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Element Scheme (element + scheme)

Distribution by Scientific Domains
Engineering65%
Chemistry10%

Kinds of Element Scheme

  • finite element scheme
    		•

    Selected Abstracts

    Transport and deformation of droplets in a microdevice using dielectrophoresis

    ELECTROPHORESIS, Issue 4 2007
    Pushpendra Singh Professor
    Abstract In microfluidic devices the fluid can be manipulated either as continuous streams or droplets. The latter is particularly attractive as individual droplets can not only move but also split and fuse, thus offering great flexibility for applications such as laboratory-on-a-chip. We consider the transport of liquid drops immersed in a surrounding liquid by means of the dielectrophoretic force generated by electrodes mounted at the bottom of a microdevice. The direct numerical simulation (DNS) approach is used to study the motion of droplets subjected to both hydrodynamic and electrostatic forces. Our technique is based on a finite element scheme using the fundamental equations of motion for both the droplets and surrounding fluid. The interface is tracked by the level set method and the electrostatic forces are computed using the Maxwell stress tensor. The DNS results show that the droplets move, and deform, under the action of nonuniform electric stresses on their surfaces. The deformation increases as the drop moves closer to the electrodes. The extent to which the isolated drops deform depends on the electric Weber number. When the electric Weber number is small, the drops remain spherical; otherwise, the drops stretch. Two droplets, however, that are sufficiently close to each other, can deform and coalesce, even if the electric Weber number is small. This phenomenon does not rely on the magnitude of the electric stresses generated by the bulk electric field, but instead is due to the attractive electrostatic drop,drop interaction overcoming the surface tension force. Experimental results are also presented and found to be in agreement with the DNS results. [source]

    A parallel, adaptive finite element scheme for modeling chemotactic biological systems

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2009
    Benjamin S. Kirk
    Abstract This paper considers the numerical approximation of complex spatial patterns and rapidly evolving transients in chemotactic biological systems using parallel adaptive multiscale schemes and algorithms. Transport processes in such biological systems are typically modeled by coupled systems of nonlinear reaction,diffusion equations. For example, a model of this form has been proposed for studying chemotaxis in bacteria colonies. In the present study, we develop a variational formulation for this model leading to an approximate finite element scheme with adaptive time stepping and local adaptive mesh refinement/coarsening algorithms. The parallel adaptive solution algorithm is presented in detail and applied to investigate the effect of chemotaxis in spot formation behind concentric advancing concentrations fronts. Numerical results concerning the accuracy, efficiency, and performance of the algorithm are also presented. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    An investigation of pulsatile flow in a model cavo-pulmonary vascular system

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2009
    K. Chitra
    Abstract The complexities in the flow pattern in a cavo-pulmonary vascular system,after application of the Fontan procedure in the vicinity of the superior vena cava, inferior vena cava, and the confluence at the T-junction,are analysed. A characteristic-based split (CBS) finite element scheme involving the artificial compressibility approach is employed to compute the resulting flow. Benchmarking of the CBS scheme is carried out using standard problems and with the flow features observed in an experimental model with the help of a dye visualization technique in model scale. The transient flow variations in a total cavo-pulmonary connection (TCPC) under pulsatile conditions are investigated and compared with flow visualization studies. In addition to such qualitative flow investigations, quantitative analysis of energy loss and haemodynamic stresses have also been performed. The comparisons show good agreement between the numerical and experimental flow patterns. The numerically predicted shear stress values indicate that the pulsatile flow condition is likely to be more severe than steady flow, with regard to the long-term health of the surgically corrected TCPC. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Adaptive ICT procedure for non-linear seepage flows with free surface in porous media

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2002
    N. H. Sharif
    Abstract This paper focuses on adaptive finite element (FE)-methods for computation of the motion of viscous fluid interfaces fundamentally encountered in multiphase flow problems in porous media. An interface capturing technique (ICT)-procedure is formulated with a stabilized finite element scheme in a Eulerian framework to solve the two-dimensional (2D) and three-dimensional (3D) Navier,Stokes equation in porous media. Global mesh refinements of the discretized domain and local mesh refinements in the vicinity of the interface are used for the spatial discretization. The ICT is embedded into the finite element scheme by adding an extra advection equation and an additional unbounded degree of freedom to the number of the unknowns. Problems of non-linear free surface seepage flow in earth-fill dams are simulated in order to validate the performance of the FE-ICT. Computations for steady non-linear seepage flows in 2D and 3D are obtained for homogenous, isotropic and isothermal porous media. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Approximation of Cahn,Hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening with C1 elements

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008
    Roy H. Stogner
    Abstract A variational formulation and C1 finite element scheme with adaptive mesh refinement and coarsening are developed for phase-separation processes described by the Cahn,Hilliard diffuse interface model of transport in a mixture or alloy. The adaptive scheme is guided by a Laplacian jump indicator based on the corresponding term arising from the weak formulation of the fourth-order non-linear problem, and is implemented in a parallel solution framework. It is then applied to resolve complex evolving interfacial solution behavior for 2D and 3D simulations of the classic spinodal decomposition problem from a random initial mixture and to other phase-transformation applications of interest. Simulation results and adaptive performance are discussed. The scheme permits efficient, robust multiscale resolution and interface characterization. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Anisotropic mesh adaption for time-dependent problems,

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2008
    S. Micheletti
    Abstract We propose a space,time adaptive procedure for a model parabolic problem based on a theoretically sound anisotropic a posteriori error analysis. A space,time finite element scheme (continuous in space but discontinuous in time) is employed to discretize this problem, thus allowing for non-matching meshes at different time levels. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Numerical simulations of viscous flows using a meshless method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2008
    Changfu You
    Abstract This paper uses the element-free Galerkin (EFG) method to simulate 2D, viscous, incompressible flows. The control equations are discretized with the standard Galerkin method in space and a fractional step finite element scheme in time. Regular background cells are used for the quadrature. Several classical fluid mechanics problems were analyzed including flow in a pipe, flow past a step and flow in a driven cavity. The flow field computed with the EFG method compared well with those calculated using the finite element method (FEM) and finite difference method. The simulations show that although EFG is more expensive computationally than FEM, it is capable of dealing with cases where the nodes are poorly distributed or even overlap with each other; hence, it may be used to resolve remeshing problems in direct numerical simulations. Flows around a cylinder for different Reynolds numbers are also simulated to study the flow patterns for various conditions and the drag and lift forces exerted by the fluid on the cylinder. These forces are calculated by integrating the pressure and shear forces over the cylinder surface. The results show how the drag and lift forces oscillate for high Reynolds numbers. The calculated Strouhal number agrees well with previous results. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Retracted and replaced: A flow-condition-based interpolation finite element procedure for triangular grids

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2005
    Haruhiko Kohno
    Abstract A flow-condition-based interpolation finite element scheme is presented for use of triangular grids in the solution of the incompressible Navier,Stokes equations. The method provides spatially isotropic discretizations for low and high Reynolds number flows. Various example solutions are given to illustrate the capabilities of the procedure. This article and been retracted and replaced. See retraction and replacement notice DOI: 10.1002/fld.1247.abs. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    On Marangoni effects in a heated fluid layer with a monolayer surfactant.

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005
    Part II: finite element formulation, numerical studies
    Abstract In this part we consider the dilute surfactant model developed in Part I and construct a variational formulation and mixed finite element scheme to obtain approximate solutions. In particular, we consider the stability regimes identified in the linear stability analysis of Part I and conduct numerical experiments to explore the nature of stability for the approximate solutions in these regimes. Both 1D and 2D simulation results are provided to illustrate the behaviour. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Modeling of transport phenomena and melting kinetics of starch in a co-rotating twin-screw extruder,

    ADVANCES IN POLYMER TECHNOLOGY, Issue 1 2006
    Lijun Wang
    A mathematical model was developed to simulate fluid flow, heat transfer, and melting kinetics of starch in a co-rotating intermeshing twin-screw extruder (TSE). The partial differential equations governing the transport phenomena of the biomaterial in the extruder were solved by a finite element scheme. For validating the model, the predicted product pressure, bulk temperature at the entrance of the die, and minimum residence time of the biomaterial in the extruder were compared with experimental data. Standard errors of product pressure, bulk temperature at the die entrance, and minimum residence time were about 8.8, 2.8, and 17.3%. Simulations were carried out to investigate profiles of product pressure, bulk temperature, and melt fraction within the extruder during extrusion. © 2006 Wiley Periodicals, Inc. Adv Polym Techn 25: 22,40, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/adv.20055 [source]

    SOLID FOODS FREEZE-DRYING SIMULATION AND EXPERIMENTAL DATA

    JOURNAL OF FOOD PROCESS ENGINEERING, Issue 2 2005
    S. KHALLOUFI
    ABSTRACT This article presents a mathematical model describing the unsteady heat and mass transfer during the freeze drying of biological materials. The model was built from the mass and energy balances in the dried and frozen regions of the material undergoing freeze drying. A set of coupled nonlinear partial differential equations permitted the description of the temperature and pressure profiles, together with the position of the sublimation interface. These equations were transformed to a finite element scheme and numerically solved using the Newton-Raphson approach to represent the nonlinear problem and the interface position. Most parameters involved in the model (i.e., thermal conductivity, specific heat, density, heat and mass transfer coefficients etc.) were obtained from experimental data cited in the literature. The dehydration kinetics and the temperature profiles of potato and apple slabs were experimentally determined during freeze drying. The simulation results agreed closely with the water content experimental data. The prediction of temperature profiles within the solid was, however, less accurate. [source]

    Analysis of an Euler implicit-mixed finite element scheme for reactive solute transport in porous media

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2010
    Florin A. Radu
    Abstract In this article, we analyze an Euler implicit-mixed finite element scheme for a porous media solute transport model. The transporting flux is not assumed given, but obtained by solving numerically the Richards equation, a model for subsurface fluid flow. We prove the convergence of the scheme by estimating the error in terms of the discretization parameters. In doing so we take into account the numerical error occurring in the approximation of the fluid flow. The article, is concluded by numerical experiments, which are in good agreement with the theoretical estimates. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 [source]

    Finite element approximation of a forward and backward anisotropic diffusion model in image denoising and form generalization

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008
    Carsten Ebmeyer
    Abstract A new forward,backward anisotropic diffusion model is introduced. The two limit cases are the Perona-Malik equation and the Total Variation flow model. A fully discrete finite element scheme is studied using C0 -piecewise linear elements in space and the backward Euler difference scheme in time. A priori estimates are proven. Numerical results in image denoising and form generalization are presented.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source]

    An adaptive displacement/pressure finite element scheme for treating incompressibility effects in elasto-plastic materials

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2001
    Franz, Theo SuttmeierArticle first published online: 13 AUG 200
    Abstract In this article, a mixed finite element formulation is described for coping with (nearly) incompressible behavior in elasto-plastic problems. In addition to the displacements, an auxiliary variable, playing the role of a pressure, is introduced resulting in Stokes-like problems. The discretization is done by a stabilized conforming Q1/Q1 -element, and the corresponding algebraic systems are solved by an adaptive multigrid scheme using a smoother of block Gauss,Seidel type. The adaptive algorithm is based on the general concept of using duality arguments to obtain weighted a posteriori error bounds. This procedure is carried out here for the described discretization of elasto-plastic problems. Efficiency and reliability of the proposed adaptive method is demonstrated at (plane strain) model problems. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:369,382, 2001 [source]

    An operator-split ALE model for large deformation analysis of geomaterials

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2007
    Y. Di
    Abstract Analysis of large deformation of geomaterials subjected to time-varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator-split arbitrary Lagrangian,Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid,fluid coupling and strong material non-linearity. Each time step of the operator-split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one-dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Kinematic modelling of shear band localization using discrete finite elements

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2003
    X. Wang
    Abstract Modelling shear band is an important problem in analysing failure of earth structures in soil mechanics. Shear banding is the result of localization of deformation in soil masses. Most finite element schemes are unable to model discrete shear band formation and propagation due to the difficulties in modelling strain and displacement discontinuities. In this paper, a framework to generate shear band elements automatically and continuously is developed. The propagating shear band is modelled using discrete shear band elements by splitting the original finite element mesh. The location or orientation of the shear band is not predetermined in the original finite element mesh. Based on the elasto-perfect plasticity with an associated flow rule, empirical bifurcation and location criteria are proposed which make band propagation as realistic as possible. Using the Mohr,Coulomb material model, various results from numerical simulations of biaxial tests and passive earth pressure problems have shown that the proposed framework is able to display actual patterns of shear banding in geomaterials. In the numerical examples, the occurrence of multiple shear bands in biaxial test and in the passive earth pressure problem is confirmed by field and laboratory observations. The effects of mesh density and mesh alignment on the shear band patterns and limit loads are also investigated. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    A class of parallel multiple-front algorithms on subdomains

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003
    A. Bose
    Abstract A class of parallel multiple-front solution algorithms is developed for solving linear systems arising from discretization of boundary value problems and evolution problems. The basic substructuring approach and frontal algorithm on each subdomain are first modified to ensure stable factorization in situations where ill-conditioning may occur due to differing material properties or the use of high degree finite elements (p methods). Next, the method is implemented on distributed-memory multiprocessor systems with the final reduced (small) Schur complement problem solved on a single processor. A novel algorithm that implements a recursive partitioning approach on the subdomain interfaces is then developed. Both algorithms are implemented and compared in a least-squares finite-element scheme for viscous incompressible flow computation using h - and p -finite element schemes. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Efficient solution techniques for implicit finite element schemes with flux limiters

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2007
    M. MöllerArticle first published online: 20 MAR 200
    Abstract The algebraic flux correction (AFC) paradigm is equipped with efficient solution strategies for implicit time-stepping schemes. It is shown that Newton-like techniques can be applied to the nonlinear systems of equations resulting from the application of high-resolution flux limiting schemes. To this end, the Jacobian matrix is approximated by means of first- or second-order finite differences. The edge-based formulation of AFC schemes can be exploited to devise an efficient assembly procedure for the Jacobian. Each matrix entry is constructed from a differential and an average contribution edge by edge. The perturbation of solution values affects the nodal correction factors at neighbouring vertices so that the stencil for each individual node needs to be extended. Two alternative strategies for constructing the corresponding sparsity pattern of the resulting Jacobian are proposed. For nonlinear governing equations, the contribution to the Newton matrix which is associated with the discrete transport operator is approximated by means of divided differences and assembled edge by edge. Numerical examples for both linear and nonlinear benchmark problems are presented to illustrate the superiority of Newton methods as compared to the standard defect correction approach. Copyright © 2007 John Wiley & Sons, Ltd. [source]