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Finite Volume (finite + volume)

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Engineering63%

Terms modified by Finite Volume

  • finite volume formulation
  • finite volume method
    		•
  • finite volume methods
  • finite volume scheme
    		•

    Selected Abstracts

    From mixed finite elements to finite volumes for elliptic PDEs in two and three dimensions

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004
    Anis Younes
    Abstract The link between Mixed Finite Element (MFE) and Finite Volume (FV) methods applied to elliptic partial differential equations has been investigated by many authors. Recently, a FV formulation of the mixed approach has been developed. This approach was restricted to 2D problems with a scalar for the parameter used to calculate fluxes from the state variable gradient. This new approach is extended to 2D problems with a full parameter tensor and to 3D problems. The objective of this new formulation is to reduce the total number of unknowns while keeping the same accuracy. This is achieved by defining one new variable per element. For the 2D case with full parameter tensor, this new formulation exists for any kind of triangulation. It allows the reduction of the number of unknowns to the number of elements instead of the number of edges. No additional assumptions are required concerning the averaging of the parameter in hetero- geneous domains. For 3D problems, we demonstrate that the new formulation cannot exist for a general 3D tetrahedral discretization, unlike in the 2D problem. However, it does exist when the tetrahedrons are regular, or deduced from rectangular parallelepipeds, and allows reduction of the number of unknowns. Numerical experiments and comparisons between both formulations in 2D show the efficiency of the new formulation. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Discrete Bose-Einstein systems in a box with low adiabatic invariant

    FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 4-5 2003
    V.I. Vlad
    The Bose-Einstein energy spectrum of an ideal quantum gas confined in a box is discrete and strongly dependent on the box geometry and temperature, for low product of the atomic mass number, Aat and the adiabatic invariant, TV2/3, i.e. on , = Aat TV2/3. Even within the approximation of non-interacting particles in the gas, the calculation of the thermodynamic properties of Bose-Einstein systems turns out to be a difficult mathematical problem. The present study compares the total number of particles, the total energy and the specific heat obtained by sums over the discrete states to the results of the approximate integrals (for defined values of ,) and shows the noticeable errors of the last ones at low adiabatic invariant (around condensation). Then, more rigorous and precise analytical approximations of sums are found in the case of finite number of atoms (correlated with the existence of a zero energy level) and the finite volume of the gas. The corrected thermodynamic functions depend on , (for fixed fugacity). The condensation temperature is corrected also in order to describe more accurately the discrete Bose-Einstein systems. Under these circumstances, the analysis of the specific heat leads to the conclusion that it shows no discontinuity, for the entire range of , values. [source]

    Required source distribution for interferometry of waves and diffusive fields

    GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2009
    Yuanzhong Fan
    SUMMARY The Green's function that describes wave propagation between two receivers can be reconstructed by cross-correlation provided that the receivers are surrounded by sources on a closed surface. This technique is referred to as ,interferometry' in exploration seismology. The same technique for Green's function extraction can be applied to the solution of the diffusion equation if there are sources throughout in the volume. In practice, we have only a finite number of active sources. The issues of the required source distribution is investigated, as is the feasibility of reconstructing the Green's function of the diffusion equation using a limited number of sources within a finite volume. We study these questions for homogeneous and heterogeneous media for wave propagation and homogeneous media for diffusion using numerical simulations. These simulations show that for the used model, the angular distribution of sources is critical in wave problems in homogeneous media. In heterogeneous media, the position and size of the heterogeneous area with respect to the sources determine the required source distribution. For diffusion, the sensitivity to the sources decays from the midpoint between the two receivers. The required width of the source distribution decreases with frequency, with the result that the required source distribution for early- and late-time reconstruction is different. The derived source distribution criterion for diffusion suggests that the cross-correlation-based interferometry is difficult to apply in field condition. [source]

    Finite element and finite volume simulation and error assessment of polymer melt flow in closed channels

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2006
    M. Vaz Jr.
    Abstract This work aims at evaluating the discretization errors associated to the finite volume and finite element methods of polymer melt flow in closed channels. Two strategies are discussed: (i) Richardson extrapolation and (ii) a posteriori error estimation based on projection/smoothing techniques. The numerical model accounts for the full interaction between the thermal effects caused by viscous heating and the momentum diffusion effects dictated by a shear rate and temperature-dependent constitutive model. The simulations have been performed for the commercial polymer Polyacetal POM-M90-44. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    An adaptive multiresolution method for parabolic PDEs with time-step control

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2009
    M. O. Domingues
    Abstract We present an efficient adaptive numerical scheme for parabolic partial differential equations based on a finite volume (FV) discretization with explicit time discretization using embedded Runge,Kutta (RK) schemes. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. The costly fluxes are evaluated on the adaptive grid only. Compact RK methods of second and third order are then used to choose automatically the new time step while controlling the approximation error in time. Non-admissible choices of the time step are avoided by limiting its variation. The implementation of the multiresolution representation uses a dynamic tree data structure, which allows memory compression and CPU time reduction. This new numerical scheme is validated using different classical test problems in one, two and three space dimensions. The gain in memory and CPU time with respect to the FV scheme on a regular grid is reported, which demonstrates the efficiency of the new method. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003
    G. A. Taylor
    Abstract A vertex-based finite volume (FV) method is presented for the computational solution of quasi-static solid mechanics problems involving material non-linearity and infinitesimal strains. The problems are analysed numerically with fully unstructured meshes that consist of a variety of two- and three-dimensional element types. A detailed comparison between the vertex-based FV and the standard Galerkin FE methods is provided with regard to discretization, solution accuracy and computational efficiency. For some problem classes a direct equivalence of the two methods is demonstrated, both theoretically and numerically. However, for other problems some interesting advantages and disadvantages of the FV formulation over the Galerkin FE method are highlighted. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Volume-dependent pressure loading and its influence on the stability of structures

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003
    T. Rumpel
    Abstract Deformation-dependent pressure loading on solid structures is created by the interaction of gas with the deformable surface of a structure. Such fairly simple load models are valid for static and quasi-static analyses and they are a very efficient tool to represent the influence of gas on the behaviour of structures. Completing previous studies on the deformation dependence of the loading with the assumption of infinite gas volumes, the current contribution is focusing on the influence of modifications of the size and shape of a finite volume containing the gas in particular on the stability of structures. The linearization of the corresponding virtual work expression necessary for a Newton-type solution leads to additional terms for the volume dependence. Investigating these terms the conservativeness of the problem can be proven by the symmetry of the linearized form. The discretization with finite elements leads to standard stiffness matrix forms plus the so-called load stiffness matrices and a rank-one update for each enclosed volume part, if the loaded surface segments are identical with element surfaces. Some numerical examples show first the effectiveness of the approach and the necessity to take the corresponding terms in the variational expression and in the following linearization into account, and second the particular influence of this term on the stability of structures is shown with some specific examples. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    A fully implicit method for steady and unsteady viscous flow simulations

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2003
    Jie Li
    Abstract In this paper a time-accurate, fully implicit method has been applied to solve a variety of steady and unsteady viscous flow problems. It uses a finite volume cell-centred formulation on structured grids and employs central space discretization with artificial dissipation for the residual computation. In order to obtain a second-order time-accurate implicit scheme, a Newton-like subiteration is performed in the original LU-SGS method to converge the calculations at each physical time step by means of a dual-time approach proposed by Jameson. The numerical experiments show that the present method is very efficient, reliable, and robust for steady and unsteady viscous flow simulations, especially for some low speed flow problems. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    A finite volume,multigrid method for flow simulation on stratified porous media on curvilinear co-ordinate systems

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2001
    Pablo Calvo
    Abstract This paper presents a numerical study of infiltration processes on stratified porous media. The study is carried out to examine the performance of a finite volume method on problems with discontinuous solutions due to the transmission conditions in the interfaces. To discretize the problem, a curvilinear co-ordinate system is used. This permits matching the interface with the boundary of the control volumes that interchange fluxes between layers. The use of the multigrid algorithm for the resulting systems of equations allows problems involving a large number of nodes with low computational cost to be solved. Finally, some numerical experiments, which show the capillary barrier behaviour depending on the material used for the different layers and the geometric design of the interface, are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Spectral analysis of flux vector splitting finite volume methods

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2001
    Tapan K. Sengupta
    Abstract New results are presented here for finite volume (FV) methods that use flux vector splitting (FVS) along with higher-order reconstruction schemes. Apart from spectral accuracy of the resultant methods, the numerical stability is investigated which restricts the allowable time step or the Courant,Friedrich,Lewy (CFL) number. Also the dispersion relation preservation (DRP) property of various spatial and temporal discretization schemes is investigated. The DRP property simultaneously fixes space and time steps. This aspect of numerical schemes is important for simulation of high-Reynolds number flows, compressible flows with shock(s) and computational aero-acoustics. It is shown here that for direct numerical simulation applications, the DRP property is more restrictive than stability criteria. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Effects of aging and gender on the spatial organization of nuclei in single human skeletal muscle cells

    AGING CELL, Issue 5 2010
    Alexander Cristea
    Summary The skeletal muscle fibre is a syncitium where each myonucleus regulates the gene products in a finite volume of the cytoplasm, i.e., the myonuclear domain (MND). We analysed aging- and gender-related effects on myonuclei organization and the MND size in single muscle fibres from six young (21,31 years) and nine old men (72,96 years), and from six young (24,32 years) and nine old women (65,96 years), using a novel image analysis algorithm applied to confocal images. Muscle fibres were classified according to myosin heavy chain (MyHC) isoform expression. Our image analysis algorithm was effective in determining the spatial organization of myonuclei and the distribution of individual MNDs along the single fibre segments. Significant linear relations were observed between MND size and fibre size, irrespective age, gender and MyHC isoform expression. The spatial organization of individual myonuclei, calculated as the distribution of nearest neighbour distances in 3D, and MND size were affected in old age, but changes were dependent on MyHC isoform expression. In type I muscle fibres, average NN-values were lower and showed an increased variability in old age, reflecting an aggregation of myonuclei in old age. Average MND size did not change in old age, but there was an increased MND size variability. In type IIa fibres, average NN-values and MND sizes were lower in old age, reflecting the smaller size of these muscle fibres in old age. It is suggested that these changes have a significant impact on protein synthesis and degradation during the aging process. [source]

    An upwind finite volume scheme and its maximum-principle-preserving ADI splitting for unsteady-state advection-diffusion equations

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2003
    Hong Wang
    Abstract We develop an upwind finite volume (UFV) scheme for unsteady-state advection-diffusion partial differential equations (PDEs) in multiple space dimensions. We apply an alternating direction implicit (ADI) splitting technique to accelerate the solution process of the numerical scheme. We investigate and analyze the reason why the conventional ADI splitting does not satisfy maximum principle in the context of advection-diffusion PDEs. Based on the analysis, we propose a new ADI splitting of the upwind finite volume scheme, the alternating-direction implicit, upwind finite volume (ADFV) scheme. We prove that both UFV and ADFV schemes satisfy maximum principle and are unconditionally stable. We also derive their error estimates. Numerical results are presented to observe the performance of these schemes. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 211,226, 2003 [source]

    On the subdomain-Galerkin/least squares method for 2- and 3-D mixed elliptic problems with reaction terms

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2002
    Suh-Yuh Yang
    Abstract In this article we apply the subdomain-Galerkin/least squares method, which is first proposed by Chang and Gunzburger for first-order elliptic systems without reaction terms in the plane, to solve second-order non-selfadjoint elliptic problems in two- and three-dimensional bounded domains with triangular or tetrahedral regular triangulations. This method can be viewed as a combination of a direct cell vertex finite volume discretization step and an algebraic least-squares minimization step in which the pressure is approximated by piecewise linear elements and the flux by the lowest order Raviart-Thomas space. This combined approach has the advantages of both finite volume and least-squares methods. Among other things, the combined method is not subject to the Ladyzhenskaya-Babus,ka-Brezzi condition, and the resulting linear system is symmetric and positive definite. An optimal error estimate in the H1(,) × H(div; ,) norm is derived. An equivalent residual-type a posteriori error estimator is also given. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 738,751, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10030. [source]

    Computational Fluid Dynamics and Vascular Access

    ARTIFICIAL ORGANS, Issue 7 2002
    Ulf Krueger
    Abstract: Anastomotic intimal hyperplasia caused by unphysiological hemodynamics is generally accepted as a reason for dialysis access graft occlusion. Optimizing the venous anastomosis can improve the patency rate of arteriovenous grafts. The purpose of this study was to examine, evaluate, and characterize the local hemodynamics and, in particular, the wall shear stresses in conventional venous end-to-side anastomosis and in patch form anastomosis (Venaflo) by three-dimensional computational fluid dynamics (CFD). We investigated the conventional form of end-to-side anastomosis and a new patch form by numerical simulation of blood flow. The numerical simulation was done with a finite volume-based algorithm. The anastomotic forms were constructed with usual size and fixed walls. Subdividing the flow domain into multiple control volumes solved the fundamental equations. The boundary conditions were identical for both forms. The velocity profile of the patch form is better than that for the conventional form. The region of high static pressure caused by flow stagnation is reduced on the vein floor. The anastomotic wall shear stress is decreased. The results of this study strongly support patch form use to reduce the incidence of intimal hyperplasia and venous anastomotic stenoses. [source]

    A moving-mesh finite-volume method to solve free-surface seepage problem in arbitrary geometries

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2007
    M. Darbandi
    Abstract The main objective of this work is to develop a novel moving-mesh finite-volume method capable of solving the seepage problem in domains with arbitrary geometries. One major difficulty in analysing the seepage problem is the position of phreatic boundary which is unknown at the beginning of solution. In the current algorithm, we first choose an arbitrary solution domain with a hypothetical phreatic boundary and distribute the finite volumes therein. Then, we derive the conservative statement on a curvilinear co-ordinate system for each cell and implement the known boundary conditions all over the solution domain. Defining a consistency factor, the inconsistency between the hypothesis boundary and the known boundary conditions is measured at the phreatic boundary. Subsequently, the preceding mesh is suitably deformed so that its upper boundary matches the new location of the phreatic surface. This tactic results in a moving-mesh procedure which is continued until the nonlinear boundary conditions are fully satisfied at the phreatic boundary. To validate the developed algorithm, a number of seepage models, which have been previously targeted by the other investigators, are solved. Comparisons between the current results and those of other numerical methods as well as the experimental data show that the current moving-grid finite-volume method is highly robust and it provides sufficient accuracy and reliability. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    A finite volume method for large strain analysis of incompressible hyperelastic materials

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2005
    I. Bijelonja
    Abstract This paper describes development of a displacement,pressure based finite volume formulation for modelling of large strain problems involving incompressible hyperelastic materials. The method is based on the solution of the integral conservation equations governing momentum balance in total Lagrangian description. The incompressibility constraint is enforced by employing the integral form of the mass conservation equation in deformed configurations of the body. A Mooney,Rivlin incompressible material model is used for material description. A collocated variable arrangement is used and the spatial domain is discretized using finite volumes of an arbitrary polyhedral shape. A segregated approach is employed to solve resulting set of coupled non-linear algebraic equations, utilizing a SIMPLE based algorithm for displacement,pressure coupling. Comparisons of numerical and analytical results show a very good agreement. For the limited range of cell topologies tested the developed method appears to be locking free. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    From mixed finite elements to finite volumes for elliptic PDEs in two and three dimensions

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004
    Anis Younes
    Abstract The link between Mixed Finite Element (MFE) and Finite Volume (FV) methods applied to elliptic partial differential equations has been investigated by many authors. Recently, a FV formulation of the mixed approach has been developed. This approach was restricted to 2D problems with a scalar for the parameter used to calculate fluxes from the state variable gradient. This new approach is extended to 2D problems with a full parameter tensor and to 3D problems. The objective of this new formulation is to reduce the total number of unknowns while keeping the same accuracy. This is achieved by defining one new variable per element. For the 2D case with full parameter tensor, this new formulation exists for any kind of triangulation. It allows the reduction of the number of unknowns to the number of elements instead of the number of edges. No additional assumptions are required concerning the averaging of the parameter in hetero- geneous domains. For 3D problems, we demonstrate that the new formulation cannot exist for a general 3D tetrahedral discretization, unlike in the 2D problem. However, it does exist when the tetrahedrons are regular, or deduced from rectangular parallelepipeds, and allows reduction of the number of unknowns. Numerical experiments and comparisons between both formulations in 2D show the efficiency of the new formulation. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Conservative semi-Lagrangian advection on adaptive unstructured meshes

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2004
    Armin Iske
    Abstract A conservative semi-Lagrangian method is designed in order to solve linear advection equations in two space variables. The advection scheme works with finite volumes on an unstructured mesh, which is given by a Voronoi diagram. Moreover, the mesh is subject to adaptive modifications during the simulation, which serves to effectively combine good approximation quality with small computational costs. The required adaption rules for the refinement and the coarsening of the mesh rely on a customized error indicator. The implementation of boundary conditions is addressed. Numerical results finally confirm the good performance of the proposed conservative and adaptive advection scheme. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 388,411, 2004 [source]

    Large-eddy simulation of shock-turbulence interaction with finite volumes and the Approximate Deconvolution Model

    PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
    R. von Kaenel Dipl.-Ing.
    The supersonic flow over a compression corner is computed by Large-Eddy Simulation (LES) using the Approximate Deconvolution Model (ADM) and a finite volume method. Results are in excellent agreement with DNS. [source]