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Mixed Finite Element Formulation (mixed + finite_element_formulation)

Distribution by Scientific Domains

Engineering	80%

Selected Abstracts

Mixed finite element formulation of algorithms for double-diffusive convection in a fluid-saturated porous medium

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2007
J. C.-F.
Abstract The consistent splitting scheme involving a mixed finite element method for considering the influence of the Forchheimer-extended Brinkman,Darcy model in the momentum equation is applied to double-diffusive convection in a fluid-saturated porous medium. It is shown that the method is robust and can accurately predict flow, pressure distribution, temperature and concentration fields. The numerical scheme may be an alternative to some other existing methods for the solution of porous thermosolutal convection problems since its implementation is very handy. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Localized remeshing techniques for three-dimensional metal forming simulations with linear tetrahedral elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006
Il-Heon Son
Abstract The localized remeshing technique for three-dimensional metal forming simulations is proposed based on a mixed finite element formulation with linear tetrahedral elements in the present study. The numerical algorithm to generate linear tetrahedral elements is developed for finite element analyses using the advancing front technique with local optimization method which keeps the advancing fronts smooth. The surface mesh generation using mesh manipulations of the boundary elements of the old mesh system was made to improve mesh quality of the boundary surface elements, resulting in reduction of volume change in forming simulations. The mesh quality generated was compared with that obtained from the commercial CAD package for the complex geometry like lumbar. The simulation results of backward extrusion and bevel gear and spider forgings indicate that the currently developed simulation technique with the localized remeshing can be used effectively to simulate the three-dimensional forming processes with a reduced computation time. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Stabilized finite element method for viscoplastic flow: formulation with state variable evolution

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003
Antoinette M. Maniatty
Abstract A stabilized, mixed finite element formulation for modelling viscoplastic flow, which can be used to model approximately steady-state metal-forming processes, is presented. The mixed formulation is expressed in terms of the velocity, pressure and state variable fields, where the state variable is used to describe the evolution of the material's resistance to plastic flow. The resulting system of equations has two sources of well-known instabilities, one due to the incompressibility constraint and one due to the convection-type state variable equation. Both of these instabilities are handled by adding mesh-dependent stabilization terms, which are functions of the Euler,Lagrange equations, to the usual Galerkin method. Linearization of the weak form is derived to enable a Newton,Raphson implementation into an object-oriented finite element framework. A progressive solution strategy is used for improving convergence for highly non-linear material behaviour, typical for metals. Numerical experiments using the stabilization method with hierarchic shape functions for the velocity, pressure and state variable fields in viscoplastic flow and metal-forming problems show that the stabilized finite element method is effective and efficient for non-linear steady forming problems. Finally, the results are discussed and conclusions are inferred. Copyright © 2002 John Wiley & Sons, Ltd. [source]

On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problem

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009
D. Z. Turner
Abstract In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the method of weighted residuals. This new formulation allows equal-order interpolation for the velocity and pressure fields. Finally, we show by counterexample that a direct equivalence between subgrid-based stabilized finite element methods and Galerkin methods enriched by bubble functions cannot be constructed for quadrilateral and hexahedral elements using standard bubble functions. Copyright © 2008 John Wiley & Sons, Ltd. [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]