Finite volume methods for the incompressible Navier-Stokes equations on unstructured grids

Energy Technology Data Exchange (ETDEWEB)

Meese, Ernst Arne

1998-07-01

Most solution methods of computational fluid dynamics (CFD) use structured grids based on curvilinear coordinates for compliance with complex geometries. In a typical industry application, about 80% of the time used to produce the results is spent constructing computational grids. Recently the use of unstructured grids has been strongly advocated. For unstructured grids there are methods for generating them automatically on quite complex domains. This thesis focuses on the design of Navier-Stokes solvers that can cope with unstructured grids and ''low quality grids'', thus reducing the need for human intervention in the grid generation.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Energy Technology Data Exchange (ETDEWEB)

Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)

2005-07-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

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

KAUST Repository

Chu, Chunlei

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations. © 2011 Elsevier B.V.

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.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Energy Technology Data Exchange (ETDEWEB)

Bailey, Teresa S. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: baileyte@tamu.edu; Adams, Marvin L. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: mladams@tamu.edu; Yang, Brian [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Zika, Michael R. [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States)], E-mail: zika@llnl.gov

2008-04-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

International Nuclear Information System (INIS)

Bailey, Teresa S.; Adams, Marvin L.; Yang, Brian; Zika, Michael R.

2008-01-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids

A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids

KAUST Repository

Wheeler, Mary F.

2011-01-01

In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since they are developed within a variational framework as mixed finite element methods with special approximating spaces and quadrature rules. The latter allows for local flux elimination giving a cell-centered system for the scalar variable. We study two versions of the method: with a symmetric quadrature rule on smooth grids and a non-symmetric quadrature rule on rough grids. Theoretical and numerical results demonstrate first order convergence for problems with full-tensor coefficients. Second order superconvergence is observed on smooth grids. © 2011 Published by Elsevier Ltd.

Hydrothermal analysis in engineering using control volume finite element method

CERN Document Server

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),

Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

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

Double-grid finite-difference frequency-domain (DG-FDFD) method for scattering from chiral objects

CERN Document Server

Alkan, Erdogan; Elsherbeni, Atef

2013-01-01

This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid

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)

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.

Solving hyperbolic equations with finite volume methods

CERN Document Server

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...

A Monte Carlo method and finite volume method coupled optical simulation method for parabolic trough solar collectors

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

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

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced

Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid

Science.gov (United States)

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

A Three-Dimensional, Immersed Boundary, Finite Volume Method for the Simulation of Incompressible Heat Transfer Flows around Complex Geometries

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.

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

Science.gov (United States)

Housman, Jeffrey A.; Kiris, Cetin

2016-01-01

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

Development of a high-order finite volume method with multiblock partition techniques

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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.

Finite Volume Method for Pricing European Call Option with Regime-switching Volatility

Science.gov (United States)

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.

A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids

KAUST Repository

Wheeler, Mary F.; Xue, Guangri; Yotov, Ivan

2011-01-01

In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since

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)

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

Study of grid independence of finite element method on MHD free convective casson fluid flow with slip effect

Science.gov (United States)

Raju, R. Srinivasa; Ramesh, K.

2018-05-01

The purpose of this work is to study the grid independence of finite element method on MHD Casson fluid flow past a vertically inclined plate filled in a porous medium in presence of chemical reaction, heat absorption, an external magnetic field and slip effect has been investigated. For this study of grid independence, a mathematical model is developed and analyzed by using appropriate mathematical technique, called finite element method. Grid study discussed with the help of numerical values of velocity, temperature and concentration profiles in tabular form. avourable comparisons with previously published work on various special cases of the problem are obtained.

Optimal variable-grid finite-difference modeling for porous media

International Nuclear Information System (INIS)

Liu, Xinxin; Yin, Xingyao; Li, Haishan

2014-01-01

Numerical modeling of poroelastic waves by the finite-difference (FD) method is more expensive than that of acoustic or elastic waves. To improve the accuracy and computational efficiency of seismic modeling, variable-grid FD methods have been developed. In this paper, we derived optimal staggered-grid finite difference schemes with variable grid-spacing and time-step for seismic modeling in porous media. FD operators with small grid-spacing and time-step are adopted for low-velocity or small-scale geological bodies, while FD operators with big grid-spacing and time-step are adopted for high-velocity or large-scale regions. The dispersion relations of FD schemes were derived based on the plane wave theory, then the FD coefficients were obtained using the Taylor expansion. Dispersion analysis and modeling results demonstrated that the proposed method has higher accuracy with lower computational cost for poroelastic wave simulation in heterogeneous reservoirs. (paper)

A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows; Un schema elements finis non-conformes/volumes finis pour l'approximation en maillages non-structures des ecoulements a faible nombre de Mach

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)

Adaptive mesh refinement for a finite volume method for flow and transport of radionuclides in heterogeneous porous media

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)

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

Science.gov (United States)

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.

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

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.

Adaptive moving grid methods for two-phase flow in porous media

KAUST Repository

Dong, Hao

2014-08-01

In this paper, we present an application of the moving mesh method for approximating numerical solutions of the two-phase flow model in porous media. The numerical schemes combine a mixed finite element method and a finite volume method, which can handle the nonlinearities of the governing equations in an efficient way. The adaptive moving grid method is then used to distribute more grid points near the sharp interfaces, which enables us to obtain accurate numerical solutions with fewer computational resources. The numerical experiments indicate that the proposed moving mesh strategy could be an effective way to approximate two-phase flows in porous media. © 2013 Elsevier B.V. All rights reserved.

Grid Generation Techniques Utilizing the Volume Grid Manipulator

Science.gov (United States)

Alter, Stephen J.

1998-01-01

This paper presents grid generation techniques available in the Volume Grid Manipulation (VGM) code. The VGM code is designed to manipulate existing line, surface and volume grids to improve the quality of the data. It embodies an easy to read rich language of commands that enables such alterations as topology changes, grid adaption and smoothing. Additionally, the VGM code can be used to construct simplified straight lines, splines, and conic sections which are common curves used in the generation and manipulation of points, lines, surfaces and volumes (i.e., grid data). These simple geometric curves are essential in the construction of domain discretizations for computational fluid dynamic simulations. By comparison to previously established methods of generating these curves interactively, the VGM code provides control of slope continuity and grid point-to-point stretchings as well as quick changes in the controlling parameters. The VGM code offers the capability to couple the generation of these geometries with an extensive manipulation methodology in a scripting language. The scripting language allows parametric studies of a vehicle geometry to be efficiently performed to evaluate favorable trends in the design process. As examples of the powerful capabilities of the VGM code, a wake flow field domain will be appended to an existing X33 Venturestar volume grid; negative volumes resulting from grid expansions to enable flow field capture on a simple geometry, will be corrected; and geometrical changes to a vehicle component of the X33 Venturestar will be shown.

Finite Volumes for Complex Applications VII

CERN Document Server

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...

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

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.

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....

Three-Dimensional Phase Field Simulations of Hysteresis and Butterfly Loops by the Finite Volume Method

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)

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.

Comparative study of finite element method, isogeometric analysis, and finite volume method in elastic wave propagation of stress discontinuities

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

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.

An efficicient data structure for three-dimensional vertex based finite volume method

Science.gov (United States)

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.

Wind turbine aerodynamics using an incompressible overset grid method

DEFF Research Database (Denmark)

Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

2007-01-01

In this paper 3D Navier-Stokes simulations of the unsteady flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations...

Dual-mixed finite elements for the three-field Stokes model as a finite volume method on staggered grids

KAUST Repository

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

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...

A grid-doubling finite-element technique for calculating dynamic three-dimensional spontaneous rupture on an earthquake fault

Science.gov (United States)

Barall, Michael

2009-01-01

We present a new finite-element technique for calculating dynamic 3-D spontaneous rupture on an earthquake fault, which can reduce the required computational resources by a factor of six or more, without loss of accuracy. The grid-doubling technique employs small cells in a thin layer surrounding the fault. The remainder of the modelling volume is filled with larger cells, typically two or four times as large as the small cells. In the resulting non-conforming mesh, an interpolation method is used to join the thin layer of smaller cells to the volume of larger cells. Grid-doubling is effective because spontaneous rupture calculations typically require higher spatial resolution on and near the fault than elsewhere in the model volume. The technique can be applied to non-planar faults by morphing, or smoothly distorting, the entire mesh to produce the desired 3-D fault geometry. Using our FaultMod finite-element software, we have tested grid-doubling with both slip-weakening and rate-and-state friction laws, by running the SCEC/USGS 3-D dynamic rupture benchmark problems. We have also applied it to a model of the Hayward fault, Northern California, which uses realistic fault geometry and rock properties. FaultMod implements fault slip using common nodes, which represent motion common to both sides of the fault, and differential nodes, which represent motion of one side of the fault relative to the other side. We describe how to modify the traction-at-split-nodes method to work with common and differential nodes, using an implicit time stepping algorithm.

Development op finite volume methods for fluid dynamics; Developpement de methodes de volumes finis pour la mecanique des fluides

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)

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.

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

Science.gov (United States)

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.

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...

Modeling seismic wave propagation using staggered-grid mimetic finite differences

Directory of Open Access Journals (Sweden)

Freysimar Solano-Feo

2017-04-01

Full Text Available Mimetic finite difference (MFD approximations of continuous gradient and divergence operators satisfy a discrete version of the Gauss-Divergence theorem on staggered grids. On the mimetic approximation of this integral conservation principle, an unique boundary flux operator is introduced that also intervenes on the discretization of a given boundary value problem (BVP. In this work, we present a second-order MFD scheme for seismic wave propagation on staggered grids that discretized free surface and absorbing boundary conditions (ABC with same accuracy order. This scheme is time explicit after coupling a central three-level finite difference (FD stencil for numerical integration. Here, we briefly discuss the convergence properties of this scheme and show its higher accuracy on a challenging test when compared to a traditional FD method. Preliminary applications to 2-D seismic scenarios are also presented and show the potential of the mimetic finite difference method.

An element-based finite-volume method approach for naturally fractured compositional reservoir simulation

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)

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

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

Science.gov (United States)

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.

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

Directory of Open Access Journals (Sweden)

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.

Flow Applications of the Least Squares Finite Element Method

Science.gov (United States)

Jiang, Bo-Nan

1998-01-01

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

Grid Generating Automatically Method of Finite Element Analysis for Rotator Structure%旋转体结构有限元网格自动划分法

Institute of Scientific and Technical Information of China (English)

许贤泽

2000-01-01

The finite element analysis is applied to structure and freedom-system analysis. Its grid generating method is important to the finite element modeling,which generates the grid automatically by the sectional division method and gets the finite element grid model, thus accomplishing the pre-work of the finite element analysis.%用有限元法对进行结构和自由度体系进行分析，其网格的生成是建立有限元模型的重要技术，利用分块分割法对网格自动划分，从而形成有限元网格模型，完成有限元分析的前处理。

Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

DEFF Research Database (Denmark)

Amini Afshar, Mostafa; Bingham, Harry B.

2017-01-01

. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...

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.

8th conference on Finite Volumes for Complex Applications

CERN Document Server

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...

Wind turbine rotor-tower interaction using an incompressible overset grid method

DEFF Research Database (Denmark)

Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

2007-01-01

In this paper 3D Navier-Stokes simulations of the flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations are pres...

A Monotone, Higher-Order Accurate, Fixed-Grid Finite-Volume Method for Advection Problems with Moving Boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2008-01-01

textabstractIn this paper, 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

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

Science.gov (United States)

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.

A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods

Science.gov (United States)

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.

Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

Science.gov (United States)

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

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...

A multiscale mortar multipoint flux mixed finite element method

KAUST Repository

Wheeler, Mary Fanett

2012-02-03

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.

A finite integration method for conformal, structured-grid, electromagnetic simulation

International Nuclear Information System (INIS)

Cooke, S.J.; Shtokhamer, R.; Mondelli, A.A.; Levush, B.

2006-01-01

We describe a numerical scheme for solving Maxwell's equations in the frequency domain on a conformal, structured, non-orthogonal, multi-block mesh. By considering Maxwell's equations in a volume parameterized by dimensionless curvilinear coordinates, we obtain a set of tensor equations that are a continuum analogue of common circuit equations, and that separate the metrical and metric-free parts of Maxwell's equations and the material constitutive relations. We discretize these equations using a new formulation that treats the electric field and magnetic induction using simple basis-function representations to obtain a discrete form of Faraday's law of induction, but that uses finite integral representations for the displacement current and magnetic field to obtain a discrete form of Ampere's law, as in the finite integration technique [T. Weiland, A discretization method for the solution of Maxwell's equations for six-component fields, Electron. Commun. (AE U) 31 (1977) 116; T. Weiland, Time domain electromagnetic field computation with finite difference methods, Int. J. Numer. Model: Electron. Netw. Dev. Field 9 (1996) 295-319]. We thereby derive new projection operators for the discrete tensor material equations and obtain a compact numerical scheme for the discrete differential operators. This scheme is shown to exhibit significantly reduced numerical dispersion when compared to the standard linear finite element method. We take advantage of the mesh structure on a block-by-block basis to implement these numerical operators efficiently, and achieve computational speed with modest memory requirements when compared to explicit sparse matrix storage. Using the Jacobi-Davidson [G.L.G. Sleijpen, H.A. van der Vorst, A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl. 17 (2) (1996) 401-425; S.J. Cooke, B. Levush, Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi

SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids

KAUST Repository

Gao, Longfei

2018-02-16

We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid restriction on finite difference methods and allow the grids to be block-wise uniform with nonconforming interfaces. In doing so, variations in the wave speeds of the subterranean media can be accounted for more efficiently. Staggered grid finite difference operators satisfying the summation-by-parts (SBP) property are devised to approximate the spatial derivatives appearing in the acoustic wave equation. These operators are applied within each block independently. The coupling between blocks is achieved through simultaneous approximation terms (SATs), which impose the interface condition weakly, i.e., by penalty. Ratio of the grid spacing of neighboring blocks is allowed to be rational number, for which specially designed interpolation formulas are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate and stable simulation results.

A mixed Fourier–Galerkin–finite-volume method to solve the fluid dynamics equations in cylindrical geometries

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)

Angular finite volume method for solving the multigroup transport equation with piecewise average scattering cross sections

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)

Hybrid finite difference/finite element immersed boundary method.

Science.gov (United States)

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.

A hybrid finite-volume and finite difference scheme for depth-integrated non-hydrostatic model

Science.gov (United States)

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.

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.)

Finite volume model for two-dimensional shallow environmental flow

Science.gov (United States)

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.

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

Angular finite volume method for solving the multigroup transport equation with piecewise average scattering cross sections

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)

An Eulerian-Lagrangian finite-element method for modeling crack growth in creeping materials

International Nuclear Information System (INIS)

Lee Hae Sung.

1991-01-01

This study is concerned with the development of finite-element-solution methods for analysis of quasi-static, ductile crack growth in history-dependent materials. The mixed Eulerian-Langrangian description (ELD) kinematic model is shown to have several desirable properties for modeling inelastic crack growth. Accordingly, a variational statement based on the ELD for history-dependent materials is developed, and a new moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method is applied to the analysis of transient, quasi-static, mode-III crack growth in creeping materials. A generalized Petrov-Galerkin method (GPG) is developed that simultaneously stabilizes the statement to admit L 2 basis functions for the nonlinear strain field. Quasi-static, model-III crack growth in creeping materials under small-scale-yielding (SSY) conditions is considered. The GPG/ELD moving-grid finite-element formulation is used to model a transient crack-growth problem. The GPG/ELD results compare favorably with previously-published numerical results and the asymptotic solutions

Adaptive solution of the multigroup diffusion equation on irregular structured grids using a conforming finite element method formulation

International Nuclear Information System (INIS)

Ragusa, J. C.

2004-01-01

In this paper, a method for performing spatially adaptive computations in the framework of multigroup diffusion on 2-D and 3-D Cartesian grids is investigated. The numerical error, intrinsic to any computer simulation of physical phenomena, is monitored through an a posteriori error estimator. In a posteriori analysis, the computed solution itself is used to assess the accuracy. By efficiently estimating the spatial error, the entire computational process is controlled through successively adapted grids. Our analysis is based on a finite element solution of the diffusion equation. Bilinear test functions are used. The derived a posteriori error estimator is therefore based on the Hessian of the numerical solution. (authors)

Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure

Science.gov (United States)

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.

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

Science.gov (United States)

Tsiveriotis, K.; Brown, R. A.

1993-01-01

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

Simulation of 3D parachute fluid–structure interaction based on nonlinear finite element method and preconditioning finite volume method

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.

A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries

Science.gov (United States)

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.

Monte Carlo Finite Volume Element Methods for the Convection-Diffusion Equation with a Random Diffusion Coefficient

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.

Adaptive Method Using Controlled Grid Deformation

Directory of Open Access Journals (Sweden)

Florin FRUNZULICA

2011-09-01

Full Text Available The paper presents an adaptive method using the controlled grid deformation over an elastic, isotropic and continuous domain. The adaptive process is controlled with the principal strains and principal strain directions and uses the finite elements method. Numerical results are presented for several test cases.

3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

Science.gov (United States)

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids

Energy Technology Data Exchange (ETDEWEB)

Bungartz, H.J. [Technische Universitaet Muenchen (Germany)

1996-12-31

In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.

A Parallel Multiblock Structured Grid Method with Automated Interblocked Unstructured Grids for Chemically Reacting Flows

Science.gov (United States)

Spiegel, Seth Christian

An automated method for using unstructured grids to patch non- C0 interfaces between structured blocks has been developed in conjunction with a finite-volume method for solving chemically reacting flows on unstructured grids. Although the standalone unstructured solver, FVFLO-NCSU, is capable of resolving flows for high-speed aeropropulsion devices with complex geometries, unstructured-mesh algorithms are inherently inefficient when compared to their structured counterparts. However, the advantages of structured algorithms in developing a flow solution in a timely manner can be negated by the amount of time required to develop a mesh for complex geometries. The global domain can be split up into numerous smaller blocks during the grid-generation process to alleviate some of the difficulties in creating these complex meshes. An even greater abatement can be found by allowing the nodes on abutting block interfaces to be nonmatching or non-C 0 continuous. One code capable of solving chemically reacting flows on these multiblock grids is VULCAN, which uses a nonconservative approach for patching non-C0 block interfaces. The developed automated unstructured-grid patching algorithm has been installed within VULCAN to provide it the capability of a fully conservative approach for patching non-C0 block interfaces. Additionally, the FVFLO-NCSU solver algorithms have been deeply intertwined with the VULCAN source code to solve chemically reacting flows on these unstructured patches. Finally, the CGNS software library was added to the VULCAN postprocessor so structured and unstructured data can be stored in a single compact file. This final upgrade to VULCAN has been successfully installed and verified using test cases with particular interest towards those involving grids with non- C0 block interfaces.

A multiscale mortar multipoint flux mixed finite element method

KAUST Repository

Wheeler, Mary Fanett; Xue, Guangri; Yotov, Ivan

2012-01-01

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite

Solution of the square lid-driven cavity flow of a Bingham plastic using the finite volume method

OpenAIRE

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...

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)

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

Science.gov (United States)

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%.

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

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

Science.gov (United States)

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.

A cell-centred finite volume method for the Poisson problem on non-graded quadtrees with second order accurate gradients

Science.gov (United States)

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.

Development and application of a parallel finite volume method for flow simulation on unstructured grids with local refinement; Entwicklung und Anwendung eines parallelen Finite-Volumen-Verfahrens zur Stroemungssimulation auf unstrukturierten Gittern mit lokaler Verfeinerung

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.)

A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows

Science.gov (United States)

Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.

1995-01-01

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.

Mixed isogeometric finite cell methods for the stokes problem

NARCIS (Netherlands)

Hoang, T.; Verhoosel, C.V.; Auricchio, F.; van Brummelen, E.H.; Reali, A.

2017-01-01

We study the application of the Isogeometric Finite Cell Method (IGA-FCM) to mixed formulations in the context of the Stokes problem. We investigate the performance of the IGA-FCM when utilizing some isogeometric mixed finite elements, namely: Taylor-Hood, Sub-grid, Raviart-Thomas, and Nédélec

A new ghost-node method for linking different models and initial investigations of heterogeneity and nonmatching grids

Science.gov (United States)

Dickinson, J.E.; James, S.C.; Mehl, S.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Faunt, C.C.; Eddebbarh, A.-A.

2007-01-01

A flexible, robust method for linking parent (regional-scale) and child (local-scale) grids of locally refined models that use different numerical methods is developed based on a new, iterative ghost-node method. Tests are presented for two-dimensional and three-dimensional pumped systems that are homogeneous or that have simple heterogeneity. The parent and child grids are simulated using the block-centered finite-difference MODFLOW and control-volume finite-element FEHM models, respectively. The models are solved iteratively through head-dependent (child model) and specified-flow (parent model) boundary conditions. Boundary conditions for models with nonmatching grids or zones of different hydraulic conductivity are derived and tested against heads and flows from analytical or globally-refined models. Results indicate that for homogeneous two- and three-dimensional models with matched grids (integer number of child cells per parent cell), the new method is nearly as accurate as the coupling of two MODFLOW models using the shared-node method and, surprisingly, errors are slightly lower for nonmatching grids (noninteger number of child cells per parent cell). For heterogeneous three-dimensional systems, this paper compares two methods for each of the two sets of boundary conditions: external heads at head-dependent boundary conditions for the child model are calculated using bilinear interpolation or a Darcy-weighted interpolation; specified-flow boundary conditions for the parent model are calculated using model-grid or hydrogeologic-unit hydraulic conductivities. Results suggest that significantly more accurate heads and flows are produced when both Darcy-weighted interpolation and hydrogeologic-unit hydraulic conductivities are used, while the other methods produce larger errors at the boundary between the regional and local models. The tests suggest that, if posed correctly, the ghost-node method performs well. Additional testing is needed for highly

A control volume based finite difference method for solving the equilibrium equations in terms of displacements

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....

Domain decomposition method for nonconforming finite element approximations of anisotropic elliptic problems on nonmatching grids

Energy Technology Data Exchange (ETDEWEB)

Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)

1996-12-31

An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains

Science.gov (United States)

Johansen, Hans; Colella, Phillip

1998-11-01

We present a numerical method for solving Poisson's equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. We treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservative differencing of second-order accurate fluxes on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows us to use multigrid iterations with a simple point relaxation strategy. We have combined this with an adaptive mesh refinement (AMR) procedure. We provide evidence that the algorithm is second-order accurate on various exact solutions and compare the adaptive and nonadaptive calculations.

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.

Numerical comparison of robustness of some reduction methods in rough grids

KAUST Repository

Hou, Jiangyong

2014-04-09

In this article, we present three nonsymmetric mixed hybrid RT 1 2 methods and compare with some recently developed reduction methods which are suitable for the single-phase Darcy flow problem with full anisotropic and highly heterogeneous permeability on general quadrilateral grids. The methods reviewed are multipoint flux approximation (MPFA), multipoint flux mixed finite element method, mixed-finite element with broken RT 1 2 method, MPFA-type mimetic finite difference method, and symmetric mixed-hybrid finite element method. The numerical experiments of these methods on different distorted meshes are compared, as well as their differences in performance of fluxes are discussed. © 2014 Wiley Periodicals, Inc.

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.

6th international symposium on finite volumes for complex applications

CERN Document Server

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

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.

A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra

KAUST Repository

Wheeler, Mary

2011-11-06

In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields a positive definite cell-centered system for the pressure by eliminating local velocities. The method is shown to be accurate on highly distorted rough quadrilateral and hexahedral grids, including hexahedra with non-planar faces. Theoretical and numerical results indicate first-order convergence for the pressure and face fluxes. © 2011 Springer-Verlag.

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.

The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

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.

The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

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.

Coupling of a 3-D vortex particle-mesh method with a finite volume near-wall solver

Science.gov (United States)

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.

The use of the spectral method within the fast adaptive composite grid method

Energy Technology Data Exchange (ETDEWEB)

McKay, S.M.

1994-12-31

The use of efficient algorithms for the solution of partial differential equations has been sought for many years. The fast adaptive composite grid (FAC) method combines an efficient algorithm with high accuracy to obtain low cost solutions to partial differential equations. The FAC method achieves fast solution by combining solutions on different grids with varying discretizations and using multigrid like techniques to find fast solution. Recently, the continuous FAC (CFAC) method has been developed which utilizes an analytic solution within a subdomain to iterate to a solution of the problem. This has been shown to achieve excellent results when the analytic solution can be found. The CFAC method will be extended to allow solvers which construct a function for the solution, e.g., spectral and finite element methods. In this discussion, the spectral methods will be used to provide a fast, accurate solution to the partial differential equation. As spectral methods are more accurate than finite difference methods, the ensuing accuracy from this hybrid method outside of the subdomain will be investigated.

ALE finite volume method for free-surface Bingham plastic fluids with general curvilinear coordinates

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.

ALE finite volume method for free-surface Bingham plastic fluids with general curvilinear coordinates

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Multi-phase Volume Segmentation with Tetrahedral Mesh

DEFF Research Database (Denmark)

Nguyen Trung, Tuan; Dahl, Vedrana Andersen; Bærentzen, Jakob Andreas

Volume segmentation is efficient for reconstructing material structure, which is important for several analyses, e.g. simulation with finite element method, measurement of quantitative information like surface area, surface curvature, volume, etc. We are concerned about the representations of the 3......D volumes, which can be categorized into two groups: fixed voxel grids [1] and unstructured meshes [2]. Among these two representations, the voxel grids are more popular since manipulating a fixed grid is easier than an unstructured mesh, but they are less efficient for quantitative measurements....... In many cases, the voxel grids are converted to explicit meshes, however the conversion may reduce the accuracy of the segmentations, and the effort for meshing is also not trivial. On the other side, methods using unstructured meshes have difficulty in handling topology changes. To reduce the complexity...

A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra

KAUST Repository

Wheeler, Mary; Xue, Guangri; Yotov, Ivan

2011-01-01

In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields

New ghost-node method for linking different models with varied grid refinement

Science.gov (United States)

James, S.C.; Dickinson, J.E.; Mehl, S.W.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Eddebbarh, A.-A.

2006-01-01

A flexible, robust method for linking grids of locally refined ground-water flow models constructed with different numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method for a refined "child" model that is contained within a larger and coarser "parent" model that is based on the iterative method of Steffen W. Mehl and Mary C. Hill (2002, Advances in Water Res., 25, p. 497-511; 2004, Advances in Water Res., 27, p. 899-912). The method is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that has matching grids (parent cells border an integer number of child cells) or nonmatching grids. The coupled grids are simulated by using the finite-difference and finite-element models MODFLOW and FEHM, respectively. The simulations require no alteration of the MODFLOW or FEHM models and are executed using a batch file on Windows operating systems. Results indicate that when the grids are matched spatially so that nodes and child-cell boundaries are aligned, the new coupling technique has error nearly equal to that when coupling two MODFLOW models. When the grids are nonmatching, model accuracy is slightly increased compared to that for matching-grid cases. Overall, results indicate that the ghost-node technique is a viable means to couple distinct models because the overall head and flow errors relative to the analytical solution are less than if only the regional coarse-grid model was used to simulate flow in the child model's domain.

Evaluation of a new welding process used to joint grids thimbles properly in 16 x 16 fuel assemblies, using the finite element method

Energy Technology Data Exchange (ETDEWEB)

Schettino, Carlos Frederico Mattos, E-mail: DPNcarlosschettino@inb.gov.b [Industrias Nucleares do Brasil S.A. (DPN/INB), Resende, RJ (Brazil). Diretoria de Producao Nuclear; Silva, Marcio Adriano Coelho da, E-mail: marcio.adriano@inb.gov.b [Industrias Nucleares do Brasil S.A. (GEACON/INB), Resende, RJ (Brazil). Gerencia de Analise Tecnica do Combustivel

2011-07-01

The present work aims to evaluate structurally the new welding process used to join the grids to the guide thimbles properly in 16 x 16 fuel assemblies. This new process is an increase of the number of welding points, 4 to 8, between grids and guide thimbles, giving more stiffness to the whole structure. A finite element model of the fuel assembly design was generated in the program ANSYS 12.1. To build this model were used elements BEAM-4 and several spring type elements. The analysis covered specific loads and displacements, simulating the boundaries conditions found during small deflection acting on the entire structure. The method used to development this analysis was the simulation of a finite element model performing a fuel assembly with four weld points on each grid cell containing the guide thimbles, and then the results of it was compare with another model, with eight weld points on each grid cell containing the guide thimbles. The behavior of the structure under the acting displacement and the related results of the analysis, mainly the stiffness, were satisfied. The results of this analysis were used to prove that the new grid to guide thimble welding process improve the dimensional stability when submitted to loads and displacements required on the fuel assembly design. The performed analysis provided INB to get more information of extreme importance, for the continuity of the development of new process of manufacturing and to improve the design of the current fuel assemblies used in reactors. (author)

Evaluation of a new welding process used to joint grids thimbles properly in 16 x 16 fuel assemblies, using the finite element method

International Nuclear Information System (INIS)

Schettino, Carlos Frederico Mattos; Silva, Marcio Adriano Coelho da

2011-01-01

The present work aims to evaluate structurally the new welding process used to join the grids to the guide thimbles properly in 16 x 16 fuel assemblies. This new process is an increase of the number of welding points, 4 to 8, between grids and guide thimbles, giving more stiffness to the whole structure. A finite element model of the fuel assembly design was generated in the program ANSYS 12.1. To build this model were used elements BEAM-4 and several spring type elements. The analysis covered specific loads and displacements, simulating the boundaries conditions found during small deflection acting on the entire structure. The method used to development this analysis was the simulation of a finite element model performing a fuel assembly with four weld points on each grid cell containing the guide thimbles, and then the results of it was compare with another model, with eight weld points on each grid cell containing the guide thimbles. The behavior of the structure under the acting displacement and the related results of the analysis, mainly the stiffness, were satisfied. The results of this analysis were used to prove that the new grid to guide thimble welding process improve the dimensional stability when submitted to loads and displacements required on the fuel assembly design. The performed analysis provided INB to get more information of extreme importance, for the continuity of the development of new process of manufacturing and to improve the design of the current fuel assemblies used in reactors. (author)

An h-adaptive finite element method for turbulent heat transfer

Energy Technology Data Exchange (ETDEWEB)

Carriington, David B [Los Alamos National Laboratory

2009-01-01

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

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

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

Science.gov (United States)

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.

New Ghost-node method for linking different models with varied grid refinement

International Nuclear Information System (INIS)

Mehl, Steffen W.; Hill, Mary Catherine; James, Scott Carlton; Leake, Stanley A.; Zyvoloski, George A.; Dickinson, Jesse E.; Eddebbarh, Al A.

2006-01-01

A flexible, robust method for linking grids of locally refined models constructed with different numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method for a refined 'child' model that is contained within a larger and coarser 'parent' model that is based on the iterative method of Mehl and Hill (2002, 2004). The method is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that has either matching grids (parent cells border an integer number of child cells; Figure 2a) or non-matching grids (parent cells border a non-integer number of child cells; Figure 2b). The coupled grids are simulated using the finite-difference and finite-element models MODFLOW and FEHM, respectively. The simulations require no alteration of the MODFLOW or FEHM models and are executed using a batch file on Windows operating systems. Results indicate that when the grids are matched spatially so that nodes and child cell boundaries are aligned, the new coupling technique has error nearly equal to that when coupling two MODFLOW models (Mehl and Hill, 2002). When the grids are non-matching, model accuracy is slightly increased over matching-grid cases. Overall, results indicate that the ghost-node technique is a viable means to accurately couple distinct models because the overall error is less than if only the regional model was used to simulate flow in the child model's domain

GRIZ: Visualization of finite element analysis results on unstructured grids

International Nuclear Information System (INIS)

Dovey, D.; Loomis, M.D.

1994-01-01

GRIZ is a general-purpose post-processing application that supports interactive visualization of finite element analysis results on three-dimensional unstructured grids. GRIZ includes direct-to-videodisc animation capabilities and is being used as a production tool for creating engineering animations

Development of a partitioned finite volume-finite element fluid-structure interaction scheme for strongly-coupled problems

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...

A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method.

Science.gov (United States)

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.

Chiral crossover transition in a finite volume

Science.gov (United States)

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)

An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

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.

Parallel SOR methods with a parabolic-diffusion acceleration technique for solving an unstructured-grid Poisson equation on 3D arbitrary geometries

Science.gov (United States)

Zapata, M. A. Uh; Van Bang, D. Pham; Nguyen, K. D.

2016-05-01

This paper presents a parallel algorithm for the finite-volume discretisation of the Poisson equation on three-dimensional arbitrary geometries. The proposed method is formulated by using a 2D horizontal block domain decomposition and interprocessor data communication techniques with message passing interface. The horizontal unstructured-grid cells are reordered according to the neighbouring relations and decomposed into blocks using a load-balanced distribution to give all processors an equal amount of elements. In this algorithm, two parallel successive over-relaxation methods are presented: a multi-colour ordering technique for unstructured grids based on distributed memory and a block method using reordering index following similar ideas of the partitioning for structured grids. In all cases, the parallel algorithms are implemented with a combination of an acceleration iterative solver. This solver is based on a parabolic-diffusion equation introduced to obtain faster solutions of the linear systems arising from the discretisation. Numerical results are given to evaluate the performances of the methods showing speedups better than linear.

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

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)

Development of a higher-order finite volume method for simulation of thermal oil recovery process using moving mesh strategy

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.

Mass, momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equations

International Nuclear Information System (INIS)

Hof, Bas van’t; Veldman, Arthur E.P.

2012-01-01

The paper explains a method by which discretizations of the continuity and momentum equations can be designed, such that they can be combined with an equation of state into a discrete energy equation. The resulting ‘MaMEC’ discretizations conserve mass, momentum as well as energy, although no explicit conservation law for the total energy is present. Essential ingredients are (i) discrete convection that leaves the discrete energy invariant, and (ii) discrete consistency between the thermodynamic terms. Of particular relevance is the way in which finite volume fluxes are related to nodal values. The method is an extension of existing methods based on skew-symmetry of discrete operators, because it allows arbitrary equations of state and a larger class of grids than earlier methods. The method is first illustrated with a one-dimensional example on a highly stretched staggered grid, in which the MaMEC method calculates qualitatively correct results and a non-skew-symmetric finite volume method becomes unstable. A further example is a two-dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid. The conservation of mass, momentum and energy is checked, and losses are found negligible up to machine accuracy.

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.)

Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method

KAUST Repository

Efendiev, Yalchin R.

2015-06-05

In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on generalized multiscale finite element method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale basis functions. These multiscale basis functions are constructed in the offline stage via local spectral problems following GMsFEM. To represent the fractures on the fine grid, we consider two approaches (1) discrete fracture model (DFM) (2) embedded fracture model (EFM) and their combination. In DFM, the fractures are resolved via the fine grid, while in EFM the fracture and the fine grid block interaction is represented as a source term. In the proposed multiscale method, additional multiscale basis functions are used to represent the long fractures, while short-size fractures are collectively represented by a single basis functions. The procedure is automatically done via local spectral problems. In this regard, our approach shares common concepts with several approaches proposed in the literature as we discuss. We would like to emphasize that our goal is not to compare DFM with EFM, but rather to develop GMsFEM framework which uses these (DFM or EFM) fine-grid discretization techniques. Numerical results are presented, where we demonstrate how one can adaptively add basis functions in the regions of interest based on error indicators. We also discuss the use of randomized snapshots (Calo et al. Randomized oversampling for generalized multiscale finite element methods, 2014), which reduces the offline computational cost.

Finite-Difference Frequency-Domain Method in Nanophotonics

DEFF Research Database (Denmark)

Ivinskaya, Aliaksandra

Optics and photonics are exciting, rapidly developing fields building their success largely on use of more and more elaborate artificially made, nanostructured materials. To further advance our understanding of light-matter interactions in these complicated artificial media, numerical modeling...... is often indispensable. This thesis presents the development of rigorous finite-difference method, a very general tool to solve Maxwell’s equations in arbitrary geometries in three dimensions, with an emphasis on the frequency-domain formulation. Enhanced performance of the perfectly matched layers...... is obtained through free space squeezing technique, and nonuniform orthogonal grids are built to greatly improve the accuracy of simulations of highly heterogeneous nanostructures. Examples of the use of the finite-difference frequency-domain method in this thesis range from simulating localized modes...

High order spectral volume and spectral difference methods on unstructured grids

Science.gov (United States)

Kannan, Ravishekar

The spectral volume (SV) and the spectral difference (SD) methods were developed by Wang and Liu and their collaborators for conservation laws on unstructured grids. They were introduced to achieve high-order accuracy in an efficient manner. Recently, these methods were extended to three-dimensional systems and to the Navier Stokes equations. The simplicity and robustness of these methods have made them competitive against other higher order methods such as the discontinuous Galerkin and residual distribution methods. Although explicit TVD Runge-Kutta schemes for the temporal advancement are easy to implement, they suffer from small time step limited by the Courant-Friedrichs-Lewy (CFL) condition. When the polynomial order is high or when the grid is stretched due to complex geometries or boundary layers, the convergence rate of explicit schemes slows down rapidly. Solution strategies to remedy this problem include implicit methods and multigrid methods. A novel implicit lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation method is employed as an iterative smoother. It is compared to the explicit TVD Runge-Kutta smoothers. For some p-multigrid calculations, combining implicit and explicit smoothers for different p-levels is also studied. The multigrid method considered is nonlinear and uses Full Approximation Scheme (FAS). An overall speed-up factor of up to 150 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Euler equations for the 3rd order SD method. A study of viscous flux formulations was carried out for the SV method. Three formulations were used to discretize the viscous fluxes: local discontinuous Galerkin (LDG), a penalty method and the 2nd method of Bassi and Rebay. Fourier analysis revealed some interesting advantages for the penalty method. These were implemented in the Navier Stokes solver. An implicit and p-multigrid method was also implemented for the above. An overall speed

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.

The finite volume method in computational fluid dynamics an advanced introduction with OpenFOAM and Matlab

CERN Document Server

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...

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.

Task oriented design of robot kinematics using grid method and its application to nuclear power plant

International Nuclear Information System (INIS)

Chang, Pyung-Hun; Park, Joon-Young

2002-01-01

This paper presents a Task Oriented Design method for robot kinematics based on grid method, widely used in finite difference method and heat transfer/fluid flow analyses. This approach drastically reduces complexities and computational burden due to previous approaches. More specifically, the grid method with a new formulation simplifies the design to a problem of three-design-variable unit grid, which does not require to solve inverse/forward kinematics. The effectiveness of the grid method has been confirmed through a kinematics design of a robot for nuclear power plants. (author)

A solution of two-dimensional magnetohydrodynamic flow using the finite volume method

Directory of Open Access Journals (Sweden)

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.

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 Tfinite-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.)

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.)

Moving finite elements: A continuously adaptive method for computational fluid dynamics

International Nuclear Information System (INIS)

Glasser, A.H.; Miller, K.; Carlson, N.

1991-01-01

Moving Finite Elements (MFE), a recently developed method for computational fluid dynamics, promises major advances in the ability of computers to model the complex behavior of liquids, gases, and plasmas. Applications of computational fluid dynamics occur in a wide range of scientifically and technologically important fields. Examples include meteorology, oceanography, global climate modeling, magnetic and inertial fusion energy research, semiconductor fabrication, biophysics, automobile and aircraft design, industrial fluid processing, chemical engineering, and combustion research. The improvements made possible by the new method could thus have substantial economic impact. Moving Finite Elements is a moving node adaptive grid method which has a tendency to pack the grid finely in regions where it is most needed at each time and to leave it coarse elsewhere. It does so in a manner which is simple and automatic, and does not require a large amount of human ingenuity to apply it to each particular problem. At the same time, it often allows the time step to be large enough to advance a moving shock by many shock thicknesses in a single time step, moving the grid smoothly with the solution and minimizing the number of time steps required for the whole problem. For 2D problems (two spatial variables) the grid is composed of irregularly shaped and irregularly connected triangles which are very flexible in their ability to adapt to the evolving solution. While other adaptive grid methods have been developed which share some of these desirable properties, this is the only method which combines them all. In many cases, the method can save orders of magnitude of computing time, equivalent to several generations of advancing computer hardware

Adaptive moving grid methods for two-phase flow in porous media

KAUST Repository

Dong, Hao; Qiao, Zhonghua; Sun, Shuyu; Tang, Tao

2014-01-01

In this paper, we present an application of the moving mesh method for approximating numerical solutions of the two-phase flow model in porous media. The numerical schemes combine a mixed finite element method and a finite volume method, which can

High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms

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

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

Local defect correction for boundary integral equation methods

NARCIS (Netherlands)

Kakuba, G.; Anthonissen, M.J.H.

2014-01-01

The aim in this paper is to develop a new local defect correction approach to gridding for problems with localised regions of high activity in the boundary element method. The technique of local defect correction has been studied for other methods as finite difference methods and finite volume

A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics

Science.gov (United States)

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.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

International Nuclear Information System (INIS)

Meyers, M.D.; Huang, C.-K.; Zeng, Y.; Yi, S.A.; Albright, B.J.

2015-01-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

Science.gov (United States)

Meyers, M. D.; Huang, C.-K.; Zeng, Y.; Yi, S. A.; Albright, B. J.

2015-09-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

Science.gov (United States)

Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang

2017-06-01

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.

A Review on the Modified Finite Point Method

Directory of Open Access Journals (Sweden)

Nan-Jing Wu

2014-01-01

Full Text Available The objective of this paper is to make a review on recent advancements of the modified finite point method, named MFPM hereafter. This MFPM method is developed for solving general partial differential equations. Benchmark examples of employing this method to solve Laplace, Poisson, convection-diffusion, Helmholtz, mild-slope, and extended mild-slope equations are verified and then illustrated in fluid flow problems. Application of MFPM to numerical generation of orthogonal grids, which is governed by Laplace equation, is also demonstrated.

Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

Science.gov (United States)

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.

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 Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers

Energy Technology Data Exchange (ETDEWEB)

Melboe, Hallgeir

2001-10-01

This thesis addresses a posteriori error estimation for finite element methods and iterative linear solvers. Adaptive finite element methods have gained a lot of popularity over the last decades due to their ability to produce accurate results with limited computer power. In these methods a posteriori error estimates play an essential role. Not only do they give information about how large the total error is, they also indicate which parts of the computational domain should be given a more sophisticated treatment in order to reduce the error. A posteriori error estimates are traditionally aimed at estimating the global error, but more recently so called goal oriented error estimators have been shown a lot of interest. The name reflects the fact that they estimate the error in user-defined local quantities. In this thesis the main focus is on global error estimators for highly stretched grids and goal oriented error estimators for flow problems on regular grids. Numerical methods for partial differential equations, such as finite element methods and other similar techniques, typically result in a linear system of equations that needs to be solved. Usually such systems are solved using some iterative procedure which due to a finite number of iterations introduces an additional error. Most such algorithms apply the residual in the stopping criterion, whereas the control of the actual error may be rather poor. A secondary focus in this thesis is on estimating the errors that are introduced during this last part of the solution procedure. The thesis contains new theoretical results regarding the behaviour of some well known, and a few new, a posteriori error estimators for finite element methods on anisotropic grids. Further, a goal oriented strategy for the computation of forces in flow problems is devised and investigated. Finally, an approach for estimating the actual errors associated with the iterative solution of linear systems of equations is suggested. (author)

Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity

KAUST Repository

Wheeler, Mary

2013-11-16

We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method and the displacements are approximated by a continuous Galerkin finite element method. First-order convergence in space and time is established in appropriate norms for the pressure, velocity, and displacement. Numerical results are presented that illustrate the behavior of the method. © Springer Science+Business Media Dordrecht 2013.

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)

Generalized Multiscale Finite Element Methods for Wave Propagation in Heterogeneous Media

KAUST Repository

Chung, Eric T.

2014-11-13

Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to their complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop efficient and accurate methods that allow the use of coarse grids. In this paper, we present a multiscale finite element method for wave propagation on a coarse grid. The proposed method is based on the generalized multiscale finite element method (GMsFEM) (see [Y. Efendiev, J. Galvis, and T. Hou, J. Comput. Phys., 251 (2012), pp. 116--135]). To construct multiscale basis functions, we start with two snapshot spaces in each coarse-grid block, where one represents the degrees of freedom on the boundary and the other represents the degrees of freedom in the interior. We use local spectral problems to identify important modes in each snapshot space. These local spectral problems are different from each other and their formulations are based on the analysis. To the best of knowledge, this is the first time that multiple snapshot spaces and multiple spectral problems are used and necessary for efficient computations. Using the dominant modes from local spectral problems, multiscale basis functions are constructed to represent the solution space locally within each coarse block. These multiscale basis functions are coupled via the symmetric interior penalty discontinuous Galerkin method which provides a block diagonal mass matrix and, consequently, results in fast computations in an explicit time discretization. Our methods\\' stability and spectral convergence are rigorously analyzed. Numerical examples are presented to show our methods\\' performance. We also test oversampling strategies. In particular, we discuss how the modes from different snapshot spaces can affect the proposed methods\\' accuracy.

Ramses-GPU: Second order MUSCL-Handcock finite volume fluid solver

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Development of a hip joint model for finite volume simulations.

Science.gov (United States)

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.

Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity

KAUST Repository

Wheeler, Mary; Xue, Guangri; Yotov, Ivan

2013-01-01

We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method

Grid generation methods

CERN Document Server

Liseikin, Vladimir D

2010-01-01

This book is an introduction to structured and unstructured grid methods in scientific computing, addressing graduate students, scientists as well as practitioners. Basic local and integral grid quality measures are formulated and new approaches to mesh generation are reviewed. In addition to the content of the successful first edition, a more detailed and practice oriented description of monitor metrics in Beltrami and diffusion equations is given for generating adaptive numerical grids. Also, new techniques developed by the author are presented, in particular a technique based on the inverted form of Beltrami’s partial differential equations with respect to control metrics. This technique allows the generation of adaptive grids for a wide variety of computational physics problems, including grid clustering to given function values and gradients, grid alignment with given vector fields, and combinations thereof. Applications of geometric methods to the analysis of numerical grid behavior as well as grid ge...

A numerical formulation using unstructured grids for modeling two-phase flows in porous media considering heterogeneities and capillarity effects

International Nuclear Information System (INIS)

Hurtado, F.S.V.; Maliska, C.R.

2005-01-01

This paper briefly describes a two-dimensional numerical formulation using unstructured grids, developed for simulating two-phase immiscible displacements in porous media. The Element-based Finite Volume Method (EbFVM) is used for discretizing the model differential equations. (authors)

A numerical formulation using unstructured grids for modeling two-phase flows in porous media considering heterogeneities and capillarity effects

Energy Technology Data Exchange (ETDEWEB)

Hurtado, F.S.V.; Maliska, C.R. [Santa Catarina Federal Univ., Computational Fluid Dynamics Lab., Mechanical Engineering Dept., Florianopolis, SC (Brazil)

2005-07-01

This paper briefly describes a two-dimensional numerical formulation using unstructured grids, developed for simulating two-phase immiscible displacements in porous media. The Element-based Finite Volume Method (EbFVM) is used for discretizing the model differential equations. (authors)

3D magnetospheric parallel hybrid multi-grid method applied to planet–plasma interactions

Energy Technology Data Exchange (ETDEWEB)

Leclercq, L., E-mail: ludivine.leclercq@latmos.ipsl.fr [LATMOS/IPSL, UVSQ Université Paris-Saclay, UPMC Univ. Paris 06, CNRS, Guyancourt (France); Modolo, R., E-mail: ronan.modolo@latmos.ipsl.fr [LATMOS/IPSL, UVSQ Université Paris-Saclay, UPMC Univ. Paris 06, CNRS, Guyancourt (France); Leblanc, F. [LATMOS/IPSL, UPMC Univ. Paris 06 Sorbonne Universités, UVSQ, CNRS, Paris (France); Hess, S. [ONERA, Toulouse (France); Mancini, M. [LUTH, Observatoire Paris-Meudon (France)

2016-03-15

We present a new method to exploit multiple refinement levels within a 3D parallel hybrid model, developed to study planet–plasma interactions. This model is based on the hybrid formalism: ions are kinetically treated whereas electrons are considered as a inertia-less fluid. Generally, ions are represented by numerical particles whose size equals the volume of the cells. Particles that leave a coarse grid subsequently entering a refined region are split into particles whose volume corresponds to the volume of the refined cells. The number of refined particles created from a coarse particle depends on the grid refinement rate. In order to conserve velocity distribution functions and to avoid calculations of average velocities, particles are not coalesced. Moreover, to ensure the constancy of particles' shape function sizes, the hybrid method is adapted to allow refined particles to move within a coarse region. Another innovation of this approach is the method developed to compute grid moments at interfaces between two refinement levels. Indeed, the hybrid method is adapted to accurately account for the special grid structure at the interfaces, avoiding any overlapping grid considerations. Some fundamental test runs were performed to validate our approach (e.g. quiet plasma flow, Alfven wave propagation). Lastly, we also show a planetary application of the model, simulating the interaction between Jupiter's moon Ganymede and the Jovian plasma.

Parallel implementation of a dynamic unstructured chimera method in the DLR finite volume TAU-code

Energy Technology Data Exchange (ETDEWEB)

Madrane, A.; Raichle, A.; Stuermer, A. [German Aerospace Center, DLR, Numerical Methods, Inst. of Aerodynamics and Flow Technology, Braunschweig (Germany)]. E-mail: aziz.madrane@dlr.de

2004-07-01

Aerodynamic problems involving moving geometries have many applications, including store separation, high-speed train entering into a tunnel, simulation of full configurations of the helicopter and fast maneuverability. Overset grid method offers the option of calculating these procedures. The solution process uses a grid system that discretizes the problem domain by using separately generated but overlapping unstructured grids that update and exchange boundary information through interpolation. However, such computations are complicated and time consuming. Parallel computing offers a very effective way to improve the productivity in doing computational fluid dynamics (CFD). Therefore the purpose of this study is to develop an efficient parallel computation algorithm for analyzing the flowfield of complex geometries using overset grids method. The strategy adopted in the parallelization of the overset grids method including the use of data structures and communication, is described. Numerical results are presented to demonstrate the efficiency of the resulting parallel overset grids method. (author)

Parallel implementation of a dynamic unstructured chimera method in the DLR finite volume TAU-code

International Nuclear Information System (INIS)

Madrane, A.; Raichle, A.; Stuermer, A.

2004-01-01

Aerodynamic problems involving moving geometries have many applications, including store separation, high-speed train entering into a tunnel, simulation of full configurations of the helicopter and fast maneuverability. Overset grid method offers the option of calculating these procedures. The solution process uses a grid system that discretizes the problem domain by using separately generated but overlapping unstructured grids that update and exchange boundary information through interpolation. However, such computations are complicated and time consuming. Parallel computing offers a very effective way to improve the productivity in doing computational fluid dynamics (CFD). Therefore the purpose of this study is to develop an efficient parallel computation algorithm for analyzing the flowfield of complex geometries using overset grids method. The strategy adopted in the parallelization of the overset grids method including the use of data structures and communication, is described. Numerical results are presented to demonstrate the efficiency of the resulting parallel overset grids method. (author)

Treating network junctions in finite volume solution of transient gas flow models

Science.gov (United States)

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 Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

Science.gov (United States)

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.

MPFA algorithm for solving stokes-brinkman equations on quadrilateral grids

KAUST Repository

Iliev, Oleg

2014-01-01

This work is concerned with the development of a robust and accurate numerical method for solving the Stokes-Brinkman system of equations, which describes a free fluid flow coupled with a flow in porous media. Quadrilateral boundary fitted grid with a sophisticated finite volume method, namely MPFA O-method, is used to discretize the system of equations. Numerical results for two examples are presented, namely, channel flow and flow in a ring with a rolled porous medium. © Springer International Publishing Switzerland 2014.

Grid generation methods

CERN Document Server

Liseikin, Vladimir D

2017-01-01

This new edition provides a description of current developments relating to grid methods, grid codes, and their applications to actual problems. Grid generation methods are indispensable for the numerical solution of differential equations. Adaptive grid-mapping techniques, in particular, are the main focus and represent a promising tool to deal with systems with singularities. This 3rd edition includes three new chapters on numerical implementations (10), control of grid properties (11), and applications to mechanical, fluid, and plasma related problems (13). Also the other chapters have been updated including new topics, such as curvatures of discrete surfaces (3). Concise descriptions of hybrid mesh generation, drag and sweeping methods, parallel algorithms for mesh generation have been included too. This new edition addresses a broad range of readers: students, researchers, and practitioners in applied mathematics, mechanics, engineering, physics and other areas of applications.

Generalized multiscale finite element methods for problems in perforated heterogeneous domains

KAUST Repository

Chung, Eric T.

2015-06-08

Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales. Moreover, these problems are intrinsically multiscale and their discretizations can yield very large linear or nonlinear systems. In this paper, we investigate multiscale approaches that attempt to solve such problems on a coarse grid by constructing multiscale basis functions in each coarse grid, where the coarse grid can contain many perforations. In particular, we are interested in cases when there is no scale separation and the perforations can have different sizes. In this regard, we mention some earlier pioneering works, where the authors develop multiscale finite element methods. In our paper, we follow Generalized Multiscale Finite Element Method (GMsFEM) and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems. We show that with a few basis functions in each coarse block, one can approximate the solution, where each coarse block can contain many small inclusions. We apply our general concept to (1) Laplace equation in perforated domains; (2) elasticity equation in perforated domains; and (3) Stokes equations in perforated domains. Numerical results are presented for these problems using two types of heterogeneous perforated domains. The analysis of the proposed methods will be presented elsewhere. © 2015 Taylor & Francis

Generalized multiscale finite element methods (GMsFEM)

KAUST Repository

Efendiev, Yalchin R.; Galvis, Juan; Hou, Thomasyizhao

2013-01-01

In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.

Generalized multiscale finite element methods (GMsFEM)

KAUST Repository

Efendiev, Yalchin R.

2013-10-01

In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.

High Resolution DNS of Turbulent Flows using an Adaptive, Finite Volume Method

Science.gov (United States)

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.

New 2D adaptive mesh refinement algorithm based on conservative finite-differences with staggered grid

Science.gov (United States)

Gerya, T.; Duretz, T.; May, D. A.

2012-04-01

We present new 2D adaptive mesh refinement (AMR) algorithm based on stress-conservative finite-differences formulated for non-uniform rectangular staggered grid. The refinement approach is based on a repetitive cell splitting organized via a quad-tree construction (every parent cell is split into 4 daughter cells of equal size). Irrespective of the level of resolution every cell has 5 staggered nodes (2 horizontal velocities, 2 vertical velocities and 1 pressure) for which respective governing equations, boundary conditions and interpolation equations are formulated. The connectivity of the grid is achieved via cross-indexing of grid cells and basic nodal points located in their corners: four corner nodes are indexed for every cell and up to 4 surrounding cells are indexed for every node. The accuracy of the approach depends critically on the formulation of the stencil used at the "hanging" velocity nodes located at the boundaries between different levels of resolution. Most accurate results are obtained for the scheme based on the volume flux balance across the resolution boundary combined with stress-based interpolation of velocity orthogonal to the boundary. We tested this new approach with a number of 2D variable viscosity analytical solutions. Our tests demonstrate that the adaptive staggered grid formulation has convergence properties similar to those obtained in case of a standard, non-adaptive staggered grid formulation. This convergence is also achieved when resolution boundary crosses sharp viscosity contrast interfaces. The convergence rates measured are found to be insensitive to scenarios when the transition in grid resolution crosses sharp viscosity contrast interfaces. We compared various grid refinement strategies based on distribution of different field variables such as viscosity, density and velocity. According to these tests the refinement allows for significant (0.5-1 order of magnitude) increase in the computational accuracy at the same

Assembly Discontinuity Factors for the Neutron Diffusion Equation discretized with the Finite Volume Method. Application to BWR

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.

Dense QCD in a Finite Volume

OpenAIRE

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 simulation of the flow around a sailing boat with unsteady motion; Hiteijo undo wo okonau hansotei no yuten taisekiho ni yoru simulation

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.

SAFE-AXISYM, Stress Analysis of Axisymmetric Composite Structure by Finite Elements Method

International Nuclear Information System (INIS)

Cornell, D.C.

1967-01-01

1 - Nature of physical problem solved: SAFE-AXISYM is a program for the analysis of multi-material axisymmetric composite structures. It is designed for the analysis of heterogeneous structures such as reinforced and/or prestressed concrete vessels. The structure is assumed to be linearly elastic, and only bodies of revolution subjected to axisymmetric loading can be treated. 2 - Method of solution: SAFE-AXISYM uses a finite element method with a modified Gauss-Seidel iteration scheme. A reference grid subdivides the structure into ring-like small, finite elements, the vertices of which are called nodes. The grid may be generated by hand, by the computer or by a combination of the two methods. Each node has two degrees of freedom, translation in the and in the axial direction. Both zero and non-zero fixed displacement constraints may be assumed, and the loading condition may be mechanical and/or thermal. 3 - Restrictions on the complexity of the problem: Multi-material structures with varying rigidities converge very slowly. Not valid for incompressible materials. Maximum number of nodes = 475. Maximum number of elements = 1100

Finite element and finite difference methods in electromagnetic scattering

CERN Document Server

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

Main formulations of the finite element method for the problems of structural mechanics. Part 2

Directory of Open Access Journals (Sweden)

Ignat’ev Aleksandr Vladimirovich

Full Text Available The author offers a classification of Finite Element formulations, which allows orienting in a great number of the published and continuing to be published works on the problem of raising the efficiency of this widespread numerical method. The second part of the article offers examination of straight formulations of FEM in the form of displacement approach, area method and classical mixed-mode method. The question of solution convergence according to FEM in the form of classical mixed-mode method is considered on the example of single-input single-output system of a beam in case of finite element grid refinement. The author draws a conclusion, that extinction of algebraic equations system of FEM in case of passage to the limit is not a peculiar feature of this method in general, but manifests itself only in some particular cases. At the same time the obtained results prove that FEM in mixed-mode form provides obtaining more stable results in case of finite element grid refinement in comparison with FEM in the form of displacement approach. It is quite obvious that the same qualities will appear also in two-dimensional systems.

Parallel Adaptive Mesh Refinement for High-Order Finite-Volume Schemes in Computational Fluid Dynamics

Science.gov (United States)

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

Final Report for DOE grant DE-FG02-07ER64432 "New Grid and Discretization Technologies for Ocean and Ice Simulations"

Energy Technology Data Exchange (ETDEWEB)

Gunzburger, Max

2013-03-12

The work reported is in pursuit of these goals: high-quality unstructured, non-uniform Voronoi and Delaunay grids; improved finite element and finite volume discretization schemes; and improved finite element and finite volume discretization schemes. These are sought for application to spherical and three-dimensional applications suitable for ocean, atmosphere, ice-sheet, and other climate modeling applications.

A spatially adaptive grid-refinement approach for the finite element solution of the even-parity Boltzmann transport equation

International Nuclear Information System (INIS)

Mirza, Anwar M.; Iqbal, Shaukat; Rahman, Faizur

2007-01-01

A spatially adaptive grid-refinement approach has been investigated to solve the even-parity Boltzmann transport equation. A residual based a posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local particle balance has been considered as an error assessment criterion. To implement the adaptive approach, a computer program ADAFENT (adaptive finite elements for neutron transport) has been developed to solve the second order even-parity Boltzmann transport equation using K + variational principle for slab geometry. The program has a core K + module which employs Lagrange polynomials as spatial basis functions for the finite element formulation and Legendre polynomials for the directional dependence of the solution. The core module is called in by the adaptive grid generator to determine local gradients and residuals to explore the possibility of grid refinements in appropriate regions of the problem. The a posteriori error estimation scheme has been implemented in the outer grid refining iteration module. Numerical experiments indicate that local errors are large in regions where the flux gradients are large. A comparison of the spatially adaptive grid-refinement approach with that of uniform meshing approach for various benchmark cases confirms its superiority in greatly enhancing the accuracy of the solution without increasing the number of unknown coefficients. A reduction in the local errors of the order of 10 2 has been achieved using the new approach in some cases

A spatially adaptive grid-refinement approach for the finite element solution of the even-parity Boltzmann transport equation

Energy Technology Data Exchange (ETDEWEB)

Mirza, Anwar M. [Department of Computer Science, National University of Computer and Emerging Sciences, NUCES-FAST, A.K. Brohi Road, H-11, Islamabad (Pakistan)], E-mail: anwar.m.mirza@gmail.com; Iqbal, Shaukat [Faculty of Computer Science and Engineering, Ghulam Ishaq Khan (GIK) Institute of Engineering Science and Technology, Topi-23460, Swabi (Pakistan)], E-mail: shaukat@giki.edu.pk; Rahman, Faizur [Department of Physics, Allama Iqbal Open University, H-8 Islamabad (Pakistan)

2007-07-15

A spatially adaptive grid-refinement approach has been investigated to solve the even-parity Boltzmann transport equation. A residual based a posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local particle balance has been considered as an error assessment criterion. To implement the adaptive approach, a computer program ADAFENT (adaptive finite elements for neutron transport) has been developed to solve the second order even-parity Boltzmann transport equation using K{sup +} variational principle for slab geometry. The program has a core K{sup +} module which employs Lagrange polynomials as spatial basis functions for the finite element formulation and Legendre polynomials for the directional dependence of the solution. The core module is called in by the adaptive grid generator to determine local gradients and residuals to explore the possibility of grid refinements in appropriate regions of the problem. The a posteriori error estimation scheme has been implemented in the outer grid refining iteration module. Numerical experiments indicate that local errors are large in regions where the flux gradients are large. A comparison of the spatially adaptive grid-refinement approach with that of uniform meshing approach for various benchmark cases confirms its superiority in greatly enhancing the accuracy of the solution without increasing the number of unknown coefficients. A reduction in the local errors of the order of 10{sup 2} has been achieved using the new approach in some cases.

Finite element analysis of the contact between fuel rod and spacer grid

Energy Technology Data Exchange (ETDEWEB)

Kim, Hyung Kyu; Kim, Young Koon; Kang, Heung Seok; Yoon, Kyung Ho; Song, Kee Nam [Korea Atomic Energy Research Institute, Taejon (Korea)

1999-01-01

For the research on the fretting failure problem of nuclear fuel, the contact length and normal stress field are evaluated for the contact between fuel rod and spacer grid by using the Finite Element Method (FEM). An assumption of semi-infiniteness is necessary for applying the Contact Mechanics which is based on the classical theory of elasticity to the present problem. For the contact problem of fuel fretting, the contact mechanical solutions could be utilized well with sufficient accuracy if the contact bodies (i.e., the cladding tube and the spacer grid) can be assumed as semi-infinite bodies. To this end, the contact length evaluated by FEM is discussed together with the relevant research which concerned the effect of dimension for the validity of the assumption of semi-infiniteness. Normal stress profile on the contact is also studied through comparing the theoretical and the FE results. For the analysis of contact problem by FEM, ANSYS code (Version 5.3) is utilized and the geometry is chosen to be the Hertzian (cylinder-to-cylinder), the strip-to-cylinder and the fuel rod/spacer grid contact (strip-to-tube). Present research will be utilized for accessing the fuel fretting problem by FEM together with the theoretical (i.e., contact mechanical) analysis which has been published as KAERI/TR-1113/98. (author). 15 refs., 44 figs., 4 tabs.

A finite volume procedure for fluid flow, heat transfer and solid-body stress analysis

KAUST Repository

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.

Mixed finite element - discontinuous finite volume element discretization of a general class of multicontinuum models

Science.gov (United States)

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

Analysis of the optimized H type grid spring by a characterization test and the finite element method under the in-grid boundary

International Nuclear Information System (INIS)

Yoon, Kyung Ho; Lee, Kang Hee; Kang, Heung Seok; Song, Kee Nam

2006-01-01

Characterization tests (load vs. displacement curve) are conducted for the springs of Zirconium alloy spacer grids for an advanced LWR fuel assembly. Twofold testing is employed: strap-based and assembly-based tests. The assembly-based test satisfies the in situ boundary conditions of the spring within the grid assembly. The aim of the characterization test via the aforementioned two methods is to establish an appropriate assembly-based test method that fulfills the actual boundary conditions. A characterization test under the spacer grid assembly boundary condition is also conducted to investigate the actual behavior of the spring in the core. The stiffness of the characteristic curve is smaller than that of the strap-wised boundary condition. This phenomenon may cause the strap slit condition. A spacer grid consists of horizontal and vertical straps. The strap slit positions are differentiated from each other. They affords examination of the variation of the external load distribution in the grid spring. Localized regions of high stress and their values are analyzed, as they may be affected by the spring shape. Through a comparison of the results of the test and FE analysis, it is concluded that the present assembly-based analysis model and procedure are reasonably well conducted and can be used for spring characterization in the core. Guidelines for improving the mechanical integrity of the spring are also discussed

Discontinuous Galerkin finite element method with anisotropic local grid refinement for inviscid compressible flows

NARCIS (Netherlands)

van der Vegt, Jacobus J.W.; van der Ven, H.

1998-01-01

A new discretization method for the three-dimensional Euler equations of gas dynamics is presented, which is based on the discontinuous Galerkin finite element method. Special attention is paid to an efficient implementation of the discontinuous Galerkin method that minimizes the number of flux

Multiscale Finite Element Methods for Flows on Rough Surfaces

KAUST Repository

Efendiev, Yalchin

2013-01-01

In this paper, we present the Multiscale Finite Element Method (MsFEM) for problems on rough heterogeneous surfaces. We consider the diffusion equation on oscillatory surfaces. Our objective is to represent small-scale features of the solution via multiscale basis functions described on a coarse grid. This problem arises in many applications where processes occur on surfaces or thin layers. We present a unified multiscale finite element framework that entails the use of transformations that map the reference surface to the deformed surface. The main ingredients of MsFEM are (1) the construction of multiscale basis functions and (2) a global coupling of these basis functions. For the construction of multiscale basis functions, our approach uses the transformation of the reference surface to a deformed surface. On the deformed surface, multiscale basis functions are defined where reduced (1D) problems are solved along the edges of coarse-grid blocks to calculate nodalmultiscale basis functions. Furthermore, these basis functions are transformed back to the reference configuration. We discuss the use of appropriate transformation operators that improve the accuracy of the method. The method has an optimal convergence if the transformed surface is smooth and the image of the coarse partition in the reference configuration forms a quasiuniform partition. In this paper, we consider such transformations based on harmonic coordinates (following H. Owhadi and L. Zhang [Comm. Pure and Applied Math., LX(2007), pp. 675-723]) and discuss gridding issues in the reference configuration. Numerical results are presented where we compare the MsFEM when two types of deformations are used formultiscale basis construction. The first deformation employs local information and the second deformation employs a global information. Our numerical results showthat one can improve the accuracy of the simulations when a global information is used. © 2013 Global-Science Press.

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.

Microscopic deformation and strain hardening analysis of ferrite–bainite dual-phase steels using micro-grid method

International Nuclear Information System (INIS)

Ishikawa, Nobuyuki; Yasuda, Kyono; Sueyoshi, Hitoshi; Endo, Shigeru; Ikeda, Hiroshi; Morikawa, Tatsuya; Higashida, Kenji

2015-01-01

The local strain measurement method using nanometer-scaled micro grids printed on the surface of a specimen by an electron lithography technique (the micro-grid method) has been established. Microscopic deformation behavior of the ferrite–bainite steels with different bainite volume fraction, 16% and 40% of bainite, was evaluated. Strain localization in the ferrite phase adjacent to the ferrite/bainite boundary was clearly observed and visualized. Highly strained regions expanded toward the inner region of the ferrite phase and connected each other with an increase of macroscopic strain. The existence of hard bainite phase plays an important role for inducing strain localization in the ferrite phase by plastic constraint in the boundary parallel to the tensile direction. In order to obtain further understanding of microscopic deformation behavior, finite element analysis using the representative volume element, which is expressed by the axisymmetric unit cell containing a hard phase surrounded by a soft phase matrix, was conducted. It was found that the macroscopic stress–strain behavior of ferrite–bainite steels was well simulated by the unit cell models. Strain concentration in the ferrite phase was highly enhanced for the ferrite-40% bainite steel, and this imposed higher internal stress in the bainite phase, resulting in higher strain hardening rate in the early stage of the deformation. However, smaller ferrite volume fraction of ferrite-40% bainite steel induced bainite plastic deformation in order to fulfill the macroscopic strain of the steel. Accordingly, strain hardening capacity of the ferrite-40% bainite steel was reduced to a significant degree, resulting in a smaller uniform elongation than the ferrite-16% bainite steel

Dynamic visual cryptography on deformable finite element grids

Science.gov (United States)

Aleksiene, S.; Vaidelys, M.; Aleksa, A.; Ragulskis, M.

2017-07-01

Dynamic visual cryptography scheme based on time averaged moiré fringes on deformable finite element grids is introduced in this paper. A predefined Eigenshape function is used for the selection of the pitch of the moiré grating. The relationship between the pitch of moiré grating, the roots of the zero order Bessel function of the first kind and the amplitude of harmonic oscillations is derived and validated by computational experiments. Phase regularization algorithm is used in the entire area of the cover image in order to embed the secret image and to avoid large fluctuations of the moiré grating. Computational simulations are used to demonstrate the efficiency and the applicability of the proposed image hiding technique.

The application of finite volume methods for modelling three-dimensional incompressible flow on an unstructured mesh

Science.gov (United States)

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 finite-volume method for convection problems with embedded moving boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2009-01-01

htmlabstractAn accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. Moving interior boundary conditions are embedded in the fixed-grid fluxes in the direct neighborhood of the moving boundaries. Tailor-made limiters are

Pseudo-spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

KAUST Repository

Zou, Peng

2017-05-10

Staggering grid is a very effective way to reduce the Nyquist errors and to suppress the non-causal ringing artefacts in the pseudo-spectral solution of first-order elastic wave equations. However, the straightforward use of a staggered-grid pseudo-spectral method is problematic for simulating wave propagation when the anisotropy level is greater than orthorhombic or when the anisotropic symmetries are not aligned with the computational grids. Inspired by the idea of rotated staggered-grid finite-difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using the Lebedev grids, the rotated staggered-grid-based pseudo-spectral method possesses the best balance between the mitigation of artefacts and efficiency. A 2D example on a transversely isotropic model with tilted symmetry axis verifies its effectiveness to suppress the ringing artefacts. Two 3D examples of increasing anisotropy levels demonstrate that the rotated staggered-grid-based pseudo-spectral method can successfully simulate complex wavefields in such anisotropic formations.

A maximum-principle preserving finite element method for scalar conservation equations

KAUST Repository

Guermond, Jean-Luc; Nazarov, Murtazo

2014-01-01

This paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions. © 2014 Elsevier B.V.

A maximum-principle preserving finite element method for scalar conservation equations

KAUST Repository

Guermond, Jean-Luc

2014-04-01

This paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions. © 2014 Elsevier B.V.

Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations

KAUST Repository

Iliev, Oleg P.

2010-01-01

We present a two-scale finite element method for solving Brinkman\\'s equations with piece-wise constant coefficients. This system of equations model fluid flows in highly porous, heterogeneous media with complex topology of the heterogeneities. We make use of the recently proposed discontinuous Galerkin FEM for Stokes equations by Wang and Ye in [12] and the concept of subgrid approximation developed for Darcy\\'s equations by Arbogast in [4]. In order to reduce the error along the coarse-grid interfaces we have added a alternating Schwarz iteration using patches around the coarse-grid boundaries. We have implemented the subgrid method using Deal.II FEM library, [7], and we present the computational results for a number of model problems. © 2010 Springer-Verlag Berlin Heidelberg.

Bending Moment Calculations for Piles Based on the Finite Element Method

Directory of Open Access Journals (Sweden)

Yu-xin Jie

2013-01-01

Full Text Available Using the finite element analysis program ABAQUS, a series of calculations on a cantilever beam, pile, and sheet pile wall were made to investigate the bending moment computational methods. The analyses demonstrated that the shear locking is not significant for the passive pile embedded in soil. Therefore, higher-order elements are not always necessary in the computation. The number of grids across the pile section is important for bending moment calculated with stress and less significant for that calculated with displacement. Although computing bending moment with displacement requires fewer grid numbers across the pile section, it sometimes results in variation of the results. For displacement calculation, a pile row can be suitably represented by an equivalent sheet pile wall, whereas the resulting bending moments may be different. Calculated results of bending moment may differ greatly with different grid partitions and computational methods. Therefore, a comparison of results is necessary when performing the analysis.

Volume-of-fluid algorithm on a non-orthogonal grid

International Nuclear Information System (INIS)

Jang, W.; Lien, F.S.; Ji, H.

2005-01-01

In the present study, a novel VOF method on a non-orthogonal grid is proposed and tested for several benchmark problems, including a simple translation test, a reversed single vortex flow and a shearing flow, with the objective to demonstrate the feasibility and accuracy of the present approach. Excellent agreement between the solutions obtained on both orthogonal and non-orthogonal meshes is achieved. The sensitivity of various methods to the L 1 error in evaluating the interface normal and volume flux at each face of a non-orthogonal cell is examined. Time integration methods based on the operator-splitting approach in curvilinear coordinates, including the explicit-implicit (EX-IM) and explicit-explicit (EX-EX) combinations, are tested. (author)

Variational Multiscale Finite Element Method for Flows in Highly Porous Media

KAUST Repository

Iliev, O.; Lazarov, R.; Willems, J.

2011-01-01

We present a two-scale finite element method (FEM) for solving Brinkman's and Darcy's equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes' equations by Wang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy's equations. In order to reduce the "resonance error" and to ensure convergence to the global fine solution, the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems. © 2011 Society for Industrial and Applied Mathematics.

Variational Multiscale Finite Element Method for Flows in Highly Porous Media

KAUST Repository

Iliev, O.

2011-10-01

We present a two-scale finite element method (FEM) for solving Brinkman\\'s and Darcy\\'s equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes\\' equations by Wang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy\\'s equations. In order to reduce the "resonance error" and to ensure convergence to the global fine solution, the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems. © 2011 Society for Industrial and Applied Mathematics.

Finite Volume Element Predictor-corrector Method for a Class of Nonlinear Parabolic Systems%一类非线性抛物型方程组的有限体积元预估-校正方法

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.

Finite volume effects on the electric polarizability of neutral hadrons in lattice QCD

Science.gov (United States)

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.

Parameterized Finite Element Modeling and Buckling Analysis of Six Typical Composite Grid Cylindrical Shells

Science.gov (United States)

Lai, Changliang; Wang, Junbiao; Liu, Chuang

2014-10-01

Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.

Generalized multiscale finite element methods: Oversampling strategies

KAUST Repository

Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael

2014-01-01

In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local

A finite volume study for pressure waves propagation in a straight section of pipeline with caviation

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.

Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws

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

Geometrically Unfitted Finite Element Methods and Applications : Proceedings of the UCL Workshop 2016

CERN Document Server

Burman, Erik; Larson, Mats; Olshanskii, Maxim

2017-01-01

This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and aug...

Basic Finite Element Method

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.

Maxwell's equations in axisymmetrical geometry: coupling H(curl) finite element in volume and H(div) finite element in surface. The numerical code FuMel

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)

Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

KAUST Repository

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.

Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

KAUST Repository

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.

Numerical modeling of contaminant transport in fractured porous media using mixed finite-element and finitevolume methods

KAUST Repository

Dong, Chen; Sun, Shuyu; Taylor, Glenn A.

2011-01-01

A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods; i.e., the mixed finite-element (MFE) method and the finite-volume method. Adaptive

Generalized multiscale finite element methods. nonlinear elliptic equations

KAUST Repository

Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael

2013-01-01

In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.

Groundwater flow analysis using mixed hybrid finite element method for radioactive waste disposal facilities

International Nuclear Information System (INIS)

Aoki, Hiroomi; Shimomura, Masanori; Kawakami, Hiroto; Suzuki, Shunichi

2011-01-01

In safety assessments of radioactive waste disposal facilities, ground water flow analysis are used for calculating the radionuclide transport pathway and the infiltration flow rate of groundwater into the disposal facilities. For this type of calculations, the mixed hybrid finite element method has been used and discussed about the accuracy of ones in Europe. This paper puts great emphasis on the infiltration flow rate of groundwater into the disposal facilities, and describes the accuracy of results obtained from mixed hybrid finite element method by comparing of local water mass conservation and the reliability of the element breakdown numbers among the mixed hybrid finite element method, finite volume method and nondegenerated finite element method. (author)

Finite element analysis of optimized H shape spring in a nuclear fuel spacer grid by using contact definition

International Nuclear Information System (INIS)

Kim, Jae-Yong; Yoon, Kyung-Ho

2007-01-01

The primary role of the grid springs in spacer grid is to hold the fuel rods in an appropriate position using friction force and to prevent the fuel rods dropping during reactor operation. The spring force decreases as the fuel burn-up increases since the spring stiffness is degraded due to the high temperature and the irradiation effect in the reactor core. So this phenomenon has to be considered when the initial spring force of grid spring is designed. To check whether the spring have suitable spring force, the characterization test of spring is conducted. In this paper, finite element analysis using contact definition is established for prediction the spring stiffness without test. The test and analysis results are compared to check the availability of finite element model for investing the spring characteristics in assembly condition. (author)

A finite difference method for free boundary problems

KAUST Repository

Fornberg, Bengt

2010-01-01

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax

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

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

A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

KAUST Repository

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.

A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

KAUST Repository

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.

A NEW THREE-DIMENSIONAL SOLAR WIND MODEL IN SPHERICAL COORDINATES WITH A SIX-COMPONENT GRID

Energy Technology Data Exchange (ETDEWEB)

Feng, Xueshang; Zhang, Man; Zhou, Yufen, E-mail: fengx@spaceweather.ac.cn [SIGMA Weather Group, State Key Laboratory for Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190 (China)

2014-09-01

In this paper, we introduce a new three-dimensional magnetohydrodynamics numerical model to simulate the steady state ambient solar wind from the solar surface to 215 R {sub s} or beyond, and the model adopts a splitting finite-volume scheme based on a six-component grid system in spherical coordinates. By splitting the magnetohydrodynamics equations into a fluid part and a magnetic part, a finite volume method can be used for the fluid part and a constrained-transport method able to maintain the divergence-free constraint on the magnetic field can be used for the magnetic induction part. This new second-order model in space and time is validated when modeling the large-scale structure of the solar wind. The numerical results for Carrington rotation 2064 show its ability to produce structured solar wind in agreement with observations.

Analysis of global multiscale finite element methods for wave equations with continuum spatial scales

KAUST Repository

Jiang, Lijian; Efendiev, Yalchin; Ginting, Victor

2010-01-01

In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.

Analysis of global multiscale finite element methods for wave equations with continuum spatial scales

KAUST Repository

Jiang, Lijian

2010-08-01

In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.

NUMERICAL SIMULATION OF ELECTRICAL IMPEDANCE TOMOGRAPHY PROBLEM AND STUDY OF APPROACH BASED ON FINITE VOLUME METHOD

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.

Finite-volume effects due to spatially non-local operators arXiv

CERN Document Server

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 ...

Hybrid Multiscale Finite Volume method for multiresolution simulations of flow and reactive transport in porous media

Science.gov (United States)

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.

Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation

Science.gov (United States)

Prentice, J. S. C.

2012-01-01

An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…

A-Posteriori Error Estimates for Mixed Finite Element and Finite Volume Methods for Problems Coupled Through a Boundary with Non-Matching Grids

Science.gov (United States)

2013-08-01

both MFE and GFV, are often similar in size. As a gross measure of the effect of geometric projection and of the use of quadrature, we also report the...interest MFE ∑(e,ψ) or GFV ∑(e,ψ). Tables 1 and 2 show this using coarse and fine forward solutions. Table 1. The forward problem with solution (4.1) is run...adjoint data components ψu and ψp are constant everywhere and ψξ = 0. adj. grid MFE ∑(e,ψ) ∑MFEi ratio GFV ∑(e,ψ) ∑GFV i ratio 20x20 : 32x32 1.96E−3

Finite volume QCD at fixed topological charge

OpenAIRE

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...

Finite Element Methods On Very Large, Dynamic Tubular Grid Encoded Implicit Surfaces

DEFF Research Database (Denmark)

Nemitz, Oliver; Nielsen, Michael Bang; Rumpf, Martin

2009-01-01

dynamic tubular grid encoding format for a narrow band. A reaction diffusion model on a fixed surface and surface evolution driven by a nonlinear geometric diffusion approach, by isotropic or truly anisotropic curvature motion, are investigated as characteristic model problems. The proposed methods...

Cosmos++: relativistic magnetohydrodynamics on unstructured grids with local adaptive refinement

International Nuclear Information System (INIS)

Salmonson, Jay D; Anninos, Peter; Fragile, P Chris; Camarda, Karen

2007-01-01

A code and methodology are introduced for solving the fully general relativistic magnetohydrodynamic (GRMHD) equations using time-explicit, finite-volume discretization. The code has options for solving the GRMHD equations using traditional artificial-viscosity (AV) or non-oscillatory central difference (NOCD) methods, or a new extended AV (eAV) scheme using artificial-viscosity together with a dual energy-flux-conserving formulation. The dual energy approach allows for accurate modeling of highly relativistic flows at boost factors well beyond what has been achieved to date by standard artificial viscosity methods. It provides the benefit of Godunov methods in capturing high Lorentz boosted flows but without complicated Riemann solvers, and the advantages of traditional artificial viscosity methods in their speed and flexibility. Additionally, the GRMHD equations are solved on an unstructured grid that supports local adaptive mesh refinement using a fully threaded oct-tree (in three dimensions) network to traverse the grid hierarchy across levels and immediate neighbors. Some recent studies will be summarized

Numerical and adaptive grid methods for ideal magnetohydrodynamics

Science.gov (United States)

Loring, Burlen

2008-02-01

In this thesis numerical finite difference methods for ideal magnetohydrodynamics(MHD) are investigated. A review of the relevant physics, essential for interpreting the results of numerical solutions and constructing validation cases, is presented. This review includes a discusion of the propagation of small amplitude waves in the MHD system as well as a thorough discussion of MHD shocks, contacts and rarefactions and how they can be piece together to obtain a solutions to the MHD Riemann problem. Numerical issues relevant to the MHD system such as: the loss of nonlinear numerical stability in the presence of discontinuous solutions, the introduction of spurious forces due to the growth of the divergence of the magnetic flux density, the loss of pressure positivity, and the effects of non-conservative numerical methods are discussed, along with the practical approaches which can be used to remedy or minimize the negative consequences of each. The use of block structured adaptive mesh refinement is investigated in the context of a divergence free MHD code. A new method for conserving magnetic flux across AMR grid interfaces is developed and a detailed discussion of our implementation of this method using the CHOMBO AMR framework is given. A preliminary validation of the new method for conserving magnetic flux density across AMR grid interfaces illustrates that the method works. Finally a number of code validation cases are examined spurring a discussion of the strengths and weaknesses of the numerics employed.

Robust mixed finite element methods to deal with incompressibility in finite strain in an industrial framework

International Nuclear Information System (INIS)

Al-Akhrass, Dina

2014-01-01

Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)

Finite element method for radiation heat transfer in multi-dimensional graded index medium

International Nuclear Information System (INIS)

Liu, L.H.; Zhang, L.; Tan, H.P.

2006-01-01

In graded index medium, ray goes along a curved path determined by Fermat principle, and curved ray-tracing is very difficult and complex. To avoid the complicated and time-consuming computation of curved ray trajectories, a finite element method based on discrete ordinate equation is developed to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Two particular test problems of radiative transfer are taken as examples to verify this finite element method. The predicted dimensionless net radiative heat fluxes are determined by the proposed method and compared with the results obtained by finite volume method. The results show that the finite element method presented in this paper has a good accuracy in solving the multi-dimensional radiative transfer problem in semitransparent graded index medium

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.

Dense QCD in a Finite Volume

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 radiative heat transfer in an unstructured flow solver for emitting, absorbing and scattering media

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.

A matrix-free implicit unstructured multigrid finite volume method for simulating structural dynamics and fluid structure interaction

Science.gov (United States)

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.

Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method

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.

Synchronization method for grid integrated battery storage systems during asymmetrical grid faults

Directory of Open Access Journals (Sweden)

Popadić Bane

2017-01-01

Full Text Available This paper aims at presenting a robust and reliable synchronization method for battery storage systems during asymmetrical grid faults. For this purpose, a Matlab/Simulink based model for testing of the power electronic interface between the grid and the battery storage systems has been developed. The synchronization method proposed in the paper is based on the proportional integral resonant controller with the delay signal cancellation. The validity of the synchronization method has been verified using the advanced laboratory station for the control of grid connected distributed energy sources. The proposed synchronization method has eliminated unfavourable components from the estimated grid angular frequency, leading to the more accurate and reliable tracking of the grid voltage vector positive sequence during both the normal operation and the operation during asymmetrical grid faults. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. III 042004: Integrated and Interdisciplinary Research entitled: Smart Electricity Distribution Grids Based on Distribution Management System and Distributed Generation

An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

Science.gov (United States)

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.

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

3D CSEM inversion based on goal-oriented adaptive finite element method

Science.gov (United States)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with

Wavefront-ray grid FDTD algorithm

OpenAIRE

ÇİYDEM, MEHMET

2016-01-01

A finite difference time domain algorithm on a wavefront-ray grid (WRG-FDTD) is proposed in this study to reduce numerical dispersion of conventional FDTD methods. A FDTD algorithm conforming to a wavefront-ray grid can be useful to take into account anisotropy effects of numerical grids since it features directional energy flow along the rays. An explicit and second-order accurate WRG-FDTD algorithm is provided in generalized curvilinear coordinates for an inhomogeneous isotropic medium. Num...

GPU based contouring method on grid DEM data

Science.gov (United States)

Tan, Liheng; Wan, Gang; Li, Feng; Chen, Xiaohui; Du, Wenlong

2017-08-01

This paper presents a novel method to generate contour lines from grid DEM data based on the programmable GPU pipeline. The previous contouring approaches often use CPU to construct a finite element mesh from the raw DEM data, and then extract contour segments from the elements. They also need a tracing or sorting strategy to generate the final continuous contours. These approaches can be heavily CPU-costing and time-consuming. Meanwhile the generated contours would be unsmooth if the raw data is sparsely distributed. Unlike the CPU approaches, we employ the GPU's vertex shader to generate a triangular mesh with arbitrary user-defined density, in which the height of each vertex is calculated through a third-order Cardinal spline function. Then in the same frame, segments are extracted from the triangles by the geometry shader, and translated to the CPU-side with an internal order in the GPU's transform feedback stage. Finally we propose a "Grid Sorting" algorithm to achieve the continuous contour lines by travelling the segments only once. Our method makes use of multiple stages of GPU pipeline for computation, which can generate smooth contour lines, and is significantly faster than the previous CPU approaches. The algorithm can be easily implemented with OpenGL 3.3 API or higher on consumer-level PCs.

Equivalent Simplification Method of Micro-Grid

OpenAIRE

Cai Changchun; Cao Xiangqin

2013-01-01

The paper concentrates on the equivalent simplification method for the micro-grid system connection into distributed network. The equivalent simplification method proposed for interaction study between micro-grid and distributed network. Micro-grid network, composite load, gas turbine synchronous generation, wind generation are equivalent simplification and parallel connect into the point of common coupling. A micro-grid system is built and three phase and single phase grounded faults are per...

Review of the modified finite particle method and application to incompressible solids

Directory of Open Access Journals (Sweden)

D Asprone

2016-10-01

Full Text Available This paper focuses on the application of the Modified Finite Particle Method (MFPM on incompressibile elasticity problems. MFPM belongs to the class of meshless methods, nowadays widely investigated due to their characteristics of being totally free of any kind of grid or mesh. This characteristic makes meshless methods potentially useful for the study of large deformations problems and fluid dynamics. In particular, the aim of the work is to compare the results obtained with a simple displacement-based formulation, in the limit of incompressibility, and some formulations proposed in the literature for full incompressibility, where the typical divergence-free constraint is replaced by a different equation, the so-called Pressure Poisson Equation. The obtained results show that the MFPM achieves the expected second-order accuracy on formulation where the equations imposed as constraint satisfies also the original incompressibility equation. Other formulations, differently, do not satisfy the incompressibility constraint, and thus, they are not successfully applicable with the Modified Finite Particle Method.

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

Science.gov (United States)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

A parallel finite-difference method for computational aerodynamics

International Nuclear Information System (INIS)

Swisshelm, J.M.

1989-01-01

A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed. 14 refs

3D modeling of forces between magnet and HTS in a levitation system using new approach of the control volume method based on an unstructured grid

Energy Technology Data Exchange (ETDEWEB)

Alloui, L., E-mail: lotfi.alloui@lgep.supelec.fr [Laboratoire de Genie Electrique de Paris - LGEP, CNRS UMR 8507, Supelec, Universite Pierre et Marie Curie-Paris 6, Universite Paris Sud-Paris 11, Plateau de Moulon, 11 rue Joliot Curie, 91192 Gif-Sur-Yvette Cedex (France); Laboratoire de modelisation des systemes energetiques (LMSE), Universite de Biskra, 07000 Biskra (Algeria); Bouillault, F., E-mail: bouillault@lgep.supelec.fr [Laboratoire de Genie Electrique de Paris - LGEP, CNRS UMR 8507, Supelec, Universite Pierre et Marie Curie-Paris 6, Universite Paris Sud-Paris 11, Plateau de Moulon, 11 rue Joliot Curie, 91192 Gif-Sur-Yvette Cedex (France); Bernard, L., E-mail: laurent.bernardl@lgep.supelc.fr [Laboratoire de Genie Electrique de Paris - LGEP, CNRS UMR 8507, Supelec, Universite Pierre et Marie Curie-Paris 6, Universite Paris Sud-Paris 11, Plateau de Moulon, 11 rue Joliot Curie, 91192 Gif-Sur-Yvette Cedex (France); Leveque, J., E-mail: jean.leveque@green.uhp-nancy.fr [Groupe de recherche en electronique et electrotechnique de Nancy, Universite Henry Poincare, BP 239, 54506 Vandoeuvre les Nancy (France)

2012-05-15

In this paper we present new 3D numerical model to calculate the vertical and the guidance forces in high temperature superconductors taking into account the influence of the flux creep phenomena. In the suggested numerical model, we adopt a new approach of the control volume method. This approach is based on the use of an unstructured grid which can be used to model more complex geometries. A comparison of the control volume method results with experiments verifies the validity of this approach and the proposed numerical model. Based on this model, the levitation force's relaxation at different temperatures was also studied.

On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids

KAUST Repository

Gao, Longfei; Ketcheson, David I.; Keyes, David E.

2017-01-01

We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application

Development and Implementation of a Transport Method for the Transport and Reaction Simulation Engine (TaRSE) based on the Godunov-Mixed Finite Element Method

Science.gov (United States)

James, Andrew I.; Jawitz, James W.; Munoz-Carpena, Rafael

2009-01-01

A model to simulate transport of materials in surface water and ground water has been developed to numerically approximate solutions to the advection-dispersion equation. This model, known as the Transport and Reaction Simulation Engine (TaRSE), uses an algorithm that incorporates a time-splitting technique where the advective part of the equation is solved separately from the dispersive part. An explicit finite-volume Godunov method is used to approximate the advective part, while a mixed-finite element technique is used to approximate the dispersive part. The dispersive part uses an implicit discretization, which allows it to run stably with a larger time step than the explicit advective step. The potential exists to develop algorithms that run several advective steps, and then one dispersive step that encompasses the time interval of the advective steps. Because the dispersive step is computationally most expensive, schemes can be implemented that are more computationally efficient than non-time-split algorithms. This technique enables scientists to solve problems with high grid Peclet numbers, such as transport problems with sharp solute fronts, without spurious oscillations in the numerical approximation to the solution and with virtually no artificial diffusion.

Additive Schwarz preconditioner for the finite volume element discretization of symmetric elliptic problems

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

Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping

Science.gov (United States)

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.

Transonic Airfoil Flow Simulation. Part I: Mesh Generation and Inviscid Method

Directory of Open Access Journals (Sweden)

Vladimir CARDOS

2010-06-01

Full Text Available A calculation method for the subsonic and transonic viscous flow over airfoil using thedisplacement surface concept is described. Part I presents a mesh generation method forcomputational grid and a finite volume method for the time-dependent Euler equations. The inviscidsolution is used for the inviscid-viscous coupling procedure presented in the Part II.

From Pore Scale to Turbulent Flow with the Unstructured Lattice Boltzmann Method

DEFF Research Database (Denmark)

Matin, Rastin

Abstract: The lattice Boltzmann method is a class of methods in computational fluid dynamics for simulating fluid flow. Implementations on unstructured grids are particularly relevant for various engineering applications, where geometric flexibility or high resolution near a body or a wall...... is required. The main topic of this thesis is to further develop unstructured lattice Boltzmann methods for simulations of Newtonian fluid flow in three dimensions, in particular porous flow. Two methods are considered in this thesis based on the finite volume method and finite element method, respectively...

Numerical investigation of finite-volume effects for the HVP

Science.gov (United States)

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.

Robust Grid-Current-Feedback Resonance Suppression Method for LCL-Type Grid-Connected Inverter Connected to Weak Grid

DEFF Research Database (Denmark)

Zhou, Xiaoping; Zhou, Leming; Chen, Yandong

2018-01-01

In this paper, a robust grid-current-feedback reso-nance suppression (GCFRS) method for LCL-type grid-connected inverter is proposed to enhance the system damping without introducing the switching noise and eliminate the impact of control delay on system robustness against grid-impedance variation....... It is composed of GCFRS method, the full duty-ratio and zero-beat-lag PWM method, and the lead-grid-current-feedback-resonance-suppression (LGCFRS) method. Firstly, the GCFRS is used to suppress the LCL-resonant peak well and avoid introducing the switching noise. Secondly, the proposed full duty-ratio and zero......-beat-lag PWM method is used to elimi-nate the one-beat-lag computation delay without introducing duty cycle limitations. Moreover, it can also realize the smooth switching from positive to negative half-wave of the grid current and improve the waveform quality. Thirdly, the proposed LGCFRS is used to further...

Numerical modeling of contaminant transport in fractured porous media using mixed finite-element and finitevolume methods

KAUST Repository

Dong, Chen

2011-01-01

A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods; i.e., the mixed finite-element (MFE) method and the finite-volume method. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocity fields for both the fractures and matrix, which are crucial to the convection part of the transport equation. The finite-volume method and the standard MFE method are used to approximate the convection and dispersion terms, respectively. The temporary evolution for the pressure distributions, streamline fields, and concentration profiles are obtained for six different arrangements of fractures. The results clearly show the distorted concentration effects caused by the ordered and disordered (random) patterns of the fractures and illustrate the robustness and efficiency of the proposed numerical model. © 2011 by Begell House Inc.

Numerical Simulation of Two-Fluid Mingling Using the Particle Finite Element Method with Applications to Magmatic and Volcanic Processes

Science.gov (United States)

de Mier, M.; Costa, F.; Idelsohn, S.

2008-12-01

Many magmatic and volcanic processes (e.g., magma differentiation, mingling, transport in the volcanic conduit) are controlled by the physical properties and flow styles of high-temperature silicate melts. Such processes can be experimentally investigated using analog systems and scaling methods, but it is difficult to find the suitable material and it is generally not possible to quantitatively extrapolate the results to the natural system. An alternative means of studying fluid dynamics in volcanic systems is with numerical models. We have chosen the Particle Finite Element Method (PFEM), which is based on a Delaunay mesh that moves with the fluid velocity, the Navier-Stokes equations in Lagrangian formulation, and linear elements for velocity, pressure, and temperature. Remeshing is performed when the grid becomes too distorted [E. Oñate et al., 2004. The Particle Finite Element Method: An Overview. Int. J. Comput. Meth. 1, 267-307]. The method is ideal for tracking material interfaces between different fluids or media. Methods based on Eulerian reference frames need special techniques, such as level-set or volume-of-fluid, to capture the interface position, and these techniques add a significant numerical diffusion at the interface. We have performed a series of two-dimensional simulations of a classical problem of fluid dynamics in magmatic and volcanic systems: intrusion of a basaltic melt in a silica-rich magma reservoir. We have used realistic physical properties and equations of state for the silicate melts (e.g., temperature, viscosity, and density) and tracked the changes in the system for geologically relevant time scales (up to 100 years). The problem is modeled by the low-Mach-number equations derived from an asymptotic analysis of the compressible Navier-Stokes equations that removes shock waves from the flow but allows however large variations of density due to temperature variations. Non-constant viscosity and volume changes are taken into account

Fast Prediction Method for Steady-State Heat Convection

KAUST Repository

Wáng, Yì

2012-03-14

A reduced model by proper orthogonal decomposition (POD) and Galerkin projection methods for steady-state heat convection is established on a nonuniform grid. It was verified by thousands of examples that the results are in good agreement with the results obtained from the finite volume method. This model can also predict the cases where model parameters far exceed the sample scope. Moreover, the calculation time needed by the model is much shorter than that needed for the finite volume method. Thus, the nonuniform POD-Galerkin projection method exhibits high accuracy, good suitability, and fast computation. It has universal significance for accurate and fast prediction. Also, the methodology can be applied to more complex modeling in chemical engineering and technology, such as reaction and turbulence. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Finite-volume discretizations and immersed boundaries

NARCIS (Netherlands)

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

NARCIS (Netherlands)

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

Radiative transfer with finite elements. Pt. 1. Basic method and tests

Energy Technology Data Exchange (ETDEWEB)

Richling, S. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Astrophysik; Meinkoehn, E. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Astrophysik]|[Heidelberg Univ. (Germany). Inst. fuer Angewandte Mathematik; Kryzhevoi, N. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Astrophysik]|[Heidelberg Univ. (DE). Interdisziplinaeres Zentrum fuer Wissenschaftliches Rechnen (IWR); Kanschat, G. [Heidelberg Univ. (Germany). Inst. fuer Angewandte Mathematik]|[Heidelberg Univ. (DE). Interdisziplinaeres Zentrum fuer Wissenschaftliches Rechnen (IWR)

2001-10-01

A finite element method for solving the monochromatic radiation transfer equation including scattering in three dimensions is presented. The algorithm employs unstructured grids which are adaptively refined. Adaptivity as well as ordinate parallelization reduce memory requirements and execution time and make it possible to calculate the radiation field across several length scales for objects with strong opacity gradients. An a posteriori error estimate for one particular quantity is obtained by solving the dual problem. The application to a sample of test problems reveals the properties of the implementation. (orig.)

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.

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...

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

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

Numerical study on flow fields and aerodynamics of tilt rotor aircraft in conversion mode based on embedded grid and actuator model

Directory of Open Access Journals (Sweden)

Ying Zhang

2015-02-01

Full Text Available A method combining rotor actuator disk model and embedded grid technique is presented in this paper, aimed at predicting the flow fields and aerodynamic characteristics of tilt rotor aircraft in conversion mode more efficiently and effectively. In this method, rotor’s influence is considered in terms of the momentum it impacts to the fluid around it; transformation matrixes among different coordinate systems are deduced to extend actuator method’s utility to conversion mode flow fields’ calculation. Meanwhile, an embedded grid system is designed, in which grids generated around fuselage and actuator disk are regarded as background grid and minor grid respectively, and a new method is presented for ‘donor searching’ and ‘hole cutting’ during grid assembling. Based on the above methods, flow fields of tilt rotor aircraft in conversion mode are simulated, with three-dimensional Navier–Stokes equations discretized by a second-order upwind finite-volume scheme and an implicit lower–upper symmetric Gauss–Seidel (LU-SGS time-stepping scheme. Numerical results demonstrate that the proposed CFD method is very effective in simulating the conversion mode flow fields of tilt rotor aircraft.

Comparison tomography relocation hypocenter grid search and guided grid search method in Java island

International Nuclear Information System (INIS)

Nurdian, S. W.; Adu, N.; Palupi, I. R.; Raharjo, W.

2016-01-01

The main data in this research is earthquake data recorded from 1952 to 2012 with 9162 P wave and 2426 events are recorded by 30 stations located around Java island. Relocation hypocenter processed using grid search and guidded grid search method. Then the result of relocation hypocenter become input for tomography pseudo bending inversion process. It can be used to identification the velocity distribution in subsurface. The result of relocation hypocenter by grid search and guided grid search method after tomography process shown in locally and globally. In locally area grid search method result is better than guided grid search according to geological reseach area. But in globally area the result of guided grid search method is better for a broad area because the velocity variation is more diverse than the other one and in accordance with local geological research conditions. (paper)

An adaptive grid refinement strategy for the simulation of negative streamers

International Nuclear Information System (INIS)

Montijn, C.; Hundsdorfer, W.; Ebert, U.

2006-01-01

The evolution of negative streamers during electric breakdown of a non-attaching gas can be described by a two-fluid model for electrons and positive ions. It consists of continuity equations for the charged particles including drift, diffusion and reaction in the local electric field, coupled to the Poisson equation for the electric potential. The model generates field enhancement and steep propagating ionization fronts at the tip of growing ionized filaments. An adaptive grid refinement method for the simulation of these structures is presented. It uses finite volume spatial discretizations and explicit time stepping, which allows the decoupling of the grids for the continuity equations from those for the Poisson equation. Standard refinement methods in which the refinement criterion is based on local error monitors fail due to the pulled character of the streamer front that propagates into a linearly unstable state. We present a refinement method which deals with all these features. Tests on one-dimensional streamer fronts as well as on three-dimensional streamers with cylindrical symmetry (hence effectively 2D for numerical purposes) are carried out successfully. Results on fine grids are presented, they show that such an adaptive grid method is needed to capture the streamer characteristics well. This refinement strategy enables us to adequately compute negative streamers in pure gases in the parameter regime where a physical instability appears: branching streamers

A posteriori estimator and adaptive mesh refinement for finite volume finite element method for monophasic flow and solute transport in porous media

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

Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

Science.gov (United States)

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.

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.

Chimera Grid Tools

Science.gov (United States)

Chan, William M.; Rogers, Stuart E.; Nash, Steven M.; Buning, Pieter G.; Meakin, Robert

2005-01-01

Chimera Grid Tools (CGT) is a software package for performing computational fluid dynamics (CFD) analysis utilizing the Chimera-overset-grid method. For modeling flows with viscosity about geometrically complex bodies in relative motion, the Chimera-overset-grid method is among the most computationally cost-effective methods for obtaining accurate aerodynamic results. CGT contains a large collection of tools for generating overset grids, preparing inputs for computer programs that solve equations of flow on the grids, and post-processing of flow-solution data. The tools in CGT include grid editing tools, surface-grid-generation tools, volume-grid-generation tools, utility scripts, configuration scripts, and tools for post-processing (including generation of animated images of flows and calculating forces and moments exerted on affected bodies). One of the tools, denoted OVERGRID, is a graphical user interface (GUI) that serves to visualize the grids and flow solutions and provides central access to many other tools. The GUI facilitates the generation of grids for a new flow-field configuration. Scripts that follow the grid generation process can then be constructed to mostly automate grid generation for similar configurations. CGT is designed for use in conjunction with a computer-aided-design program that provides the geometry description of the bodies, and a flow-solver program.

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 finite difference method for free boundary problems

KAUST Repository

Fornberg, Bengt

2010-04-01

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.

An inverse analysis of a transient 2-D conduction-radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm

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

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

Science.gov (United States)

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

2018-05-01

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

High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics [High Order Curvilinear Finite Elements for Lagrangian Hydrodynamics

Energy Technology Data Exchange (ETDEWEB)

Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2012-09-20

The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered-grid

Conservative and bounded volume-of-fluid advection on unstructured grids

Science.gov (United States)

Ivey, Christopher B.; Moin, Parviz

2017-12-01

This paper presents a novel Eulerian-Lagrangian piecewise-linear interface calculation (PLIC) volume-of-fluid (VOF) advection method, which is three-dimensional, unsplit, and discretely conservative and bounded. The approach is developed with reference to a collocated node-based finite-volume two-phase flow solver that utilizes the median-dual mesh constructed from non-convex polyhedra. The proposed advection algorithm satisfies conservation and boundedness of the liquid volume fraction irrespective of the underlying flux polyhedron geometry, which differs from contemporary unsplit VOF schemes that prescribe topologically complicated flux polyhedron geometries in efforts to satisfy conservation. Instead of prescribing complicated flux-polyhedron geometries, which are prone to topological failures, our VOF advection scheme, the non-intersecting flux polyhedron advection (NIFPA) method, builds the flux polyhedron iteratively such that its intersection with neighboring flux polyhedra, and any other unavailable volume, is empty and its total volume matches the calculated flux volume. During each iteration, a candidate nominal flux polyhedron is extruded using an iteration dependent scalar. The candidate is subsequently intersected with the volume guaranteed available to it at the time of the flux calculation to generate the candidate flux polyhedron. The difference in the volume of the candidate flux polyhedron and the actual flux volume is used to calculate extrusion during the next iteration. The choice in nominal flux polyhedron impacts the cost and accuracy of the scheme; however, it does not impact the methods underlying conservation and boundedness. As such, various robust nominal flux polyhedron are proposed and tested using canonical periodic kinematic test cases: Zalesak's disk and two- and three-dimensional deformation. The tests are conducted on the median duals of a quadrilateral and triangular primal mesh, in two-dimensions, and on the median duals of a

Twisted finite-volume corrections to K{sub l3} decays with partially-quenched and rooted-staggered quarks

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.

3D Staggered-Grid Finite-Difference Simulation of Acoustic Waves in Turbulent Moving Media

Science.gov (United States)

Symons, N. P.; Aldridge, D. F.; Marlin, D.; Wilson, D. K.; Sullivan, P.; Ostashev, V.

2003-12-01

Acoustic wave propagation in a three-dimensional heterogeneous moving atmosphere is accurately simulated with a numerical algorithm recently developed under the DOD Common High Performance Computing Software Support Initiative (CHSSI). Sound waves within such a dynamic environment are mathematically described by a set of four, coupled, first-order partial differential equations governing small-amplitude fluctuations in pressure and particle velocity. The system is rigorously derived from fundamental principles of continuum mechanics, ideal-fluid constitutive relations, and reasonable assumptions that the ambient atmospheric motion is adiabatic and divergence-free. An explicit, time-domain, finite-difference (FD) numerical scheme is used to solve the system for both pressure and particle velocity wavefields. The atmosphere is characterized by 3D gridded models of sound speed, mass density, and the three components of the wind velocity vector. Dependent variables are stored on staggered spatial and temporal grids, and centered FD operators possess 2nd-order and 4th-order space/time accuracy. Accurate sound wave simulation is achieved provided grid intervals are chosen appropriately. The gridding must be fine enough to reduce numerical dispersion artifacts to an acceptable level and maintain stability. The algorithm is designed to execute on parallel computational platforms by utilizing a spatial domain-decomposition strategy. Currently, the algorithm has been validated on four different computational platforms, and parallel scalability of approximately 85% has been demonstrated. Comparisons with analytic solutions for uniform and vertically stratified wind models indicate that the FD algorithm generates accurate results with either a vanishing pressure or vanishing vertical-particle velocity boundary condition. Simulations are performed using a kinematic turbulence wind profile developed with the quasi-wavelet method. In addition, preliminary results are presented

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

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.

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

Science.gov (United States)

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.

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)

Analysis for pressure transient of coalbed methane reservoir based on Laplace transform finite difference method

Directory of Open Access Journals (Sweden)

Lei Wang

2015-09-01

Full Text Available Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace transform finite difference method is used to solve the mathematical model. With Stehfest numerical inversion, the distribution of dimensionless well bore flowing pressure and its derivative was obtained in real space. According to compare with the results from the analytical method, the result from Laplace transform finite difference method turns out to be accurate. The influence factors are analyzed, including fractal dimension, fractal index, skin factor, well bore storage coefficient, energy storage ratio, interporosity flow coefficient and the adsorption factor. The calculating error of Laplace transform difference method is small. Laplace transform difference method has advantages in well-test application since any moment simulation does not rely on other moment results and space grid.

Effect of Finite Particle Size on Convergence of Point Particle Models in Euler-Lagrange Multiphase Dispersed Flow

Science.gov (United States)

Nili, Samaun; Park, Chanyoung; Haftka, Raphael T.; Kim, Nam H.; Balachandar, S.

2017-11-01

Point particle methods are extensively used in simulating Euler-Lagrange multiphase dispersed flow. When particles are much smaller than the Eulerian grid the point particle model is on firm theoretical ground. However, this standard approach of evaluating the gas-particle coupling at the particle center fails to converge as the Eulerian grid is reduced below particle size. We present an approach to model the interaction between particles and fluid for finite size particles that permits convergence. We use the generalized Faxen form to compute the force on a particle and compare the results against traditional point particle method. We apportion the different force components on the particle to fluid cells based on the fraction of particle volume or surface in the cell. The application is to a one-dimensional model of shock propagation through a particle-laden field at moderate volume fraction, where the convergence is achieved for a well-formulated force model and back coupling for finite size particles. Comparison with 3D direct fully resolved numerical simulations will be used to check if the approach also improves accuracy compared to the point particle model. Work supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.

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.

A Grid Voltage Measurement Method for Wind Power Systems during Grid Fault Conditions

Directory of Open Access Journals (Sweden)

Cheol-Hee Yoo

2014-11-01

Full Text Available Grid codes in many countries require low-voltage ride-through (LVRT capability to maintain power system stability and reliability during grid fault conditions. To meet the LVRT requirement, wind power systems must stay connected to the grid and also supply reactive currents to the grid to support the recovery from fault voltages. This paper presents a new fault detection method and inverter control scheme to improve the LVRT capability for full-scale permanent magnet synchronous generator (PMSG wind power systems. Fast fault detection can help the wind power systems maintain the DC-link voltage in a safe region. The proposed fault detection method is based on on-line adaptive parameter estimation. The performance of the proposed method is verified in comparison to the conventional voltage measurement method defined in the IEC 61400-21 standard.

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...

OPTIMIZATION OF I-SECTION PROFILE DESIGN BY THE FINITE ELEMENT METHOD

Directory of Open Access Journals (Sweden)

Patryk Różyło

2016-03-01

Full Text Available This paper discusses the problem of design optimization for an I-section profile. The optimization process was performed using the Abaqus program. The numerical analysis of a strictly static problem was based on the finite element method. The scope of the analysis involved both determination of stresses and displacements in the profile and structure topology optimization. The main focus of the numerical analysis was put on reducing profile volume while maintaining the same load and similar stresses prior to and after optimization. The solution of the optimization problem is just an example of the potential of using this method in combination with the finite element method in the Abaqus environment. Nowadays numerical analysis is the most effective cost-reducing alternative to experimental tests and it enables structure examination by means of a computer.

Estimating the two-particle $K$-matrix for multiple partial waves and decay channels from finite-volume energies

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...

A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

KAUST Repository

Paszyński, Maciej R.

2013-04-01

This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.

A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

KAUST Repository

Paszyński, Maciej R.; Calo, Victor M.; Pardo, David

2013-01-01

This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.

Grid sensitivity capability for large scale structures

Science.gov (United States)

Nagendra, Gopal K.; Wallerstein, David V.

1989-01-01

The considerations and the resultant approach used to implement design sensitivity capability for grids into a large scale, general purpose finite element system (MSC/NASTRAN) are presented. The design variables are grid perturbations with a rather general linking capability. Moreover, shape and sizing variables may be linked together. The design is general enough to facilitate geometric modeling techniques for generating design variable linking schemes in an easy and straightforward manner. Test cases have been run and validated by comparison with the overall finite difference method. The linking of a design sensitivity capability for shape variables in MSC/NASTRAN with an optimizer would give designers a powerful, automated tool to carry out practical optimization design of real life, complicated structures.

Discretization of convection-diffusion equations with finite-difference scheme derived from simplified analytical solutions

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

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.

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.)

A Grid Voltage Measurement Method for Wind Power Systems during Grid Fault Conditions

OpenAIRE

Yoo, Cheol-Hee; Chung, Il-Yop; Yoo, Hyun-Jae; Hong, Sung-Soo

2014-01-01

Grid codes in many countries require low-voltage ride-through (LVRT) capability to maintain power system stability and reliability during grid fault conditions. To meet the LVRT requirement, wind power systems must stay connected to the grid and also supply reactive currents to the grid to support the recovery from fault voltages. This paper presents a new fault detection method and inverter control scheme to improve the LVRT capability for full-scale permanent magnet synchronous generator (P...

Class of reconstructed discontinuous Galerkin methods in computational fluid dynamics

International Nuclear Information System (INIS)

Luo, Hong; Xia, Yidong; Nourgaliev, Robert

2011-01-01

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness. (author)

Determination of finite-difference weights using scaled binomial windows

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.

Determination of finite-difference weights using scaled binomial windows

KAUST Repository

Chu, Chunlei

2012-05-01

The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.

Finite grid radius and thickness effects on retarding potential analyzer measured suprathermal electron density and temperature

International Nuclear Information System (INIS)

Knudsen, W.C.

1992-01-01

The effect of finite grid radius and thickness on the electron current measured by planar retarding potential analyzers (RPAs) is analyzed numerically. Depending on the plasma environment, the current is significantly reduced below that which is calculated using a theoretical equation derived for an idealized RPA having grids with infinite radius and vanishingly small thickness. A correction factor to the idealized theoretical equation is derived for the Pioneer Venus (PV) orbiter RPA (ORPA) for electron gases consisting of one or more components obeying Maxwell statistics. The error in density and temperature of Maxwellian electron distributions previously derived from ORPA data using the theoretical expression for the idealized ORPA is evaluated by comparing the densities and temperatures derived from a sample of PV ORPA data using the theoretical expression with and without the correction factor

High‐order rotated staggered finite difference modeling of 3D elastic wave propagation in general anisotropic media

KAUST Repository

Chu, Chunlei

2009-01-01

We analyze the dispersion properties and stability conditions of the high‐order convolutional finite difference operators and compare them with the conventional finite difference schemes. We observe that the convolutional finite difference method has better dispersion properties and becomes more efficient than the conventional finite difference method with the increasing order of accuracy. This makes the high‐order convolutional operator a good choice for anisotropic elastic wave simulations on rotated staggered grids since its enhanced dispersion properties can help to suppress the numerical dispersion error that is inherent in the rotated staggered grid structure and its efficiency can help us tackle 3D problems cost‐effectively.

Analysis of Grid-Scored Sandwich Structures of Different Curvatures and Grid Sizes For Wind Turbine Blades

DEFF Research Database (Denmark)

Laustsen, Steffen; Thomsen, Ole Thybo; Lund, Erik

2012-01-01

The stress and strain field developed locally in-situ the core of grid-scored sandwich structures in wind turbine blades is investigated. Due to the many singularities occurring from the “tri-material corners”, a full 3D analysis of the sandwich structure in terms of the Finite Element Method is ...

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.)

Domain decomposition methods for mortar finite elements

Energy Technology Data Exchange (ETDEWEB)

Widlund, O.

1996-12-31

In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.

Implicit and fully implicit exponential finite difference methods

Indian Academy of Sciences (India)

Burgers' equation; exponential finite difference method; implicit exponential finite difference method; ... This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. ... Current Issue

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

Science.gov (United States)

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.

A finite-elements method for turbulent flow analysis

International Nuclear Information System (INIS)

Autret, A.

1986-03-01

The work discussed here covers turbulent flow calculations using GALERKIN's finite-element method. In our specific case, we have to deal with monophasic incompressible flow in Boussinesq approximation in the normal operating conditions of a primary circuit of nuclear power plant. Turbulence effects on the mean field are taken into account by the k-epsilon model with two evolution equations: one for the kinetic energy of the turbulence, and one for the energy dissipation rate. The wall zone is covered by wall laws, and by REICHARDT's law in particular. A Law is advanced for the epsilon input profile, and a numerical solution is proposed for the physically aberrant values of k and epsilon generated by the model. Single-equation models are reviewed comparatively with the k-epsilon model. A comparison between calculated and analytical solutions or calculated and experimental results is presented for decreasing turbulence behind a grid, for the flow between parallel flat plates with three REYNOLDS numbers, and for backward facing step [fr

A finite-elements method for turbulent flow analysis

International Nuclear Information System (INIS)

Autret, A.

1986-03-01

The work discussed here covers turbulent flow calculations using GALERKIN's finite-element method. Turbulence effects on the mean field are taken into account by the k-epsilon model with two evolution equations: one for the kinetic energy of the turbulence, and one for the energy dissipation rate. The wall zone is covered by wall laws, and by REICHARDT's law in particular. A law is advanced for the epsilon input profile, and a numerical solution is proposed for the physically aberrant values of k and epsilon generated by the model. Single-equation models are reviewed comparatively with the k-epsilon model. A comparison between calculated and analytical solutions or calculated and experimental results is presented for decreasing turbulence behind a grid, for the flow between parallel flat plates with three REYNOLDS numbers, and for backward facing step. This part contains graphs and curves corresponding to results of the calculations presented in part one [fr

The Experiment Method for Manufacturing Grid Development on Single Computer

Institute of Scientific and Technical Information of China (English)

XIAO Youan; ZHOU Zude

2006-01-01

In this paper, an experiment method for the Manufacturing Grid application system development in the single personal computer environment is proposed. The characteristic of the proposed method is constructing a full prototype Manufacturing Grid application system which is hosted on a single personal computer with the virtual machine technology. Firstly, it builds all the Manufacturing Grid physical resource nodes on an abstraction layer of a single personal computer with the virtual machine technology. Secondly, all the virtual Manufacturing Grid resource nodes will be connected with virtual network and the application software will be deployed on each Manufacturing Grid nodes. Then, we can obtain a prototype Manufacturing Grid application system which is working in the single personal computer, and can carry on the experiment on this foundation. Compared with the known experiment methods for the Manufacturing Grid application system development, the proposed method has the advantages of the known methods, such as cost inexpensively, operation simple, and can get the confidence experiment result easily. The Manufacturing Grid application system constructed with the proposed method has the high scalability, stability and reliability. It is can be migrated to the real application environment rapidly.

Post-Processing in the Material-Point Method

DEFF Research Database (Denmark)

Andersen, Søren; Andersen, Lars Vabbersgaard

The material-point method (MPM) is a numerical method for dynamic or static analysis of solids using a discretization in time and space. The method has shown to be successful in modelling physical problems involving large deformations, which are difficult to model with traditional numerical tools...... such as the finite element method. In the material-point method, a set of material points is utilized to track the problem in time and space, while a computational background grid is utilized to obtain spatial derivatives relevant to the physical problem. Currently, the research within the material-point method......-point method. The first idea involves associating a volume with each material point and displaying the deformation of this volume. In the discretization process, the physical domain is divided into a number of smaller volumes each represented by a simple shape; here quadrilaterals are chosen for the presented...

Solving the Einstein constraint equations on multi-block triangulations using finite element methods

Energy Technology Data Exchange (ETDEWEB)

Korobkin, Oleg; Pazos, Enrique [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 (United States); Aksoylu, Burak [Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803 (United States); Holst, Michael [Department of Mathematics, University of California at San Diego 9500 Gilman Drive La Jolla, CA 92093-0112 (United States); Tiglio, Manuel [Department of Physics, University of Maryland, College Park, MD 20742 (United States)

2009-07-21

In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor psi. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high-order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.

Solving the Einstein constraint equations on multi-block triangulations using finite element methods

International Nuclear Information System (INIS)

Korobkin, Oleg; Pazos, Enrique; Aksoylu, Burak; Holst, Michael; Tiglio, Manuel

2009-01-01

In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor ψ. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high-order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.

Programming the finite element method

CERN Document Server

Smith, I M; Margetts, L

2013-01-01

Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c

A Study of the Transient Response of Duct Junctions: Measurements and Gas-Dynamic Modeling with a Staggered Mesh Finite Volume Approach

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.

An outgoing energy flux boundary condition for finite difference ICRP antenna models

International Nuclear Information System (INIS)

Batchelor, D.B.; Carter, M.D.

1992-11-01

For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods

Ion diode simulation with a finite-volume PIC approach for the numerical solution of the Maxwell-Lorentz system

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.

Ion diode simulation with a finite-volume PIC approach for the numerical solution of the Maxwell-Lorentz system

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

An unstructured finite volume solver for two phase water/vapour flows based on an elliptic oriented fractional step method

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)

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...

A parallel electrostatic Particle-in-Cell method on unstructured tetrahedral grids for large-scale bounded collisionless plasma simulations

Science.gov (United States)

Averkin, Sergey N.; Gatsonis, Nikolaos A.

2018-06-01

An unstructured electrostatic Particle-In-Cell (EUPIC) method is developed on arbitrary tetrahedral grids for simulation of plasmas bounded by arbitrary geometries. The electric potential in EUPIC is obtained on cell vertices from a finite volume Multi-Point Flux Approximation of Gauss' law using the indirect dual cell with Dirichlet, Neumann and external circuit boundary conditions. The resulting matrix equation for the nodal potential is solved with a restarted generalized minimal residual method (GMRES) and an ILU(0) preconditioner algorithm, parallelized using a combination of node coloring and level scheduling approaches. The electric field on vertices is obtained using the gradient theorem applied to the indirect dual cell. The algorithms for injection, particle loading, particle motion, and particle tracking are parallelized for unstructured tetrahedral grids. The algorithms for the potential solver, electric field evaluation, loading, scatter-gather algorithms are verified using analytic solutions for test cases subject to Laplace and Poisson equations. Grid sensitivity analysis examines the L2 and L∞ norms of the relative error in potential, field, and charge density as a function of edge-averaged and volume-averaged cell size. Analysis shows second order of convergence for the potential and first order of convergence for the electric field and charge density. Temporal sensitivity analysis is performed and the momentum and energy conservation properties of the particle integrators in EUPIC are examined. The effects of cell size and timestep on heating, slowing-down and the deflection times are quantified. The heating, slowing-down and the deflection times are found to be almost linearly dependent on number of particles per cell. EUPIC simulations of current collection by cylindrical Langmuir probes in collisionless plasmas show good comparison with previous experimentally validated numerical results. These simulations were also used in a parallelization

NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

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.

Finite element method for computational fluid dynamics with any type of elements; Finite Element Methode zur numerischen Stroemungsberechnung mit beliebigen Elementen

Energy Technology Data Exchange (ETDEWEB)

Steibler, P.

2000-07-01

The unsteady, turbulent flow is to be calculated in a complex geometry. For this purpose a stabilized finite element formulation in which the same functions for velocity and pressure are used is developed. Thus the process remains independent of the type of elements. This simplifies the application. Above all, it is easier to deal with the boundary conditions. The independency from the elements is also achieved by the extended uzawa-algorithm which uses quadratic functions for velocity and an element-constant pressure. This method is also programmed. In order to produce the unstructured grids, an algorithm is implemented which produces meshes consisting of triangular and tetrahedral elements with flow-dependent adaptation. With standard geometries both calculation methods are compared with results. Finally the flow in a draft tube of a Kaplan turbine is calculated and compared with results from model tests. (orig.) [German] Die instationaere, turbulente Stroemung in einer komplexen Geometrie soll berechnet werden. Dazu wird eine Stabilisierte Finite Element Formulierung entwickelt, bei der die gleichen Ansatzfunktionen fuer Geschwindigkeiten und Druck verwendet werden. Das Verfahren wird damit unabhaengig von der Form der Elemente. Dies vereinfacht die Anwendung. Vor allem wird der Umgang mit den Randbedingungen erleichert. Die Elementunabhaengigkeit erreicht man auch mit dem erweiterten Uzawa-Algorithmus, welcher quadratische Ansatzfunktionen fuer die Geschwindigkeiten und elementweisen konstanten Druck verwendet. Dieses Verfahren wird ebenso implementiert. Zur Erstellung der unstrukturierten Gitter wird ein Algorithmus erzeugt, der Netze aus Dreiecks- und Tetraederelementen erstellt, welche stroemungsabhaengige Groessen besitzen koennen. Anhand einiger Standardgeometrien werden die beiden Berechnungsmethoden mit Ergebnissen aus der Literatur verglichen. Als praxisrelevantes Beispiel wird abschliessend die Stroemung in einem Saugrohr einer Kaplanturbine berechnet

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

Science.gov (United States)

Melvin, Thomas

2018-02-01

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

Collocated electrodynamic FDTD schemes using overlapping Yee grids and higher-order Hodge duals

Science.gov (United States)

Deimert, C.; Potter, M. E.; Okoniewski, M.

2016-12-01

The collocated Lebedev grid has previously been proposed as an alternative to the Yee grid for electromagnetic finite-difference time-domain (FDTD) simulations. While it performs better in anisotropic media, it performs poorly in isotropic media because it is equivalent to four overlapping, uncoupled Yee grids. We propose to couple the four Yee grids and fix the Lebedev method using discrete exterior calculus (DEC) with higher-order Hodge duals. We find that higher-order Hodge duals do improve the performance of the Lebedev grid, but they also improve the Yee grid by a similar amount. The effectiveness of coupling overlapping Yee grids with a higher-order Hodge dual is thus questionable. However, the theoretical foundations developed to derive these methods may be of interest in other problems.

Discontinuous finite element and characteristics methods for neutrons transport equation solution in heterogeneous grids

International Nuclear Information System (INIS)

Masiello, E.

2006-01-01

The principal goal of this manuscript is devoted to the investigation of a new type of heterogeneous mesh adapted to the shape of the fuel pins (fuel-clad-moderator). The new heterogeneous mesh guarantees the spatial modelling of the pin-cell with a minimum of regions. Two methods are investigated for the spatial discretization of the transport equation: the discontinuous finite element method and the method of characteristics for structured cells. These methods together with the new representation of the pin-cell result in an appreciable reduction of calculation points. They allow an exact modelling of the fuel pin-cell without spatial homogenization. A new synthetic acceleration technique based on an angular multigrid is also presented for the speed up of the inner iterations. These methods are good candidates for transport calculations for a nuclear reactor core. A second objective of this work is the application of method of characteristics for non-structured geometries to the study of double heterogeneity problem. The letters is characterized by fuel material with a stochastic dispersion of heterogeneous grains, and until now was solved with a model based on collision probabilities. We propose a new statistical model based on renewal-Markovian theory, which makes possible to take into account the stochastic nature of the problem and to avoid the approximations of the collision probability model. The numerical solution of this model is guaranteed by the method of characteristics. (author)

A three-dimensional electrostatic particle-in-cell methodology on unstructured Delaunay-Voronoi grids

International Nuclear Information System (INIS)

Gatsonis, Nikolaos A.; Spirkin, Anton

2009-01-01

The mathematical formulation and computational implementation of a three-dimensional particle-in-cell methodology on unstructured Delaunay-Voronoi tetrahedral grids is presented. The method allows simulation of plasmas in complex domains and incorporates the duality of the Delaunay-Voronoi in all aspects of the particle-in-cell cycle. Charge assignment and field interpolation weighting schemes of zero- and first-order are formulated based on the theory of long-range constraints. Electric potential and fields are derived from a finite-volume formulation of Gauss' law using the Voronoi-Delaunay dual. Boundary conditions and the algorithms for injection, particle loading, particle motion, and particle tracking are implemented for unstructured Delaunay grids. Error and sensitivity analysis examines the effects of particles/cell, grid scaling, and timestep on the numerical heating, the slowing-down time, and the deflection times. The problem of current collection by cylindrical Langmuir probes in collisionless plasmas is used for validation. Numerical results compare favorably with previous numerical and analytical solutions for a wide range of probe radius to Debye length ratios, probe potentials, and electron to ion temperature ratios. The versatility of the methodology is demonstrated with the simulation of a complex plasma microsensor, a directional micro-retarding potential analyzer that includes a low transparency micro-grid.

Optimized waveform relaxation domain decomposition method for discrete finite volume non stationary convection diffusion equation

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

Finite element methods a practical guide

CERN Document Server

Whiteley, Jonathan

2017-01-01

This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.

Permeability computation on a REV with an immersed finite element method

International Nuclear Information System (INIS)

Laure, P.; Puaux, G.; Silva, L.; Vincent, M.

2011-01-01

An efficient method to compute permeability of fibrous media is presented. An immersed domain approach is used to represent the porous material at its microscopic scale and the flow motion is computed with a stabilized mixed finite element method. Therefore the Stokes equation is solved on the whole domain (including solid part) using a penalty method. The accuracy is controlled by refining the mesh around the solid-fluid interface defined by a level set function. Using homogenisation techniques, the permeability of a representative elementary volume (REV) is computed. The computed permeabilities of regular fibre packings are compared to classical analytical relations found in the bibliography.

New mixed finite-element methods

International Nuclear Information System (INIS)

Franca, L.P.

1987-01-01

New finite-element methods are proposed for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least-squares like terms. The additional terms involve integrals over element interiors, and include mesh-parameter dependent coefficients. The methods are designed to enhance stability. Consistency is achieved in the sense that exact solutions identically satisfy the variational equations.Applied to several problems, simple finite-element interpolations are rendered convergent, including convenient equal-order interpolations generally unstable within the Galerkin approach. The methods are subdivided into two classes according to the manner in which stability is attained: (1) circumventing Babuska-Brezzi condition methods; (2) satisfying Babuska-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class of methods is applied to the Poisson, Timoshenko beam and incompressible elasticity problems. Numerical results demonstrate the good stability and accuracy of the methods, and confirm the error estimates

Modified momentum exchange method for fluid-particle interactions in the lattice Boltzmann method.

Science.gov (United States)

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

2015-03-01

In this paper, a modified momentum exchange method for fluid-particle interactions is proposed based on the finite-volume lattice Boltzmann method. The idea of the improvement is to remove the restriction that the boundary points must be set as the midpoints of the grid lines or the intersection of the grid lines with the solid boundaries. The particle surface is represented by a set of arc (area) elements, and the interior fluid is used which the geometric conservation law is naturally satisfied. The interactions between fluid and arc (area) elements of particle boundary are considered using the momentum exchange method, and the mass of the fluid particles which collide with an arc (area) element is obtained by means of numerical integration in the control volume. The fluid field is corrected with the help of the smooth kernel function. Moreover, a generalized explicit time marching scheme is introduced to resolve the motion of particle in the problems with the ratio of particle density to fluid density is close to or less than 1. Finally, some numerical case studies of particle sedimentation are carried out to validate the present method. The corresponding results have a good agreement with the previous literature, which strongly demonstrates the capability of the improved method.

Finite Element Method in Machining Processes

CERN Document Server

Markopoulos, Angelos P

2013-01-01

Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...

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

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

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.

A Novel Polygonal Finite Element Method: Virtual Node Method

Science.gov (United States)

Tang, X. H.; Zheng, C.; Zhang, J. H.

2010-05-01

Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

Science.gov (United States)

Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

2018-04-01

In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

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

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.

A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

Science.gov (United States)

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.

Peridynamic Multiscale Finite Element Methods

Energy Technology Data Exchange (ETDEWEB)

Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-12-01

The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the

Parallel iterative procedures for approximate solutions of wave propagation by finite element and finite difference methods

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.

Structural modeling techniques by finite element method

International Nuclear Information System (INIS)

Kang, Yeong Jin; Kim, Geung Hwan; Ju, Gwan Jeong

1991-01-01

This book includes introduction table of contents chapter 1 finite element idealization introduction summary of the finite element method equilibrium and compatibility in the finite element solution degrees of freedom symmetry and anti symmetry modeling guidelines local analysis example references chapter 2 static analysis structural geometry finite element models analysis procedure modeling guidelines references chapter 3 dynamic analysis models for dynamic analysis dynamic analysis procedures modeling guidelines and modeling guidelines.

Radiative transfer modelling in combusting systems using discrete ordinates method on three-dimensional unstructured grids; Modelisation des transferts radiatifs en combustion par methode aux ordonnees discretes sur des maillages non structures tridimensionnels

Energy Technology Data Exchange (ETDEWEB)

Joseph, D.

2004-04-01

The prediction of pollutant species such as soots and NO{sub x} emissions and lifetime of the walls in a combustion chamber is strongly dependant on heat transfer by radiation at high temperatures. This work deals with the development of a code based on the Discrete Ordinates Method (DOM) aiming at providing radiative source terms and wall fluxes with a good compromise between cpu time and accuracy. Radiative heat transfers are calculated using the unstructured grids defined by the Computational Fluid Dynamics (CFD) codes. The spectral properties of the combustion gases are taken into account by a statistical narrow bands correlated-k model (SNB-ck). Various types of angular quadrature are tested and three different spatial differencing schemes were integrated and compared. The validation tests show the limit at strong optical thicknesses of the finite volume approximation used the Discrete Ordinates Method. The first calculations performed on LES solutions are presented, it provides instantaneous radiative source terms and wall heat fluxes. Those results represent a first step towards radiation/combustion coupling. (author)

Constitutive Modelling in Thermomechanical Processes, Using The Control Volume Method on Staggered Grid

DEFF Research Database (Denmark)

Thorborg, Jesper

, however, is constituted by the implementation of the $J_2$ flow theory in the control volume method. To apply the control volume formulation on the process of hardening concrete viscoelastic stress-strain models has been examined in terms of various rheological models. The generalized 3D models are based...... on two different suggestions in the literature, that is compressible or incompressible behaviour of the viscos response in the dashpot element. Numerical implementation of the models has shown very good agreement with corresponding analytical solutions. The viscoelastic solid mechanical model is used...

Application of a non-contiguous grid generation method to complex configurations

International Nuclear Information System (INIS)

Chen, S.; McIlwain, S.; Khalid, M.

2003-01-01

An economical non-contiguous grid generation method was developed to efficiently generate structured grids for complex 3D problems. Compared with traditional contiguous grids, this new approach generated grids for different block clusters independently and was able to distribute the grid points more economically according to the user's specific topology design. The method was evaluated by applying it to a Navier-Stokes computation of flow past a hypersonic projectile. Both the flow velocity and the heat transfer characteristics of the projectile agreed qualitatively with other numerical data in the literature and with available field data. Detailed grid topology designs for 3D geometries were addressed, and the advantages of this approach were analysed and compared with traditional contiguous grid generation methods. (author)

New non-orthogonality treatment for atmospheric boundary layer flow simulation above highly non-uniform terrains

Directory of Open Access Journals (Sweden)

Mirkov Nikola S.

2016-01-01

Full Text Available In this paper we validate an improved finite volume approximation of Reynolds Averaged Navier-Stokes equations for simulation of wind flows in body-fitted grids generated by algebraic extrusion from digital terrain elevation data, proposed in N. Mirkov et. al. J. Comput. Phys. 287, 18-45(2015, [1]. The approach is based on second-order accurate finite volume method with collocated variable arrangement and pressure-velocity coupling trough SIMPLE algorithm. The main objective is the attenuation of spurious pressure field oscillations in regions with discontinuity in grid line slopes, as encountered in grids representing highly non-uniform terrains. Moreover, the approach relaxes the need for grid generation based on elliptic PDEs or grid smoothing by applying fixed point iterations (i.e. Gauss-Seidel to initial grid node positions resulting from algebraic grid generators. Drawbacks of previous approaches which ignored treatment of finite volume grid cell cases with intersection point offset in non-orthogonality corrections are removed. Application to real-life wind farm project at Dobrič (Srvljig, Serbia is used to assess the effectiveness of the method. The results validate the view in which accurate discretization of governing equations play more important role than the choice of turbulence modelling closures. [Projekat Ministarstva nauke Republike Srbije, br. TR-33036

Introduction to finite and spectral element methods using Matlab

CERN Document Server

Pozrikidis, Constantine

2014-01-01

The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.

A blended continuous–discontinuous finite element method for solving the multi-fluid plasma model

Energy Technology Data Exchange (ETDEWEB)

Sousa, E.M., E-mail: sousae@uw.edu; Shumlak, U., E-mail: shumlak@uw.edu

2016-12-01

The multi-fluid plasma model represents electrons, multiple ion species, and multiple neutral species as separate fluids that interact through short-range collisions and long-range electromagnetic fields. The model spans a large range of temporal and spatial scales, which renders the model stiff and presents numerical challenges. To address the large range of timescales, a blended continuous and discontinuous Galerkin method is proposed, where the massive ion and neutral species are modeled using an explicit discontinuous Galerkin method while the electrons and electromagnetic fields are modeled using an implicit continuous Galerkin method. This approach is able to capture large-gradient ion and neutral physics like shock formation, while resolving high-frequency electron dynamics in a computationally efficient manner. The details of the Blended Finite Element Method (BFEM) are presented. The numerical method is benchmarked for accuracy and tested using two-fluid one-dimensional soliton problem and electromagnetic shock problem. The results are compared to conventional finite volume and finite element methods, and demonstrate that the BFEM is particularly effective in resolving physics in stiff problems involving realistic physical parameters, including realistic electron mass and speed of light. The benefit is illustrated by computing a three-fluid plasma application that demonstrates species separation in multi-component plasmas.

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

Science.gov (United States)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

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

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...

Sparse Jacobian construction for mapped grid visco-resistive magnetohydrodynamics

KAUST Repository

Reynolds, Daniel R.

2012-01-01

We apply the automatic differentiation tool OpenAD toward constructing a preconditioner for fully implicit simulations of mapped grid visco-resistive magnetohydrodynamics (MHD), used in modeling tokamak fusion devices. Our simulation framework employs a fully implicit formulation in time, and a mapped finite volume spatial discretization. We solve this model using inexact Newton-Krylov methods. Of critical importance in these iterative solvers is the development of an effective preconditioner, which typically requires knowledge of the Jacobian of the nonlinear residual function. However, due to significant nonlinearity within our PDE system, our mapped spatial discretization, and stencil adaptivity at physical boundaries, analytical derivation of these Jacobian entries is highly nontrivial. This paper therefore focuses on Jacobian construction using automatic differentiation. In particular, we discuss applying OpenAD to the case of a spatially-adaptive stencil patch that automatically handles differences between the domain interior and boundary, and configuring AD for reduced stencil approximations to the Jacobian. We investigate both scalar and vector tangent mode differentiation, along with simple finite difference approaches, to compare the resulting accuracy and efficiency of Jacobian construction in this application. © 2012 Springer-Verlag.

Analyses of the Collapse Behavior of a Spacer Grid

International Nuclear Information System (INIS)

Jang, Myung-Geun; Na, Geum Ju; Jag, Yeon-Hui; Kim, Hee Cheol; Kim, Jong-Bong; Kim, Jaeyoug

2016-01-01

In order to investigate the protection capability of a spacer grid assembly for impact load, a hammer impact test has been carried out. The crush strength is measured in the hammer impact test. Song et al. carried out the experiment and finite element analysis for the hammer impact test for various weld line depth. Park et al. designed the spacer grid shape to get required crush strength via finite element analysis. Song et al. also optimized the spacer grid shape to maximize the crush strength, and carried out the finite element analysis for the hammer impact test considering the weld properties. Kim et al. carried out finite element analysis for various guide tube hole shape and compared the crush shape and crush strength. In this study, the effect of shape defect on the crush behavior in the hammer impact test is investigated. The spacer grid cannot be exactly the square. Therefore a lateral displacement (imperfection) is imposed to square spacer grid and then hammer impact is carried out. The effect of the lateral imperfection on the crush strength is investigated. The effect of the shape defect on the crushing behavior in the hammer impact test is investigated by finite element analysis. It is shown that the collapse become severe as the lateral imperfection displacement increases, especially when the imperfection is greater than or equal to 0.7 mm