)
Bellivier, A.
2004-05-15
For 3D modelling of thermo-aeraulics in building using field codes, it is necessary to reduce the computing time in order to model increasingly larger volumes. The solution suggested in this study is to couple two modelling: a zonal approach and a CFD approach. The first part of the work that was carried out is the setting of a simplified CFD modelling. We propose rules for use of coarse grids, a constant effective viscosity law and adapted coefficients for heat exchange in the framework of building thermo-aeraulics. The second part of this work concerns the creation of fluid Macro-Elements and their coupling with a calculation of CFD finite volume type. Depending on the boundary conditions of the problem, a local description of the driving flow is proposed via the installation and use of semi-empirical evolution laws. The Macro-Elements is then inserted in CFD computation: the values of velocity calculated by the evolution laws are imposed on the CFD cells corresponding to the Macro-Element. We use these two approaches on five cases representative of thermo-aeraulics in buildings. The results are compared with experimental data and with traditional RANS simulations. We highlight the significant gain of time that our approach allows while preserving a good quality of numerical results. (author)
A Cell-Centered Multiphase ALE Scheme With Structural Coupling
Energy Technology Data Exchange (ETDEWEB)
Dunn, Timothy Alan [Univ. of California, Davis, CA (United States)
2012-04-16
A novel computational scheme has been developed for simulating compressible multiphase flows interacting with solid structures. The multiphase fluid is computed using a Godunov-type finite-volume method. This has been extended to allow computations on moving meshes using a direct arbitrary-Eulerian- Lagrangian (ALE) scheme. The method has been implemented within a Lagrangian hydrocode, which allows modeling the interaction with Lagrangian structural regions. Although the above scheme is general enough for use on many applications, the ultimate goal of the research is the simulation of heterogeneous energetic material, such as explosives or propellants. The method is powerful enough for application to all stages of the problem, including the initial burning of the material, the propagation of blast waves, and interaction with surrounding structures. The method has been tested on a number of canonical multiphase tests as well as fluid-structure interaction problems.
Alemi Ardakani, Hamid; Bridges, Thomas J.; Turner, Matthew R.
2016-06-01
A class of augmented approximate Riemann solvers due to George (2008) [12] is extended to solve the shallow-water equations in a moving vessel with variable bottom topography and variable cross-section with wetting and drying. A class of Roe-type upwind solvers for the system of balance laws is derived which respects the steady-state solutions. The numerical solutions of the new adapted augmented f-wave solvers are validated against the Roe-type solvers. The theory is extended to solve the shallow-water flows in moving vessels with arbitrary cross-section with influx-efflux boundary conditions motivated by the shallow-water sloshing in the ocean wave energy converter (WEC) proposed by Offshore Wave Energy Ltd. (OWEL) [1]. A fractional step approach is used to handle the time-dependent forcing functions. The numerical solutions are compared to an extended new Roe-type solver for the system of balance laws with a time-dependent source function. The shallow-water sloshing finite volume solver can be coupled to a Runge-Kutta integrator for the vessel motion.
Pla, D.; Sánchez-González, A.; Garbayo, I.; Salleras, M.; Morata, A.; Tarancón, A.
2015-10-01
The inherent limited capacity of current battery technology is not sufficient for covering the increasing power requirements of widely extended portable devices. Among other promising alternatives, recent advances in the field of micro-Solid Oxide Fuel Cells (μ-SOFCs) converted this disruptive technology into a serious candidate to power next generations of portable devices. However, the implementation of single cells in real devices, i.e. μ-SOFC stacks coupled to the required balance-of-plant elements like fuel reformers or post combustors, still remains unexplored. This work aims addressing this system-level research by proposing a new compact design of a vertically stacked device fuelled with ethanol. The feasibility and design optimization for achieving a thermally self-sustained regime and a rapid and low-power consuming start-up is studied by finite volume analysis. An optimal thermal insulation strategy is defined to maintain the steady-state operation temperature of the μ-SOFC at 973 K and an external temperature lower than 323 K. A hybrid start-up procedure, based on heaters embedded in the μ-SOFCs and heat released by chemical reactions in the post-combustion unit, is analyzed allowing start-up times below 1 min and energy consumption under 500 J. These results clearly demonstrate the feasibility of high temperature μ-SOFC power systems fuelled with hydrocarbons for portable applications, therefore, anticipating a new family of mobile and uninterrupted power generators.
Dobravec, Tadej; Mavrič, Boštjan; Šarler, Božidar
2017-11-01
A two-dimensional model to simulate the dendritic and eutectic growth in binary alloys is developed. A cellular automaton method is adopted to track the movement of the solid-liquid interface. The diffusion equation is solved in the solid and liquid phases by using an explicit finite volume method. The computational domain is divided into square cells that can be hierarchically refined or coarsened using an adaptive mesh based on the quadtree algorithm. Such a mesh refines the regions of the domain near the solid-liquid interface, where the highest concentration gradients are observed. In the regions where the lowest concentration gradients are observed the cells are coarsened. The originality of the work is in the novel, adaptive approach to the efficient and accurate solution of the posed multiscale problem. The model is verified and assessed by comparison with the analytical results of the Lipton-Glicksman-Kurz model for the steady growth of a dendrite tip and the Jackson-Hunt model for regular eutectic growth. Several examples of typical microstructures are simulated and the features of the method as well as further developments are discussed.
Directory of Open Access Journals (Sweden)
Gabriel Felipe Aguilera
2014-07-01
Full Text Available The hydrocyclone is one of the most used classification equipment in industry, particularly in mineral processing. Maybe its main characteristic is to be a hydrodynamic separation equipment, whereby it has a high production capability and different levels of efficiency are depending on the geometrical configuration, operational parameters and the type of material to be processed. Nevertheless, there are a few successful studies regarding the modelling and simulation of its hydrodynamic principles, because the flow behavior inside is quite complex. Most of the current models are empirical and they are not applicable to all cases and types of minerals. One of the most important problems to be solved, besides the cut size and the effect of the physical properties of the particles, is the distribution of the flow inside the hydrocyclone, because if the work of the equipment is at low slurry densities, very clear for small hydrocyclones, its mechanic behavior is a consequence of the kind of liquid used as continuous phase, being water the most common liquid. This work shows the modelling and simulation of the hydrodynamic behavior of a suspension inside a hydrocyclone, including the air core effect, through the use of finite differences method. For the developing of the model, the Reynolds Stress Model (RSM for the evaluation of turbulence, and the Volume of Fluid (VOF to study the interaction between water and air were used. Finally, the model shows to be significant for experimental data, and for different conditions of an industrial plant.
Energy Technology Data Exchange (ETDEWEB)
Akimoto, H. [Tottori University, Tottori (Japan). Faculty of Engineering
1997-06-01
A new simulation code WISDAM-7 is developed to simulate performance of a sailing boat moving three-dimensionally on a free surface. It adequately predicts forces acting on each element, such as hull, sail, keel and rudder, and use them as the inputs to solve equations of hull motion of 6 freedoms. Its major features are the grid system fit for both free and hull surfaces, generation of discrete space by the finite-volume method, handling of the velocity vectors directly as those in the Descartes system, velocity and pressure placed at the cell center, use of the moving grid system for free and object surfaces, and use of equations of hull motion of 6 freedoms. It is confirmed by comparing simulated motion of an IACC class yacht with the observed surface pressure distributions in the test tank that the new method satisfies the basic requirements for simulation of sailing boat motion and expands the applicable range of CFD to general motion conditions. 8 refs., 18 figs.
Institute of Scientific and Technical Information of China (English)
Yirang YUAN; Qing YANG; Changfeng LI; Tongjun SUN
2017-01-01
Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions.The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity.The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation.A mixed finite volume element approximation,keeping physical conservation law,is used to get numerical values of the electric potential and the accuracy is improved one order.Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences.This method can overcome numerical oscillation,dispersion and decreases computational complexity.Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened.An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations.This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.
Directory of Open Access Journals (Sweden)
Jorge Mauricio Ruiz Vera
2013-03-01
Full Text Available The Derrida-Lebowitz-Speer-Spohn (DLSS equation is a fourth order in space non-linear evolution equation. This equation arises in the study of interface fluctuations in spin systems and quantum semiconductor modelling. In this paper, we present a positive preserving finite element discrtization for a coupled-equation approach to the DLSS equation. Using the available information about the physical phenomena, we are able to set the corresponding boundary conditions for the coupled system. We prove existence of a global in time discrete solution by fixed point argument. Numerical results illustrate the quantum character of the equation. Finally a test of order of convergence of the proposed discretization scheme is presented.La ecuación de Derrida-Lebowitz-Speer-Spohn (DLSS es una ecuación de evolución no lineal de cuarto orden. Esta aparece en el estudio de las fluctuaciones de interface de sistemas de espín y en la modelación de semicoductores cuánticos. En este artículo, se presenta una discretización por elementos finitos para una formulación exponencial de la ecuación DLSS abordada como un sistema acoplado de ecuaciones. Usando la información disponible acerca del fenómeno físico, se establecen las condiciones de contorno para el sistema acoplado. Se demuestra la existencia de la solución discreta global en el tiempo via un argumento de punto fijo. Los resultados numéricos ilustran el carácter cuántico de la ecuación. Finalmente se presenta un test del orden de convergencia de la discretización porpuesta.
Martyr-Koller, R.C.; Kernkamp, H.W.J.; Van Dam, Anne A.; Mick van der Wegen,; Lucas, Lisa; Knowles, N.; Jaffe, B.; Fregoso, T.A.
2017-01-01
A linked modeling approach has been undertaken to understand the impacts of climate and infrastructure on aquatic ecology and water quality in the San Francisco Bay-Delta region. The Delft3D Flexible Mesh modeling suite is used in this effort for its 3D hydrodynamics, salinity, temperature and sediment dynamics, phytoplankton and water-quality coupling infrastructure, and linkage to a habitat suitability model. The hydrodynamic model component of the suite is D-Flow FM, a new 3D unstructured finite-volume model based on the Delft3D model. In this paper, D-Flow FM is applied to the San Francisco Bay-Delta to investigate tidal, seasonal and annual dynamics of water levels, river flows and salinity under historical environmental and infrastructural conditions. The model is driven by historical winds, tides, ocean salinity, and river flows, and includes federal, state, and local freshwater withdrawals, and regional gate and barrier operations. The model is calibrated over a 9-month period, and subsequently validated for water levels, flows, and 3D salinity dynamics over a 2 year period.Model performance was quantified using several model assessment metrics and visualized through target diagrams. These metrics indicate that the model accurately estimated water levels, flows, and salinity over wide-ranging tidal and fluvial conditions, and the model can be used to investigate detailed circulation and salinity patterns throughout the Bay-Delta. The hydrodynamics produced through this effort will be used to drive affiliated sediment, phytoplankton, and contaminant hindcast efforts and habitat suitability assessments for fish and bivalves. The modeling framework applied here will serve as a baseline to ultimately shed light on potential ecosystem change over the current century.
Martyr-Koller, R. C.; Kernkamp, H. W. J.; van Dam, A.; van der Wegen, M.; Lucas, L. V.; Knowles, N.; Jaffe, B.; Fregoso, T. A.
2017-06-01
A linked modeling approach has been undertaken to understand the impacts of climate and infrastructure on aquatic ecology and water quality in the San Francisco Bay-Delta region. The Delft3D Flexible Mesh modeling suite is used in this effort for its 3D hydrodynamics, salinity, temperature and sediment dynamics, phytoplankton and water-quality coupling infrastructure, and linkage to a habitat suitability model. The hydrodynamic model component of the suite is D-Flow FM, a new 3D unstructured finite-volume model based on the Delft3D model. In this paper, D-Flow FM is applied to the San Francisco Bay-Delta to investigate tidal, seasonal and annual dynamics of water levels, river flows and salinity under historical environmental and infrastructural conditions. The model is driven by historical winds, tides, ocean salinity, and river flows, and includes federal, state, and local freshwater withdrawals, and regional gate and barrier operations. The model is calibrated over a 9-month period, and subsequently validated for water levels, flows, and 3D salinity dynamics over a 2 year period. Model performance was quantified using several model assessment metrics and visualized through target diagrams. These metrics indicate that the model accurately estimated water levels, flows, and salinity over wide-ranging tidal and fluvial conditions, and the model can be used to investigate detailed circulation and salinity patterns throughout the Bay-Delta. The hydrodynamics produced through this effort will be used to drive affiliated sediment, phytoplankton, and contaminant hindcast efforts and habitat suitability assessments for fish and bivalves. The modeling framework applied here will serve as a baseline to ultimately shed light on potential ecosystem change over the current century.
International Nuclear Information System (INIS)
Onishi, Yuki; Takiyasu, Jumpei; Amaya, Kenji; Yakuwa, Hiroshi; Hayabusa, Keisuke
2012-01-01
Highlights: ► A novel numerical method to analyze time dependent localized corrosion is developed. ► It takes electromigration, mass diffusion, chemical reactions, and moving boundaries. ► Our method perfectly satisfies the conservation of mass and electroneutrality. ► The behavior of typical crevice corrosion is successfully simulated. ► Both verification and validation of our method are carried out. - Abstract: A novel numerical method for time-dependent localized corrosion analysis is presented. Electromigration, mass diffusion, chemical reactions, and moving boundaries are considered in the numerical simulation of localized corrosion of engineering alloys in an underwater environment. Our method combines the finite volume method (FVM) and the voxel method. The FVM is adopted in the corrosion rate calculation so that the conservation of mass is satisfied. A newly developed decoupled algorithm with a projection method is introduced in the FVM to decouple the multiphysics problem into the electrostatic, mass transport, and chemical reaction analyses with electroneutrality maintained. The polarization curves for the corroding metal are used as boundary conditions for the metal surfaces to calculate the corrosion rates. The voxel method is adopted in updating the moving boundaries of cavities without remeshing and mesh-to-mesh solution mapping. Some modifications of the standard voxel method, which represents the boundaries as zigzag-shaped surfaces, are introduced to generate smooth surfaces. Our method successfully reproduces the numerical and experimental results of a capillary electrophoresis problem. Furthermore, the numerical results are qualitatively consistent with the experimental results for several examples of crevice corrosion.
$\\delta$-Expansion at Finite Temperature
Ramos, Rudnei O.
1996-01-01
We apply the $\\delta$-expansion perturbation scheme to the $\\lambda \\phi^{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\\delta$-expansion the interaction term is written as $\\lambda (\\phi^{2})^{ 1 + \\delta}$ and $\\delta$ is considered as the perturbation parameter. We compute within this perturbative approach the renormalized mass at finite temperature at a finite order in $\\delta$. The results are compared with the usual loop-expansion at finite temperature.
Zanotti, Olindo; Dumbser, Michael
2016-01-01
We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are performed in primitive variables, rather than in conserved ones. To obtain a conservative method, the underlying finite volume scheme is still written in terms of the cell averages of the conserved quantities. Therefore, our new approach performs the spatial WENO reconstruction twice: the first WENO reconstruction is carried out on the known cell averages of the conservative variables. The WENO polynomials are then used at the cell centers to compute point values of the conserved variables, which are subsequently converted into point values of the primitive variables. This is the only place where the conversion from conservative to primitive variables is needed in the new scheme. Then, a second WENO reconstruction is performed on the point values of the primitive variables to obtain piecewise high order reconstruction polynomials of the primitive variables. The reconstruction polynomials are subsequently evolved in time with a novel space-time finite element predictor that is directly applied to the governing PDE written in primitive form. The resulting space-time polynomials of the primitive variables can then be directly used as input for the numerical fluxes at the cell boundaries in the underlying conservative finite volume scheme. Hence, the number of necessary conversions from the conserved to the primitive variables is reduced to just one single conversion at each cell center. We have verified the validity of the new approach over a wide range of hyperbolic systems, including the classical Euler equations of gas dynamics, the special relativistic hydrodynamics (RHD) and ideal magnetohydrodynamics (RMHD) equations, as well as the Baer-Nunziato model for compressible two-phase flows. In all cases we have noticed that the new ADER
Hidden measurements, hidden variables and the volume representation of transition probabilities
Oliynyk, Todd A.
2005-01-01
We construct, for any finite dimension $n$, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For $n=2$ our model is equivalent to the Aerts sphere model and serves as a generalization of it for dimensions $n \\geq 3$. We also show how to construct a hidden variables scheme based on hidden measurements and we discuss how joint distributions arise in our hidden variables scheme and th...
Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme
Lee, Duck-Joo; Hwang, Chang-Jeon; Ko, Duck-Kon; Kim, Jae-Wook
1995-01-01
Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.
Li, Bai; Tanaka, Kisei R.; Chen, Yong; Brady, Damian C.; Thomas, Andrew C.
2017-09-01
The Finite-Volume Community Ocean Model (FVCOM) is an advanced coastal circulation model widely utilized for its ability to simulate spatially and temporally evolving three-dimensional geophysical conditions of complex and dynamic coastal regions. While a body of literature evaluates model skill in surface fields, independent studies validating model skill in bottom fields over large spatial and temporal scales are scarce because these fields cannot be remotely sensed. In this study, an evaluation of FVCOM skill in modeling bottom water temperature was conducted by comparison to hourly in situ observed bottom temperatures recorded by the Environmental Monitors on Lobster Traps (eMOLT), a program that attached thermistors to commercial lobster traps from 2001 to 2013. Over 2 × 106 pairs of FVCOM-eMOLT records were evaluated by a series of statistical measures to quantify accuracy and precision of the modeled data across the Northwest Atlantic Shelf region. The overall comparison between modeled and observed data indicates reliable skill of FVCOM (r2 = 0.72; root mean squared error = 2.28 °C). Seasonally, the average absolute errors show higher model skill in spring, fall and winter than summer. We speculate that this is due to the increased difficulty of modeling high frequency variability in the exact position of the thermocline and frontal zones. The spatial patterns of the residuals suggest that there is improved similarity between modeled and observed data at higher latitudes. We speculate that this is due to increased tidal mixing at higher latitudes in our study area that reduces stratification in winter, allowing improved model accuracy. Modeled bottom water temperatures around Cape Cod, the continental shelf edges, and at one location at the entrance to Penobscot Bay were characterized by relatively high errors. Constraints for future uses of FVCOM bottom water temperature are provided based on the uncertainties in temporal-spatial patterns. This study is
A comparative study of upwind and MacCormack schemes for CAA benchmark problems
Viswanathan, K.; Sankar, L. N.
1995-01-01
In this study, upwind schemes and MacCormack schemes are evaluated as to their suitability for aeroacoustic applications. The governing equations are cast in a curvilinear coordinate system and discretized using finite volume concepts. A flux splitting procedure is used for the upwind schemes, where the signals crossing the cell faces are grouped into two categories: signals that bring information from outside into the cell, and signals that leave the cell. These signals may be computed in several ways, with the desired spatial and temporal accuracy achieved by choosing appropriate interpolating polynomials. The classical MacCormack schemes employed here are fourth order accurate in time and space. Results for categories 1, 4, and 6 of the workshop's benchmark problems are presented. Comparisons are also made with the exact solutions, where available. The main conclusions of this study are finally presented.
DEFF Research Database (Denmark)
van Leeuwen, Theo
2013-01-01
This chapter presents a framework for analysing colour schemes based on a parametric approach that includes not only hue, value and saturation, but also purity, transparency, luminosity, luminescence, lustre, modulation and differentiation.......This chapter presents a framework for analysing colour schemes based on a parametric approach that includes not only hue, value and saturation, but also purity, transparency, luminosity, luminescence, lustre, modulation and differentiation....
Institute of Scientific and Technical Information of China (English)
毕春加
2005-01-01
In this paper, we establish the maximum norm estimates of the solutions of the finite volume element method (FVE) based on the P1 conforming element for the non-selfadjoint and indefinite elliptic problems.
Institute of Scientific and Technical Information of China (English)
龙晓瀚; 毕春加
2005-01-01
In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under minimal elliptic regularity assumption.
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Finite element analysis of a finite-strain plasticity problem
International Nuclear Information System (INIS)
Crose, J.G.; Fong, H.H.
1984-01-01
A finite-strain plasticity analysis was performed of an engraving process in a plastic rotating band during the firing of a gun projectile. The aim was to verify a nonlinear feature of the NIFDI/RB code: plastic large deformation analysis of nearly incompressible materials using a deformation theory of plasticity approach and a total Lagrangian scheme. (orig.)
Godunov-type schemes for hydrodynamic and magnetohydrodynamic modeling
International Nuclear Information System (INIS)
Vides-Higueros, Jeaniffer
2014-01-01
The main objective of this thesis concerns the study, design and numerical implementation of finite volume schemes based on the so-Called Godunov-Type solvers for hyperbolic systems of nonlinear conservation laws, with special attention given to the Euler equations and ideal MHD equations. First, we derive a simple and genuinely two-Dimensional Riemann solver for general conservation laws that can be regarded as an actual 2D generalization of the HLL approach, relying heavily on the consistency with the integral formulation and on the proper use of Rankine-Hugoniot relations to yield expressions that are simple enough to be applied in the structured and unstructured contexts. Then, a comparison between two methods aiming to numerically maintain the divergence constraint of the magnetic field for the ideal MHD equations is performed and we show how the 2D Riemann solver can be employed to obtain robust divergence-Free simulations. Next, we derive a relaxation scheme that incorporates gravity source terms derived from a potential into the hydrodynamic equations, an important problem in astrophysics, and finally, we review the design of finite volume approximations in curvilinear coordinates, providing a fresher view on an alternative discretization approach. Throughout this thesis, numerous numerical results are shown. (author) [fr
Robust second-order scheme for multi-phase flow computations
Shahbazi, Khosro
2017-06-01
A robust high-order scheme for the multi-phase flow computations featuring jumps and discontinuities due to shock waves and phase interfaces is presented. The scheme is based on high-order weighted-essentially non-oscillatory (WENO) finite volume schemes and high-order limiters to ensure the maximum principle or positivity of the various field variables including the density, pressure, and order parameters identifying each phase. The two-phase flow model considered besides the Euler equations of gas dynamics consists of advection of two parameters of the stiffened-gas equation of states, characterizing each phase. The design of the high-order limiter is guided by the findings of Zhang and Shu (2011) [36], and is based on limiting the quadrature values of the density, pressure and order parameters reconstructed using a high-order WENO scheme. The proof of positivity-preserving and accuracy is given, and the convergence and the robustness of the scheme are illustrated using the smooth isentropic vortex problem with very small density and pressure. The effectiveness and robustness of the scheme in computing the challenging problem of shock wave interaction with a cluster of tightly packed air or helium bubbles placed in a body of liquid water is also demonstrated. The superior performance of the high-order schemes over the first-order Lax-Friedrichs scheme for computations of shock-bubble interaction is also shown. The scheme is implemented in two-dimensional space on parallel computers using message passing interface (MPI). The proposed scheme with limiter features approximately 50% higher number of inter-processor message communications compared to the corresponding scheme without limiter, but with only 10% higher total CPU time. The scheme is provably second-order accurate in regions requiring positivity enforcement and higher order in the rest of domain.
Energy Technology Data Exchange (ETDEWEB)
Seidl, V.
1997-11-01
A finite vomume method for calculation of steady and unsteady flow on unstructured grids is parallelized by local spatial and time decomposition. In the first case, a parallel variant of the conjugated gradient method with multiple local preconditioning is formulated and analyzed. The method is tested for simple applications (e.g. flow around a cylinder). The second part of the publication describes a direct numerical simulation of turbulent flow around a sphere at a Reynolds number of 5000 (based on flow velocity and sphere diameter). Current and Reynolds-averaged flow fields are discussed. Particular emphasis is placed on coordinate-independent representation of the anisotropy ratios of the Reynolds tensor and dissipation tensor. (orig.) [Deutsch] Ein Finite-Volumen-Verfahren fuer die Berechnung stationaerer und instationaerer Stroemungen auf unstrukturierten Netzen wird durch Gebietszerlegung im Raum und Zeit parallelisiert. Fuer die raeumliche Zerlegung wird eine parallele Variante der konjugierten Gradienten Methode mit mehrfacher, lokaler Vorkonditionierung formuliert und analysiert. Anhand einfacher Anwendungsbeispiele (Zylinderumstroemung, deckelgetriebene Nischenstroemung) wird das entwickelte Gesamtverfahren getestet und seine Effizienz bestimmt. Der zweite Teil der Arbeit beschreibt eine direkte numerische Simulation der turbulenten Kugelumstroemung bei einer Reynolds-Zahl von 5 000 (basierend auf Anstroemgeschwindigkeit und Kugeldurchmesser). In der Ergebnisauswertung werden augenblickliche und Reynolds-gemittelte Stroemungsfelder diskutiert und besonderer Wert auf eine koordinatenunabhaengige Darstellung der Anisotropieverhaeltnisse des Reynolds-Tensors und des Dissipationstensors gelegt. (orig.)
Regularization of finite temperature string theories
International Nuclear Information System (INIS)
Leblanc, Y.; Knecht, M.; Wallet, J.C.
1990-01-01
The tachyonic divergences occurring in the free energy of various string theories at finite temperature are eliminated through the use of regularization schemes and analytic continuations. For closed strings, we obtain finite expressions which, however, develop an imaginary part above the Hagedorn temperature, whereas open string theories are still plagued with dilatonic divergences. (orig.)
Simple Numerical Schemes for the Korteweg-deVries Equation
International Nuclear Information System (INIS)
McKinstrie, C. J.; Kozlov, M.V.
2000-01-01
Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves
Simple Numerical Schemes for the Korteweg-deVries Equation
Energy Technology Data Exchange (ETDEWEB)
C. J. McKinstrie; M. V. Kozlov
2000-12-01
Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves.
Saad, Bilal Mohammed; Saad, Mazen
2014-01-01
We study the convergence of a combined finite volume nonconforming finite element scheme on general meshes for a partially miscible two-phase flow model in anisotropic porous media. This model includes capillary effects and exchange between the phase. The diffusion term,which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. The convergence of the scheme is proved thanks to an estimate on the two pressures which allows to show estimates on the discrete time and compactness results in the case of degenerate relative permeabilities. A key point in the scheme is to use particular averaging formula for the dissolution function arising in the diffusion term. We show also a simulation of CO2 injection in a water saturated reservoir and nuclear waste management. Numerical results are obtained by in-house numerical code. © Springer International Publishing Switzerland 2014.
The Finite-Surface Method for incompressible flow: a step beyond staggered grid
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.
Numerical schemes for one-point closure turbulence models
International Nuclear Information System (INIS)
Larcher, Aurelien
2010-01-01
First-order Reynolds Averaged Navier-Stokes (RANS) turbulence models are studied in this thesis. These latter consist of the Navier-Stokes equations, supplemented with a system of balance equations describing the evolution of characteristic scalar quantities called 'turbulent scales'. In so doing, the contribution of the turbulent agitation to the momentum can be determined by adding a diffusive coefficient (called 'turbulent viscosity') in the Navier-Stokes equations, such that it is defined as a function of the turbulent scales. The numerical analysis problems, which are studied in this dissertation, are treated in the frame of a fractional step algorithm, consisting of an approximation on regular meshes of the Navier-Stokes equations by the nonconforming Crouzeix-Raviart finite elements, and a set of scalar convection-diffusion balance equations discretized by the standard finite volume method. A monotone numerical scheme based on the standard finite volume method is proposed so as to ensure that the turbulent scales, like the turbulent kinetic energy (k) and its dissipation rate (ε), remain positive in the case of the standard k - ε model, as well as the k - ε RNG and the extended k - ε - ν 2 models. The convergence of the proposed numerical scheme is then studied on a system composed of the incompressible Stokes equations and a steady convection-diffusion equation, which are both coupled by the viscosities and the turbulent production term. This reduced model allows to deal with the main difficulty encountered in the analysis of such problems: the definition of the turbulent production term leads to consider a class of convection-diffusion problems with an irregular right-hand side belonging to L 1 . Finally, to step towards the unsteady problem, the convergence of the finite volume scheme for a model convection-diffusion equation with L 1 data is proved. The a priori estimates on the solution and on its time derivative are obtained in discrete norms, for
International Nuclear Information System (INIS)
Wang Jianhui; Ma Yongli
2009-01-01
We generalize the scheme to characterize phase transitions of finite systems in a complex temperature plane and approach the classifications of phase transitions in ideal and weakly interacting Bose gases of a finite number of particles, confined in a cubic box of volume L 3 with different boundary conditions. For this finite ideal Bose system, by extending the classification parameters to all regions, we predict that the phase transition for periodic boundary conditions is of second order, while the transition in Dirichlet boundary conditions is of first order. For a weakly interacting Bose gas with periodic boundary conditions, we discuss the effects of finite particle numbers and inter-particle interactions on the nature of the phase transitions. We show that this homogenous weakly interacting Bose gas undergoes a second-order phase transition, which is in accordance with universality arguments for infinite systems. We also discuss the dependence of transition temperature on interaction strengths and particle numbers.
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
Characterization of resonances using finite size effects
International Nuclear Information System (INIS)
Pozsgay, B.; Takacs, G.
2006-01-01
We develop methods to extract resonance widths from finite volume spectra of (1+1)-dimensional quantum field theories. Our two methods are based on Luscher's description of finite size corrections, and are dubbed the Breit-Wigner and the improved ''mini-Hamiltonian'' method, respectively. We establish a consistent framework for the finite volume description of sufficiently narrow resonances that takes into account the finite size corrections and mass shifts properly. Using predictions from form factor perturbation theory, we test the two methods against finite size data from truncated conformal space approach, and find excellent agreement which confirms both the theoretical framework and the numerical validity of the methods. Although our investigation is carried out in 1+1 dimensions, the extension to physical 3+1 space-time dimensions appears straightforward, given sufficiently accurate finite volume spectra
International Nuclear Information System (INIS)
Mieussens, Luc
2013-01-01
The unified gas kinetic scheme (UGKS) of K. Xu et al. (2010) [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knudsen) regime, we prove that UGKS is still asymptotic preserving (AP) in this regime, but for the free transport regime as well. Moreover, this scheme is modified to include a time implicit discretization of the limit diffusion equation, and to correctly capture the solution in case of boundary layers. Contrary to many AP schemes, this method is based on a standard finite volume approach, it does neither use any decomposition of the solution, nor staggered grids. Several numerical tests demonstrate the properties of the scheme
Features of finite quantum field theories
International Nuclear Information System (INIS)
Boehm, M.; Denner, A.
1987-01-01
We analyse general features of finite quantum field theories. A quantum field theory is considered to be finite, if the corresponding renormalization constants evaluated in the dimensional regularization scheme are free from divergences in all orders of perturbation theory. We conclude that every finite renormalizable quantum field theory with fields of spin one or less must contain both scalar fields and fermion fields and nonabelian gauge fields. Some secific nonsupersymmetric models are found to be finite at the one- and two-loop level. (orig.)
Selecting registration schemes in case of interstitial lung disease follow-up in CT
International Nuclear Information System (INIS)
Vlachopoulos, Georgios; Korfiatis, Panayiotis; Skiadopoulos, Spyros; Kazantzi, Alexandra; Kalogeropoulou, Christina; Pratikakis, Ioannis; Costaridou, Lena
2015-01-01
Purpose: Primary goal of this study is to select optimal registration schemes in the framework of interstitial lung disease (ILD) follow-up analysis in CT. Methods: A set of 128 multiresolution schemes composed of multiresolution nonrigid and combinations of rigid and nonrigid registration schemes are evaluated, utilizing ten artificially warped ILD follow-up volumes, originating from ten clinical volumetric CT scans of ILD affected patients, to select candidate optimal schemes. Specifically, all combinations of four transformation models (three rigid: rigid, similarity, affine and one nonrigid: third order B-spline), four cost functions (sum-of-square distances, normalized correlation coefficient, mutual information, and normalized mutual information), four gradient descent optimizers (standard, regular step, adaptive stochastic, and finite difference), and two types of pyramids (recursive and Gaussian-smoothing) were considered. The selection process involves two stages. The first stage involves identification of schemes with deformation field singularities, according to the determinant of the Jacobian matrix. In the second stage, evaluation methodology is based on distance between corresponding landmark points in both normal lung parenchyma (NLP) and ILD affected regions. Statistical analysis was performed in order to select near optimal registration schemes per evaluation metric. Performance of the candidate registration schemes was verified on a case sample of ten clinical follow-up CT scans to obtain the selected registration schemes. Results: By considering near optimal schemes common to all ranking lists, 16 out of 128 registration schemes were initially selected. These schemes obtained submillimeter registration accuracies in terms of average distance errors 0.18 ± 0.01 mm for NLP and 0.20 ± 0.01 mm for ILD, in case of artificially generated follow-up data. Registration accuracy in terms of average distance error in clinical follow-up data was in the
Selecting registration schemes in case of interstitial lung disease follow-up in CT
Energy Technology Data Exchange (ETDEWEB)
Vlachopoulos, Georgios; Korfiatis, Panayiotis; Skiadopoulos, Spyros; Kazantzi, Alexandra [Department of Medical Physics, School of Medicine,University of Patras, Patras 26504 (Greece); Kalogeropoulou, Christina [Department of Radiology, School of Medicine, University of Patras, Patras 26504 (Greece); Pratikakis, Ioannis [Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi 67100 (Greece); Costaridou, Lena, E-mail: costarid@upatras.gr [Department of Medical Physics, School of Medicine, University of Patras, Patras 26504 (Greece)
2015-08-15
Purpose: Primary goal of this study is to select optimal registration schemes in the framework of interstitial lung disease (ILD) follow-up analysis in CT. Methods: A set of 128 multiresolution schemes composed of multiresolution nonrigid and combinations of rigid and nonrigid registration schemes are evaluated, utilizing ten artificially warped ILD follow-up volumes, originating from ten clinical volumetric CT scans of ILD affected patients, to select candidate optimal schemes. Specifically, all combinations of four transformation models (three rigid: rigid, similarity, affine and one nonrigid: third order B-spline), four cost functions (sum-of-square distances, normalized correlation coefficient, mutual information, and normalized mutual information), four gradient descent optimizers (standard, regular step, adaptive stochastic, and finite difference), and two types of pyramids (recursive and Gaussian-smoothing) were considered. The selection process involves two stages. The first stage involves identification of schemes with deformation field singularities, according to the determinant of the Jacobian matrix. In the second stage, evaluation methodology is based on distance between corresponding landmark points in both normal lung parenchyma (NLP) and ILD affected regions. Statistical analysis was performed in order to select near optimal registration schemes per evaluation metric. Performance of the candidate registration schemes was verified on a case sample of ten clinical follow-up CT scans to obtain the selected registration schemes. Results: By considering near optimal schemes common to all ranking lists, 16 out of 128 registration schemes were initially selected. These schemes obtained submillimeter registration accuracies in terms of average distance errors 0.18 ± 0.01 mm for NLP and 0.20 ± 0.01 mm for ILD, in case of artificially generated follow-up data. Registration accuracy in terms of average distance error in clinical follow-up data was in the
White, Jeffrey A.; Baurle, Robert A.; Fisher, Travis C.; Quinlan, Jesse R.; Black, William S.
2012-01-01
The 2nd-order upwind inviscid flux scheme implemented in the multi-block, structured grid, cell centered, finite volume, high-speed reacting flow code VULCAN has been modified to reduce numerical dissipation. This modification was motivated by the desire to improve the codes ability to perform large eddy simulations. The reduction in dissipation was accomplished through a hybridization of non-dissipative and dissipative discontinuity-capturing advection schemes that reduces numerical dissipation while maintaining the ability to capture shocks. A methodology for constructing hybrid-advection schemes that blends nondissipative fluxes consisting of linear combinations of divergence and product rule forms discretized using 4th-order symmetric operators, with dissipative, 3rd or 4th-order reconstruction based upwind flux schemes was developed and implemented. A series of benchmark problems with increasing spatial and fluid dynamical complexity were utilized to examine the ability of the candidate schemes to resolve and propagate structures typical of turbulent flow, their discontinuity capturing capability and their robustness. A realistic geometry typical of a high-speed propulsion system flowpath was computed using the most promising of the examined schemes and was compared with available experimental data to demonstrate simulation fidelity.
Additive operator-difference schemes splitting schemes
Vabishchevich, Petr N
2013-01-01
Applied mathematical modeling isconcerned with solving unsteady problems. This bookshows how toconstruct additive difference schemes to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods)and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for sy
Good governance for pension schemes
Thornton, Paul
2011-01-01
Regulatory and market developments have transformed the way in which UK private sector pension schemes operate. This has increased demands on trustees and advisors and the trusteeship governance model must evolve in order to remain fit for purpose. This volume brings together leading practitioners to provide an overview of what today constitutes good governance for pension schemes, from both a legal and a practical perspective. It provides the reader with an appreciation of the distinctive characteristics of UK occupational pension schemes, how they sit within the capital markets and their social and fiduciary responsibilities. Providing a holistic analysis of pension risk, both from the trustee and the corporate perspective, the essays cover the crucial role of the employer covenant, financing and investment risk, developments in longevity risk hedging and insurance de-risking, and best practice scheme administration.
A high-order solver for aerodynamic flow simulations and comparison of different numerical schemes
Mikhaylov, Sergey; Morozov, Alexander; Podaruev, Vladimir; Troshin, Alexey
2017-11-01
An implementation of high order of accuracy Discontinuous Galerkin method is presented. Reconstruction is done for the conservative variables. Gradients are calculated using the BR2 method. Coordinate transformations are done by serendipity elements. In computations with schemes of order higher than 2, curvature of the mesh lines is taken into account. A comparison with finite volume methods is performed, including WENO method with linear weights and single quadrature point on a cell side. The results of the following classical tests are presented: subsonic flow around a circular cylinder in an ideal gas, convection of two-dimensional isentropic vortex, and decay of the Taylor-Green vortex.
Matroids and quantum-secret-sharing schemes
International Nuclear Information System (INIS)
Sarvepalli, Pradeep; Raussendorf, Robert
2010-01-01
A secret-sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret-sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret-sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum-secret-sharing schemes. In addition to providing a new perspective on quantum-secret-sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum-secret-sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum-secret-sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure-state quantum-secret-sharing scheme with information rate 1.
Labonté, Ronald
2015-11-19
Despite the mythology that the global economy with its trade rules creates a 'level playing field,' international trade has never involved 'level players.' The inequalities in outcomes generated by the more powerful winning more frequently has led to innovative ideas for ex post redistribution to make the matches between the players both fairer, and in the analogy to basketball used by the authors, more interesting and even more competitive. The proposal for a Global Social Protection Fund, financed by a small tax on the winners to enhance social protection spending for the losers, presumably increasing the latter's capabilities to compete more effectively in the global market game, is one such idea. It has much to commend it. Several problems, however, stand in its way, apart from those inherent within nations themselves and to which the authors give some attention. First, much global trade is now intra-firm rather than international, making calculations of which nations win or lose exceedingly difficult. Second, tax havens persist without the transparency and global regulatory oversights that would allow a better rendering of where winnings are stashed. Third, pre-distribution inequalities (those arising from market activities before government tax and transfer measures apply) are still increasing as labour's power to wrestle global capital into some ameliorative social contract diminishes. Fourth, there are finite limits to a planet on the cusp of multiple environmental crises. These problems do not diminish the necessity of alternative policy playbooks such as the proposed Fund, but point to the need to embrace the new Sustainable Development Goals (SDGs) as a single set, such that economic growth for the bottom half of humanity includes deep structural reforms to both pre-distribution and redistribution, if the targets for environmental survival are to be met. © 2016 by Kerman University of Medical Sciences.
A multigrid solution method for mixed hybrid finite elements
Energy Technology Data Exchange (ETDEWEB)
Schmid, W. [Universitaet Augsburg (Germany)
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Lattice Boltzmann method and gas-kinetic BGK scheme in the low-Mach number viscous flow simulations
International Nuclear Information System (INIS)
Xu Kun; He Xiaoyi
2003-01-01
Both lattice Boltzmann method (LBM) and the gas-kinetic BGK scheme are based on the numerical discretization of the Boltzmann equation with collisional models, such as, the Bhatnagar-Gross-Krook (BGK) model. LBM tracks limited number of particles and the viscous flow behavior emerges automatically from the intrinsic particle stream and collisions process. On the other hand, the gas-kinetic BGK scheme is a finite volume scheme, where the time-dependent gas distribution function with continuous particle velocity space is constructed and used in the evaluation of the numerical fluxes across cell interfaces. Currently, LBM is mainly used for low Mach number, nearly incompressible flow simulation. For the gas-kinetic scheme, the application is focusing on the high speed compressible flows. In this paper, we are going to compare both schemes in the isothermal low-Mach number flow simulations. The methodology for developing both schemes will be clarified through the introduction of operator splitting Boltzmann model and operator averaging Boltzmann model. From the operator splitting Boltzmann model, the error rooted in many kinetic schemes, which are based on the decoupling of particle transport and collision, can be easily understood. As to the test case, we choose to use the 2D cavity flow since it is one of the most extensively studied cases. Detailed simulation results with different Reynolds numbers, as well as the benchmark solutions, are presented
Parallel knock-out schemes in networks
Broersma, H.J.; Fomin, F.V.; Woeginger, G.J.
2004-01-01
We consider parallel knock-out schemes, a procedure on graphs introduced by Lampert and Slater in 1997 in which each vertex eliminates exactly one of its neighbors in each round. We are considering cases in which after a finite number of rounds, where the minimimum number is called the parallel
Generation of correlated finite alphabet waveforms using gaussian random variables
Jardak, Seifallah; Ahmed, Sajid; Alouini, Mohamed-Slim
2014-01-01
, the proposed scheme is general, the main focus of this paper is to generate finite alphabet waveforms for multiple-input multiple-output radar, where correlated waveforms are used to achieve desired beampatterns. © 2014 IEEE.
Central upwind scheme for a compressible two-phase flow model.
Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul
2015-01-01
In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.
Central upwind scheme for a compressible two-phase flow model.
Directory of Open Access Journals (Sweden)
Munshoor Ahmed
Full Text Available In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.
Leamer, Micah J.
2004-01-01
Let K be a field and Q a finite directed multi-graph. In this paper I classify all path algebras KQ and admissible orders with the property that all of their finitely generated ideals have finite Groebner bases. MS
Locally Finite Root Supersystems
Yousofzadeh, Malihe
2013-01-01
We introduce the notion of locally finite root supersystems as a generalization of both locally finite root systems and generalized root systems. We classify irreducible locally finite root supersystems.
An implict LU scheme for the Euler equations applied to arbitrary cascades. [new method of factoring
Buratynski, E. K.; Caughey, D. A.
1984-01-01
An implicit scheme for solving the Euler equations is derived and demonstrated. The alternating-direction implicit (ADI) technique is modified, using two implicit-operator factors corresponding to lower-block-diagonal (L) or upper-block-diagonal (U) algebraic systems which can be easily inverted. The resulting LU scheme is implemented in finite-volume mode and applied to 2D subsonic and transonic cascade flows with differing degrees of geometric complexity. The results are presented graphically and found to be in good agreement with those of other numerical and analytical approaches. The LU method is also 2.0-3.4 times faster than ADI, suggesting its value in calculating 3D problems.
Aguayo-Ortiz, A; Mendoza, S; Olvera, D
2018-01-01
In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.
Counting Subspaces of a Finite Vector Space
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 11. Counting Subspaces of a Finite Vector Space – 1. Amritanshu Prasad. General Article Volume 15 Issue 11 November 2010 pp 977-987. Fulltext. Click here to view fulltext PDF. Permanent link:
Schiemenz, Alan R.
High-order methods are emerging in the scientific computing community as superior alternatives to the classical finite difference, finite volume, and continuous finite element methods. The discontinuous Galerkin (DG) method in particular combines many of the positive features of all of these methods. This thesis presents two projects involving the DG method. First, a Hybrid scheme is presented, which implements DG areas where the solution is considered smooth, while dropping the order of the scheme elsewhere and implementing a finite volume scheme with high-order, non-oscillatory solution reconstructions suitable for unstructured mesh. Two such reconstructions from the ENO class are considered in the Hybrid. Successful numerical results are presented for nonlinear systems of conservation laws in one dimension. Second, the high-order discontinuous Galerkin and Fourier spectral methods are applied to an application modeling three-phase fluid flow through a porous medium, undergoing solid-fluid reaction due to the reactive infiltration instability (RII). This model incorporates a solid upwelling term and an equation to track the abundance of the reacting mineral orthopyroxene (opx). After validating the numerical discretization, results are given that provide new insight into the formation of melt channels in the Earth's mantle. Mantle heterogeneities are observed to be one catalyst for the development of melt channels, and the dissolution of opx produces interesting bifurcations in the melt channels. An alternative formulation is considered where the mass transfer rate relative to velocity is taken to be infinitely large. In this setting, the stiffest terms are removed, greatly reducing the cost of time integration.
Implicit upwind schemes for computational fluid dynamics. Solution by domain decomposition
International Nuclear Information System (INIS)
Clerc, S.
1998-01-01
In this work, the numerical simulation of fluid dynamics equations is addressed. Implicit upwind schemes of finite volume type are used for this purpose. The first part of the dissertation deals with the improvement of the computational precision in unfavourable situations. A non-conservative treatment of some source terms is studied in order to correct some shortcomings of the usual operator-splitting method. Besides, finite volume schemes based on Godunov's approach are unsuited to compute low Mach number flows. A modification of the up-winding by preconditioning is introduced to correct this defect. The second part deals with the solution of steady-state problems arising from an implicit discretization of the equations. A well-posed linearized boundary value problem is formulated. We prove the convergence of a domain decomposition algorithm of Schwartz type for this problem. This algorithm is implemented either directly, or in a Schur complement framework. Finally, another approach is proposed, which consists in decomposing the non-linear steady state problem. (author)
International Nuclear Information System (INIS)
Sivkova, G.N.; Spirchenko, Yu.V.; Chvartatskij, P.V.
1981-01-01
Stressed-deformed state of toroidal field coils of the disc type with elastic couplings of the tokamaks has been investigated with provision for the effect of the central core pliability by means of the two-dimensional version of the finite element method. Numerical solution of the finite element method is performed by means of the ES 1040 computer according to the computer code permitting taking account of boundary conditions of elastic support. The calculation has been performed using as the example the project of T-20 facility coil of the disc type. Consideration of pliability of the central core of the facility inductor is accomplished by the introduction of additional rigidities to the complete matrix of rigidity. Scheme of the structure distretization includes 141 units, 211 elements. The accuracy of solution depends on the reduction accuracy of the volume load to unit forces and on the number of finite elements. Analysis of the solution convergence is performed by the comparison of solutions obtained for three different schemes of the disk discretization without regard for the inductor pliability. The comparative analysis of the results shows that transfer epures for all the three discretization versions practically coincide and stresses differ not more than by 10%. On the whole the above investigation has demonstrated good convergence of the problem solution [ru
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
International Nuclear Information System (INIS)
Ueckermann, M.P.; Lermusiaux, P.F.J.; Sapsis, T.P.
2013-01-01
The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier–Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.
International Nuclear Information System (INIS)
Girardin, Mathieu
2014-01-01
Two-phase flows in Pressurized Water Reactors belong to a wide range of Mach number flows. Computing accurate approximate solutions of those flows may be challenging from a numerical point of view as classical finite volume methods are too diffusive in the low Mach regime. In this thesis, we are interested in designing and studying some robust numerical schemes that are stable for large time steps and accurate even on coarse meshes for a wide range of flow regimes. An important feature is the strategy to construct those schemes. We use a mixed implicit-explicit strategy based on an operator splitting to solve fast and slow phenomena separately. Then, we introduce a modification of a Suliciu type relaxation scheme to improve the accuracy of the numerical scheme in some regime of interest. Two approaches have been used to assess the ability of our numerical schemes to deal with a wide range of flow regimes. The first approach, based on the asymptotic preserving property, has been used for the gas dynamics equations with stiff source terms. The second approach, based on the all-regime property, has been used for the gas dynamics equations and the homogeneous two-phase flows models HRM and HEM in the low Mach regime. We obtained some robustness and stability properties for our numerical schemes. In particular, some discrete entropy inequalities are shown. Numerical evidences, in 1D and in 2D on unstructured meshes, assess the gain in term of accuracy and CPU time of those asymptotic preserving and all-regime numerical schemes in comparison with classical finite volume methods. (author) [fr
An efficient numerical scheme for the simulation of parallel-plate active magnetic regenerators
DEFF Research Database (Denmark)
Torregrosa-Jaime, Bárbara; Corberán, José M.; Payá, Jorge
2015-01-01
A one-dimensional model of a parallel-plate active magnetic regenerator (AMR) is presented in this work. The model is based on an efficient numerical scheme which has been developed after analysing the heat transfer mechanisms in the regenerator bed. The new finite difference scheme optimally com...... to the fully implicit scheme, the proposed scheme achieves more accurate results, prevents numerical errors and requires less computational effort. In AMR simulations the new scheme can reduce the computational time by 88%....
International Nuclear Information System (INIS)
Kraloua, B.; Hennad, A.
2008-01-01
The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.
Multisymplectic Structure－Preserving in Simple Finite Element Method in High Dimensional Case
Institute of Scientific and Technical Information of China (English)
BAIYong-Qiang; LIUZhen; PEIMing; ZHENGZhu-Jun
2003-01-01
In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems in high-dhnensjonal space. With uniform mesh, we find that, the numerical scheme derived from finite element method can keep a preserved multisymplectic structure.
Multisymplectic Structure-Preserving in Simple Finite Element Method in High Dimensional Case
Institute of Scientific and Technical Information of China (English)
BAI Yong-Qiang; LIU Zhen; PEI Ming; ZHENG Zhu-Jun
2003-01-01
In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems inhigh-dimensional space. With uniform mesh, we find that, the numerical scheme derived from finite element method cankeep a preserved multisymplectic structure.
Topology optimization using the finite volume method
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Bendsøe, Martin P.; Sigmund, Ole
2005-01-01
in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...... derivative of the system matrix $\\mathbf K$ and in how one computes the discretized version of certain objective functions. Thus for a cost function for minimum dissipated energy (like minimum compliance for an elastic structure) one obtains an expression $ c = \\mathbf u^\\T \\tilde{\\mathbf K} \\mathbf u...... the arithmetic and harmonic average with the latter being the well known Reuss lower bound. [1] Bendsøe, MP and Sigmund, O 2004: Topology Optimization - Theory, Methods, and Applications. Berlin Heidelberg: Springer Verlag [2] Versteeg, HK and Malalasekera, W 1995: An introduction to Computational Fluid Dynamics...
Finite Volumes Discretization of Topology Optimization Problems
DEFF Research Database (Denmark)
Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter
, FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly...... computations is done using nite element methods (FEMs). Despite some limited recent eorts [1, 2], we have only started to develop our understanding of the interplay between the control in the coecients and FVMs. Recent advances in discrete functional analysis allow us to analyze convergence of FVM...... of the induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout...
Finite-volume discretizations and immersed boundaries
Y.J. Hassen (Yunus); B. Koren (Barry)
2009-01-01
htmlabstractIn this chapter, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed `Cartesian' grid. The essence of the present method
Finite-volume discretizations and immersed boundaries
Y.J. Hassen (Yunus); B. Koren (Barry)
2010-01-01
textabstractIn this chapter, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed Cartesian grid. The essence of the present method is
Finite difference schemes for second order systems describing black holes
International Nuclear Information System (INIS)
Motamed, Mohammad; Kreiss, H-O.; Babiuc, M.; Winicour, J.; Szilagyi, B.
2006-01-01
In the harmonic description of general relativity, the principal part of Einstein's equations reduces to 10 curved space wave equations for the components of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem
The theory of finitely generated commutative semigroups
Rédei, L; Stark, M; Gravett, K A H
1966-01-01
The Theory of Finitely Generated Commutative Semigroups describes a theory of finitely generated commutative semigroups which is founded essentially on a single """"fundamental theorem"""" and exhibits resemblance in many respects to the algebraic theory of numbers. The theory primarily involves the investigation of the F-congruences (F is the the free semimodule of the rank n, where n is a given natural number). As applications, several important special cases are given. This volume is comprised of five chapters and begins with preliminaries on finitely generated commutative semigroups before
SECRET SHARING SCHEMES WITH STRONG MULTIPLICATION AND A LARGE NUMBER OF PLAYERS FROM TORIC VARIETIES
DEFF Research Database (Denmark)
Hansen, Johan Peder
2017-01-01
This article consider Massey's construction for constructing linear secret sharing schemes from toric varieties over a finite field $\\Fq$ with $q$ elements. The number of players can be as large as $(q-1)^r-1$ for $r\\geq 1$. The schemes have strong multiplication, such schemes can be utilized in ...
Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.
2015-12-01
Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties
A Digital Signature Scheme Based on MST3 Cryptosystems
Directory of Open Access Journals (Sweden)
Haibo Hong
2014-01-01
Full Text Available As special types of factorization of finite groups, logarithmic signature and cover have been used as the main components of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like MST1, MST2, and MST3. Recently, Svaba et. al proposed a revised MST3 encryption scheme with greater security. Meanwhile, they put forward an idea of constructing signature schemes on the basis of logarithmic signatures and random covers. In this paper, we firstly design a secure digital signature scheme based on logarithmic signatures and random covers. In order to complete the task, we devise a new encryption scheme based on MST3 cryptosystems.
Conservative Semidiscrete Difference Schemes for Timoshenko Systems
Júnior, D. S. Almeida
2014-01-01
We present a parameterized family of finite-difference schemes to analyze the energy properties for linearly elastic constant-coefficient Timoshenko systems considering shear deformation and rotatory inertia. We derive numerical energies showing the positivity, and the energy conservation property and we show how to avoid a numerical anomaly known as locking phenomenon on shear force. Our method of proof relies on discrete multiplier techniques.
International Nuclear Information System (INIS)
Acharya, B.S.; Douglas, M.R.
2006-06-01
We present evidence that the number of string/M theory vacua consistent with experiments is finite. We do this both by explicit analysis of infinite sequences of vacua and by applying various mathematical finiteness theorems. (author)
Nilpotent -local finite groups
Cantarero, José; Scherer, Jérôme; Viruel, Antonio
2014-10-01
We provide characterizations of -nilpotency for fusion systems and -local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.
International Nuclear Information System (INIS)
Lee, Byeong Hae
1992-02-01
This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.
Amir, Sahar Z.
2018-01-02
The heterogeneous natures of rock fabrics, due to the existence of multi-scale fractures and geological formations, led to the deviations from unity in the flux-equations fractional-exponent magnitudes. In this paper, the resulting non-Newtonian non-Darcy fractional-derivatives flux equations are solved using physics-preserving averaging schemes that incorporates both, original and shifted, Grunwald-Letnikov (GL) approximation formulas preserving the physics, by reducing the shifting effects, while maintaining the stability of the system, by keeping one shifted expansion. The proposed way of using the GL expansions also generate symmetrical coefficient matrices that significantly reduces the discretization complexities appearing with all shifted cases from literature, and help considerably in 2D and 3D systems. Systems equations derivations and discretization details are discussed. Then, the physics-preserving averaging scheme is explained and illustrated. Finally, results are presented and reviewed. Edge-based original GL expansions are unstable as also illustrated in literatures. Shifted GL expansions are stable but add a lot of additional weights to both discretization sides affecting the physical accuracy. In comparison, the physics-preserving averaging scheme balances the physical accuracy and stability requirements leading to a more physically conservative scheme that is more stable than the original GL approximation but might be slightly less stable than the shifted GL approximations. It is a locally conservative Single-Continuum averaging scheme that applies a finite-volume viewpoint.
Amir, Sahar Z.; Sun, Shuyu
2018-01-01
The heterogeneous natures of rock fabrics, due to the existence of multi-scale fractures and geological formations, led to the deviations from unity in the flux-equations fractional-exponent magnitudes. In this paper, the resulting non-Newtonian non-Darcy fractional-derivatives flux equations are solved using physics-preserving averaging schemes that incorporates both, original and shifted, Grunwald-Letnikov (GL) approximation formulas preserving the physics, by reducing the shifting effects, while maintaining the stability of the system, by keeping one shifted expansion. The proposed way of using the GL expansions also generate symmetrical coefficient matrices that significantly reduces the discretization complexities appearing with all shifted cases from literature, and help considerably in 2D and 3D systems. Systems equations derivations and discretization details are discussed. Then, the physics-preserving averaging scheme is explained and illustrated. Finally, results are presented and reviewed. Edge-based original GL expansions are unstable as also illustrated in literatures. Shifted GL expansions are stable but add a lot of additional weights to both discretization sides affecting the physical accuracy. In comparison, the physics-preserving averaging scheme balances the physical accuracy and stability requirements leading to a more physically conservative scheme that is more stable than the original GL approximation but might be slightly less stable than the shifted GL approximations. It is a locally conservative Single-Continuum averaging scheme that applies a finite-volume viewpoint.
Alabdulmohsin, Ibrahim M.
2018-01-01
In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.
Alabdulmohsin, Ibrahim M.
2018-03-07
In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.
A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations
White, J. A.; Morrison, J. H.
1999-01-01
A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.
Hierarchical Material Properties in Finite Element Analysis: The Oilfield Infrastructure Problem.
Weiss, C. J.; Wilson, G. A.
2017-12-01
Geophysical simulation of low-frequency electromagnetic signals within built environments such as urban centers and industrial landscapes facilities is a challenging computational problem because strong conductors (e.g., pipes, fences, rail lines, rebar, etc.) are not only highly conductive and/or magnetic relative to the surrounding geology, but they are very small in one or more of their physical length coordinates. Realistic modeling of such structures as idealized conductors has long been the standard approach; however this strategy carries with it computational burdens such as cumbersome implementation of internal boundary conditions, and limited flexibility for accommodating realistic geometries. Another standard approach is "brute force" discretization (often coupled with an equivalent medium model) whereby 100's of millions of voxels are used to represent these strong conductors, but at the cost of extreme computation times (and mesh design) for a simulation result when possible. To minimize these burdens, a new finite element scheme (Weiss, Geophysics, 2017) has been developed in which the material properties reside on a hierarchy of geometric simplicies (i.e., edges, facets and volumes) within an unstructured tetrahedral mesh. This allows thin sheet—like structures, such as subsurface fractures, to be economically represented by a connected set of triangular facets, for example, that freely conform to arbitrary "real world" geometries. The same holds thin pipe/wire-like structures, such as casings or pipelines. The hierarchical finite element scheme has been applied to problems in electro- and magnetostatics for oilfield problems where the elevated, but finite, conductivity and permeability of the steel-cased oil wells must be properly accounted for, yielding results that are otherwise unobtainable, with run times as low as a few 10s of seconds. Extension of the hierarchical finite element concept to broadband electromagnetics is presently underway, as
Finite-Time Adaptive Synchronization of a New Hyperchaotic System with Uncertain Parameters
Directory of Open Access Journals (Sweden)
Ma Yongguang
2014-01-01
Full Text Available This paper presents a finite-time adaptive synchronization strategy for a class of new hyperchaotic systems with unknown slave system’s parameters. Based on the finite-time stability theory, an adaptive control law is derived to make the states of the new hyperchaotic systems synchronized in finite-time. Numerical simulations are presented to show the effectiveness of the proposed finite time synchronization scheme.
International Nuclear Information System (INIS)
Gastaldo, L.
2007-11-01
We develop in this PhD thesis a simulation tool for bubbly flows encountered in some late phases of a core-melt accident in pressurized water reactors, when the flow of molten core and vessel structures comes to chemically interact with the concrete of the containment floor. The physical modelling is based on the so-called drift-flux model, consisting of mass balance and momentum balance equations for the mixture (Navier-Stokes equations) and a mass balance equation for the gaseous phase. First, we propose a pressure correction scheme for the compressible Navier-Stokes equations based on mixed non-conforming finite elements. An ad hoc discretization of the advection operator, by a finite volume technique based on a dual mesh, ensures the stability of the velocity prediction step. A priori estimates for the velocity and the pressure yields the existence of the solution. We prove that this scheme is stable, in the sense that the discrete entropy is decreasing. For the conservation equation of the gaseous phase, we build a finite volume discretization which satisfies a discrete maximum principle. From this last property, we deduce the existence and the uniqueness of the discrete solution. Finally, on the basis of these works, a conservative and monotone scheme which is stable in the low Mach number limit, is build for the drift-flux model. This scheme enjoys, moreover, the following property: the algorithm preserves a constant pressure and velocity through moving interfaces between phases (i.e. contact discontinuities of the underlying hyperbolic system). In order to satisfy this property at the discrete level, we build an original pressure correction step which couples the mass balance equation with the transport terms of the gas mass balance equation, the remaining terms of the gas mass balance being taken into account with a splitting method. We prove the existence of a discrete solution for the pressure correction step. Numerical results are presented; they
Scheme Program Documentation Tools
DEFF Research Database (Denmark)
Nørmark, Kurt
2004-01-01
are separate and intended for different documentation purposes they are related to each other in several ways. Both tools are based on XML languages for tool setup and for documentation authoring. In addition, both tools rely on the LAML framework which---in a systematic way---makes an XML language available...... as named functions in Scheme. Finally, the Scheme Elucidator is able to integrate SchemeDoc resources as part of an internal documentation resource....
International Nuclear Information System (INIS)
Georges, Gabriel
2016-01-01
High Energy Density Physics (HEDP) flows are multi-material flows characterized by strong shock waves and large changes in the domain shape due to rare faction waves. Numerical schemes based on the Lagrangian formalism are good candidates to model this kind of flows since the computational grid follows the fluid motion. This provides accurate results around the shocks as well as a natural tracking of multi-material interfaces and free-surfaces. In particular, cell-centered Finite Volume Lagrangian schemes such as GLACE (Godunov-type Lagrangian scheme Conservative for total Energy) and EUCCLHYD (Explicit Unstructured Cell-Centered Lagrangian Hydrodynamics) provide good results on both the modeling of gas dynamics and elastic-plastic equations. The work produced during this PhD thesis is in continuity with the work of Maire and Nkonga [JCP, 2009] for the hydrodynamic part and the work of Kluth and Despres [JCP, 2010] for the hyper elasticity part. More precisely, the aim of this thesis is to develop robust and accurate methods for the 3D extension of the EUCCLHYD scheme with a second-order extension based on MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) and GRP (Generalized Riemann Problem) procedures. A particular care is taken on the preservation of symmetries and the monotonicity of the solutions. The scheme robustness and accuracy are assessed on numerous Lagrangian test cases for which the 3D extensions are very challenging. (author) [fr
The finite element response matrix method
International Nuclear Information System (INIS)
Nakata, H.; Martin, W.R.
1983-02-01
A new technique is developed with an alternative formulation of the response matrix method implemented with the finite element scheme. Two types of response matrices are generated from the Galerkin solution to the weak form of the diffusion equation subject to an arbitrary current and source. The piecewise polynomials are defined in two levels, the first for the local (assembly) calculations and the second for the global (core) response matrix calculations. This finite element response matrix technique was tested in two 2-dimensional test problems, 2D-IAEA benchmark problem and Biblis benchmark problem, with satisfatory results. The computational time, whereas the current code is not extensively optimized, is of the same order of the well estabilished coarse mesh codes. Furthermore, the application of the finite element technique in an alternative formulation of response matrix method permits the method to easily incorporate additional capabilities such as treatment of spatially dependent cross-sections, arbitrary geometrical configurations, and high heterogeneous assemblies. (Author) [pt
Parquet theory of finite temperature boson systems
International Nuclear Information System (INIS)
He, H.W.
1992-01-01
In this dissertation, the author uses the parquet summation for the two-body vertex as the framework for a perturbation theory of finite-temperature homogeneous boson systems. The present formalism is a first step toward a full description of the thermodynamic behavior of a finite temperature boson system through parquet summation. The current approximation scheme focuses on a system below the Bose-Einstein condensation temperature and considers only the contribution from Bogoliubov excitations out of a boson condensate. Comparison with the finite temperature variational theory by Campbell et al. shows strong similarities between variational theory and the current theory. Numerical results from a 4 He system and a nuclear system are discussed
Hybrid finite difference/finite element immersed boundary method.
E Griffith, Boyce; Luo, Xiaoyu
2017-12-01
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International Journal for Numerical Methods in Biomedical Engineering Published by John Wiley & Sons Ltd.
The complete flux scheme in cylindrical coordinates
Anthonissen, M.J.H.; Thije Boonkkamp, ten J.H.M.
2014-01-01
We consider the complete ¿ux (CF) scheme, a ¿nite volume method (FVM) presented in [1]. CF is based on an integral representation for the ¿uxes, found by solving a local boundary value problem that includes the source term. It performs well (second order accuracy) for both diffusion and advection
Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model
Directory of Open Access Journals (Sweden)
Oluwaseun Egbelowo
2017-05-01
Full Text Available We extend the nonstandard finite difference method of solution to the study of pharmacokinetic–pharmacodynamic models. Pharmacokinetic (PK models are commonly used to predict drug concentrations that drive controlled intravenous (I.V. transfers (or infusion and oral transfers while pharmacokinetic and pharmacodynamic (PD interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.
Phase transition in finite systems
International Nuclear Information System (INIS)
Chomaz, Ph.; Duflot, V.; Duflot, V.; Gulminelli, F.
2000-01-01
In this paper we present a review of selected aspects of Phase transitions in finite systems applied in particular to the liquid-gas phase transition in nuclei. We show that the problem of the non existence of boundary conditions can be solved by introducing a statistical ensemble with an averaged constrained volume. In such an ensemble the microcanonical heat capacity becomes negative in the transition region. We show that the caloric curve explicitly depends on the considered transformation of the volume with the excitation energy and so does not bear direct informations on the characteristics of the phase transition. Conversely, partial energy fluctuations are demonstrated to be a direct measure of the equation of state. Since the heat capacity has a negative branch in the phase transition region, the presence of abnormally large kinetic energy fluctuations is a signal of the liquid gas phase transition. (author)
Multiresolution signal decomposition schemes
J. Goutsias (John); H.J.A.M. Heijmans (Henk)
1998-01-01
textabstract[PNA-R9810] Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This report proposes a general axiomatic pyramid decomposition scheme for signal analysis
Strict finitism and the logic of mathematical applications
Ye, Feng
2011-01-01
Exploring the logic behind applied mathematics to the physical world, this volume illustrates how radical naturalism, nominalism and strict finitism can account for the applications of classical mathematics in current theories about natural phenomena.
Mülken, O.; Borrmann, P.; Harting, J.D.R.; Stamerjohanns, H.
2001-01-01
We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose systems in power-law traps within a semi-analytic
Directory of Open Access Journals (Sweden)
R. Sitharthan
2016-09-01
Full Text Available This paper aims at modelling an electronically coupled distributed energy resource with an adaptive protection scheme. The electronically coupled distributed energy resource is a microgrid framework formed by coupling the renewable energy source electronically. Further, the proposed adaptive protection scheme provides a suitable protection to the microgrid for various fault conditions irrespective of the operating mode of the microgrid: namely, grid connected mode and islanded mode. The outstanding aspect of the developed adaptive protection scheme is that it monitors the microgrid and instantly updates relay fault current according to the variations that occur in the system. The proposed adaptive protection scheme also employs auto reclosures, through which the proposed adaptive protection scheme recovers faster from the fault and thereby increases the consistency of the microgrid. The effectiveness of the proposed adaptive protection is studied through the time domain simulations carried out in the PSCAD⧹EMTDC software environment.
Fractional finite Fourier transform.
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.
International Nuclear Information System (INIS)
Lucha, W.; Neufeld, H.
1986-01-01
We investigate the relation between finiteness of a four-dimensional quantum field theory and global supersymmetry. To this end we consider the most general quantum field theory and analyse the finiteness conditions resulting from the requirement of the absence of divergent contributions to the renormalizations of the parameters of the theory. In addition to the gauge bosons, both fermions and scalar bosons turn out to be a necessary ingredient in a non-trivial finite gauge theory. In all cases discussed, the supersymmetric theory restricted by two well-known constraints on the dimensionless couplings proves to be the unique solution of the finiteness conditions. (Author)
Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case
Energy Technology Data Exchange (ETDEWEB)
Fernández-Nieto, Enrique D., E-mail: edofer@us.es [Departamento de Matemática Aplicada I, Universidad de Sevilla, E.T.S. Arquitectura, Avda, Reina Mercedes, s/n, 41012 Sevilla (Spain); Gallardo, José M., E-mail: jmgallardo@uma.es [Departamento de Análisis Matemático, Universidad de Málaga, F. Ciencias, Campus Teatinos S/N (Spain); Vigneaux, Paul, E-mail: Paul.Vigneaux@math.cnrs.fr [Unitée de Mathématiques Pures et Appliquées, Ecole Normale Supérieure de Lyon, 46 allée d' Italie, 69364 Lyon Cedex 07 (France)
2014-05-01
This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez–Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.
A faster numerical scheme for a coupled system modeling soil erosion and sediment transport
Le, M.-H.; Cordier, S.; Lucas, C.; Cerdan, O.
2015-02-01
Overland flow and soil erosion play an essential role in water quality and soil degradation. Such processes, involving the interactions between water flow and the bed sediment, are classically described by a well-established system coupling the shallow water equations and the Hairsine-Rose model. Numerical approximation of this coupled system requires advanced methods to preserve some important physical and mathematical properties; in particular, the steady states and the positivity of both water depth and sediment concentration. Recently, finite volume schemes based on Roe's solver have been proposed by Heng et al. (2009) and Kim et al. (2013) for one and two-dimensional problems. In their approach, an additional and artificial restriction on the time step is required to guarantee the positivity of sediment concentration. This artificial condition can lead the computation to be costly when dealing with very shallow flow and wet/dry fronts. The main result of this paper is to propose a new and faster scheme for which only the CFL condition of the shallow water equations is sufficient to preserve the positivity of sediment concentration. In addition, the numerical procedure of the erosion part can be used with any well-balanced and positivity preserving scheme of the shallow water equations. The proposed method is tested on classical benchmarks and also on a realistic configuration.
Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy.
Buttler, Hans-Jurg
1995-01-01
The purpose of this paper is to evaluate numerically the semi-American callable bond by means of finite difference methods. This study implies three results. First, the numerical error is greater for the callable bond price than for the straight bond price, and too large for real applications Secondly, the numerical accuracy of the callable bond price computed for the relevant range of interest rates depends entirely on the finite difference scheme which is chosen for the boundary points. Thi...
An algorithm for analysis of the structure of finitely presented Lie algebras
Directory of Open Access Journals (Sweden)
Vladimir P. Gerdt
1997-12-01
Full Text Available We consider the following problem: what is the most general Lie algebra satisfying a given set of Lie polynomial equations? The presentation of Lie algebras by a finite set of generators and defining relations is one of the most general mathematical and algorithmic schemes of their analysis. That problem is of great practical importance, covering applications ranging from mathematical physics to combinatorial algebra. Some particular applications are constructionof prolongation algebras in the Wahlquist-Estabrook method for integrability analysis of nonlinear partial differential equations and investigation of Lie algebras arising in different physical models. The finite presentations also indicate a way to q-quantize Lie algebras. To solve this problem, one should perform a large volume of algebraic transformations which is sharply increased with growth of the number of generators and relations. For this reason, in practice one needs to use a computer algebra tool. We describe here an algorithm for constructing the basis of a finitely presented Lie algebra and its commutator table, and its implementation in the C language. Some computer results illustrating our algorithmand its actual implementation are also presented.
A simple extension of Roe's scheme for real gases
Energy Technology Data Exchange (ETDEWEB)
Arabi, Sina, E-mail: sina.arabi@polymtl.ca; Trépanier, Jean-Yves; Camarero, Ricardo
2017-01-15
The purpose of this paper is to develop a highly accurate numerical algorithm to model real gas flows in local thermodynamic equilibrium (LTE). The Euler equations are solved using a finite volume method based on Roe's flux difference splitting scheme including real gas effects. A novel algorithm is proposed to calculate the Jacobian matrix which satisfies the flux difference splitting exactly in the average state for a general equation of state. This algorithm increases the robustness and accuracy of the method, especially around the contact discontinuities and shock waves where the gas properties jump appreciably. The results are compared with an exact solution of the Riemann problem for the shock tube which considers the real gas effects. In addition, the method is applied to a blunt cone to illustrate the capability of the proposed extension in solving two dimensional flows.
Flux schemes for the two-fluid models of the trio-U code
International Nuclear Information System (INIS)
Kumbaro, A.; Seignole, V.; Ghidaglia, J.M.
2000-01-01
To solve the non-conservative system of the two-phase flow model in the TRIO-U two-phase flow module, a fully unstructured finite volume formulation is chosen, and the discretization is based on the concept of flux-scheme. Our method allows to determine whether hyperbolicity is necessary to have stable and convergent numerical computations. We discuss the necessity or not to consider all the differential transfer terms between the two-phases in the up-winding of the flux. Numerical results are presented in order to study out the influence of the pressure interface term in the stability, as well as in the up-winding of the flux. (author)
A gas kinetic scheme for the Baer–Nunziato two-phase flow model
International Nuclear Information System (INIS)
Pan, Liang; Zhao, Guiping; Tian, Baolin; Wang, Shuanghu
2012-01-01
Numerical methods for the Baer–Nunziato (BN) two-phase flow model have attracted much attention in recent years. In this paper, we present a new gas kinetic scheme for the BN two-phase flow model containing non-conservative terms in the framework of finite volume method. In the view of microscopic aspect, a generalized Bhatnagar–Gross–Krook (BGK) model which matches with the BN model is constructed. Based on the integral solution of the generalized BGK model, we construct the distribution functions at the cell interface. Then numerical fluxes can be obtained by taking moments of the distribution functions, and non-conservative terms are explicitly introduced into the construction of numerical fluxes. In this method, not only the complex iterative process of exact solutions is avoided, but also the non-conservative terms included in the equation can be handled well.