Home About us Contact
|
Home About us Contact | ||
|
|
||
Stabilized Finite Element Method (stabilized + finite_element_method)
Selected AbstractsStabilized finite element method for viscoplastic flow: formulation with state variable evolutionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003Antoinette 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] ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2008Julio Garcia-Espinosa Abstract This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233,267) and arbitrary Lagrangian,Eulerian techniques (Comput. Methods Appl. Mech. Eng. 1998; 155:235,249) for the solution to free surface problems. The main innovation of this method is the application of an overlapping domain decomposition concept in the statement of the problem. The aim is to increase the accuracy in the capture of the free surface as well as in the resolution of the governing equations in the interface between the two fluids. Free surface capturing is based on the solution to a level set equation. The Navier,Stokes equations are solved using an iterative monolithic predictor,corrector algorithm (Encyclopedia of Computational Mechanics. Wiley: New York, 2004), where the correction step is based on imposing the divergence-free condition in the velocity field by means of the solution to a scalar equation for the pressure. Examples of application of the ODDLS formulation (for overlapping domain decomposition level set) to the analysis of different free surface flow problems are presented. Copyright © 2008 John Wiley & Sons, Ltd. [source] Stabilized finite element method for viscoplastic flow: formulation with state variable evolutionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003Antoinette 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] Laminar separation bubble on an Eppler 61 airfoilINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010Samir B. Savaliya Abstract Laminar separation bubble that occurs on the suction side of the Eppler 61 airfoil at Re=46000 is studied. The incompressible flow equations are solved using a stabilized finite element method. No turbulence model is used. The variation of the bubble length and its location, with the angle of attack (,), is studied in detail. An abrupt increase in the lift coefficient is observed at ,,4.5°. It is found to be related to a sudden decrease in the separation bubble length at the trailing edge of the airfoil. Significant differences are observed in the results from the 2D and 3D computations. Stall is observed in 3D simulations, but is found to be absent in 2D. The laminar bubble, which fails to reattach in 3D for ,>14°, continues to reattach for , as large as 20° in the 2D computations. Reynolds stress calculations in both 2D and 3D indicate the extent to which the outer flow is affected by the presence of bubble. It is found that the Reynolds stress components and are of comparable order of magnitude indicating that spanwise fluctuations are significant. The effect of the time window used to compute the time-averaged aerodynamic coefficients is studied. The time-averaged and root mean square (rms) value of the aerodynamic coefficients are calculated for both 2D and 3D computations and compared with the previously published experimental results. The 3D computations show good agreement with the earlier data. The variation of the rms value of the aerodynamic coefficients with angle of attack shows certain peaks. The cause of their appearance is investigated. The effect of Reynolds number is studied. The increase in Re at ,=10° is found to reduce the bubble length and cause it to move closer to the leading edge. Copyright © 2009 John Wiley & Sons, Ltd. [source] New stabilized finite element method for time-dependent incompressible flow problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2010*Article first published online: 20 FEB 200, Yueqiang Shang Abstract A new stabilized finite element method is considered for the time-dependent Stokes problem, based on the lowest-order P1,P0 and Q1,P0 elements that do not satisfy the discrete inf,sup condition. The new stabilized method is characterized by the features that it does not require approximation of the pressure derivatives, specification of mesh-dependent parameters and edge-based data structures, always leads to symmetric linear systems and hence can be applied to existing codes with a little additional effort. The stability of the method is derived under some regularity assumptions. Error estimates for the approximate velocity and pressure are obtained by applying the technique of the Galerkin finite element method. Some numerical results are also given, which show that the new stabilized method is highly efficient for the time-dependent Stokes problem. Copyright © 2009 John Wiley & Sons, Ltd. [source] Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2005A. H. Coppola-Owen Abstract In this paper we present a problem we have encountered using a stabilized finite element method on fixed grids for flows with interfaces modelled with the level set approach. We propose a solution based on enriching the pressure shape functions on the elements cut by the interface. The enrichment is used to enable the pressure gradient to be discontinuous at the interface, thus improving the ability to simulate the behaviour of fluids with different density under a gravitational force. The additional shape function used is local to each element and the corresponding degree of freedom can therefore be condensed prior to assembly, making the implementation quite simple on any existing finite element code. Copyright © 2005 John Wiley & Sons, Ltd. [source] Resolution of the flow in clarifiers by using a stabilized finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2004P. Vellando Abstract The description of the flow that takes place in clarifiers and other wastewater treatment basins may be a powerful tool to attain an optimum design of these structures, in order to make the most of the wastewater treatment plant resources. Some authors have attempted so by making use of the potential flow or the Stokes equations. When these simplifications are used, an approximation of the flow for slow creeping conditions is obtained, but only the resolution of the all-term-including Navier,Stokes equations will allow us to detect the real streamlines and the vortices that show up for even very slow water flows. The use of the Navier,Stokes formulae as the governing equations involves the appearance of complex stability problems that do not show up for the previously mentioned simplifications. In the present work a stable finite element method for the resolution of the Navier,Stokes equations is presented, verified, and used in the resolution of some wastewater treatment flow problems with very interesting results. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||