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Volume Methods (volume + methods)

Distribution by Scientific Domains
Engineering62%
Chemistry25%

Kinds of Volume Methods

  • finite volume methods
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    Selected Abstracts

    Hybrid finite element/volume method for shallow water equations

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010
    Shahrouz Aliabadi
    Abstract A hybrid numerical scheme based on finite element and finite volume methods is developed to solve shallow water equations. In the recent past, we introduced a series of hybrid methods to solve incompressible low and high Reynolds number flows for single and two-fluid flow problems. The present work extends the application of hybrid method to shallow water equations. In our hybrid shallow water flow solver, we write the governing equations in non-conservation form and solve the non-linear wave equation using finite element method with linear interpolation functions in space. On the other hand, the momentum equation is solved with highly accurate cell-center finite volume method. Our hybrid numerical scheme is truly a segregated method with primitive variables stored and solved at both node and element centers. To enhance the stability of the hybrid method around discontinuities, we introduce a new shock capturing which will act only around sharp interfaces without sacrificing the accuracy elsewhere. Matrix-free GMRES iterative solvers are used to solve both the wave and momentum equations in finite element and finite volume schemes. Several test problems are presented to demonstrate the robustness and applicability of the numerical method. Copyright © 2010 John Wiley & Sons, Ltd. [source]

    Automatic construction of non-obtuse boundary and/or interface Delaunay triangulations for control volume methods

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2002
    Nancy Hitschfeld
    Abstract A Delaunay mesh without triangles having obtuse angles opposite to boundary and interface edges (obtuse boundary/interface triangles) is the basic requirement for problems solved using the control volume method. In this paper we discuss postprocess algorithms that allow the elimination of obtuse boundary/interface triangles of any constrained Delaunay triangulation with minimum angle ,. This is performed by the Delaunay insertion of a finite number of boundary and/or interface points. Techniques for the elimination of two kinds of obtuse boundary/interface triangles are discussed in detail: 1-edge obtuse triangles, which have a boundary/interface (constrained) longest edge; and 2-edge obtuse triangles, which have both their longest and second longest edge over the boundary/interface. More complex patterns of obtuse boundary/interface triangles, namely chains of 2-edge constrained triangles forming a saw diagram and clusters of triangles that have constrained edges sharing a common vertex are managed by using a generalization of the above techniques. Examples of the use of these techniques for semiconductor device applications and a discussion on their generalization to 3-dimensions (3D) are also included. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Comparative study of lattice-Boltzmann and finite volume methods for the simulation of laminar flow through a 4:1 planar contraction

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2004
    Yarub Y. Al-Jahmany
    Abstract In the present paper, a comparative study of numerical solutions for Newtonian fluids based on the lattice-Boltzmann method (LBM) and the classical finite volume method (FVM) is presented for the laminar flow through a 4:1 planar contraction at a Reynolds number of value one, Re=1. In this study, the stress field for LBM is directly obtained from the distribution function. The calculations of the stress based on the FVM-data use the evaluations of velocity gradients with finite differences. The stress field for both LBM and FVM is expressed in the present study in terms of the shear stress and the first normal stress difference. The lateral and axial profiles of the velocity, the shear stress and the first normal stress difference for both methods are investigated. It is shown that the LBM results for the velocity and the stresses are in excellent agreement with the FVM results. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Some recent finite volume schemes to compute Euler equations using real gas EOS

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2002
    T. Gallouët
    Abstract This paper deals with the resolution by finite volume methods of Euler equations in one space dimension, with real gas state laws (namely, perfect gas EOS, Tammann EOS and Van Der Waals EOS). All tests are of unsteady shock tube type, in order to examine a wide class of solutions, involving Sod shock tube, stationary shock wave, simple contact discontinuity, occurrence of vacuum by double rarefaction wave, propagation of a one-rarefaction wave over ,vacuum', , Most of the methods computed herein are approximate Godunov solvers: VFRoe, VFFC, VFRoe ncv (,, u, p) and PVRS. The energy relaxation method with VFRoe ncv (,, u, p) and Rusanov scheme have been investigated too. Qualitative results are presented or commented for all test cases and numerical rates of convergence on some test cases have been measured for first- and second-order (Runge,Kutta 2 with MUSCL reconstruction) approximations. Note that rates are measured on solutions involving discontinuities, in order to estimate the loss of accuracy due to these discontinuities. Copyright © 2002 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]

    Implementation and Validation of the Teleshake Unit for DNA IQÔ Robotic Extraction and Development of a Large Volume DNA IQÔ Method

    JOURNAL OF FORENSIC SCIENCES, Issue 3 2010
    Jennifer C. Grubb B.A.
    Abstract:, Automated platforms used for forensic casework sample DNA extraction need to be versatile to accommodate a wide variety of sample types, thus protocols frequently need modification. In this study, DNA IQÔ methods previously developed for the Biomek® 2000 Automation Workstation were adapted for the Teleshake Unit using normal volumes and all deepwell extraction, and a large volume DNA IQÔ method developed. DNA purification without detectable contamination of adjacent reagent blanks is reported in the extraction of tissue samples containing several micrograms of DNA. Sensitivity and contamination studies demonstrated similar performance with the manual organic extraction method for bloodstain dilution samples. Mock casework samples demonstrated the effectiveness of the Teleshake and Teleshake large volume methods. Because of the performance and increased versatility of the DNA IQÔ extraction with these modifications, the Teleshake Unit has been implemented in both normal and large volume automated DNA extractions at the Virginia Department of Forensic Science. [source]

    High-order simulation of polymorphic crystallization using weighted essentially nonoscillatory methods

    AICHE JOURNAL, Issue 1 2009
    Martin Wijaya Hermanto
    Abstract Most pharmaceutical manufacturing processes include a series of crystallization processes to increase purity with the last crystallization used to produce crystals of desired size, shape, and crystal form. The fact that different crystal forms (known as polymorphs) can have vastly different characteristics has motivated efforts to understand, simulate, and control polymorphic crystallization processes. This article proposes the use of weighted essentially nonoscillatory (WENO) methods for the numerical simulation of population balance models (PBMs) for crystallization processes, which provide much higher order accuracy than previously considered methods for simulating PBMs, and also excellent accuracy for sharp or discontinuous distributions. Three different WENO methods are shown to provide substantial reductions in numerical diffusion or dispersion compared with the other finite difference and finite volume methods described in the literature for solving PBMs, in an application to the polymorphic crystallization of L -glutamic acid. © 2008 American Institute of Chemical Engineers AIChE J, 2009 [source]

    An upwind finite volume element method based on quadrilateral meshes for nonlinear convection-diffusion problems

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2009
    Fu-Zheng Gao
    Abstract Considering an upwind finite volume element method based on convex quadrilateral meshes for computing nonlinear convection-diffusion problems, some techniques, such as calculus of variations, commutating operator, and the theory of prior error estimates and techniques, are adopted. Discrete maximum principle and optimal-order error estimates in H1 norm for fully discrete method are derived to determine the errors in the approximate solution. Thus, the well-known problem [(Li et al., Generalized difference methods for differential equations: numerical analysis of finite volume methods, Marcel Dekker, New York, 2000), p 365.] has been solved. Some numerical experiments show that the method is a very effective engineering computing method for avoiding numerical dispersion and nonphysical oscillations. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009 [source]