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Bubble Functions (bubble + function)
Selected AbstractsFringe element reconstruction for front tracking for three-dimensional incompressible flow analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2005Du-Soon Choi Abstract Fringe element reconstruction technique for tracking the free surface in three-dimensional incompressible flow analysis was developed. The flow field was calculated by the mixed formulation based on a four-node tetrahedral element with a bubble function at the centroid (P1+/P1). Since an Eulerian approach was employed in this study, the flow front interface was advected by the flow through a fixed mesh. For accurate modelling of interfacial movement, a fringe element reconstruction method developed can provide not only an accurate treatment of material discontinuity but also surface tension across the interface. The effect of surface tension was modelled by imposing tensile stress directly on the constructed surface elements at the flow front interface. To verify the numerical approach developed, the developed algorithm was applied to two examples whose solutions are available in references. Good agreement was obtained between the simulation results and these solutions. Copyright © 2005 John Wiley & Sons, Ltd. [source] Development of highly accurate interpolation methodfor mesh-free flow simulations III.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003Analysis of accuracy, stability Abstract A highly accurate interpolation method, CIVA, improves the accuracy of mesh-free and grid-less methods by taking into consideration first-order spatial derivatives as variables; an approach based on the same idea as that on which CIP is based. In this study, the accuracy and stability of CIVA is evaluated by analytically and numerically. First, the general formulation of CIVA for the n -dimensional case is described. Since CIVA contains the bubble function, we consider the determination methods: constant curvature condition and utilization of another computing point. Then, the relation between the bubble function in the CIVA method and the accuracy and stability is made clear by the analysis based on the Taylor expansion. Some computations of two-dimensional passive scalar advection and advection,diffusion problems are performed for the verification of accuracy and stability. Copyright © 2003 John Wiley & Sons, Ltd. [source] A new stable space,time formulation for two-dimensional and three-dimensional incompressible viscous flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2001Donatien N'dri Abstract A space,time finite element method for the incompressible Navier,Stokes equations in a bounded domain in ,d (with d=2 or 3) is presented. The method is based on the time-discontinuous Galerkin method with the use of simplex-type meshes together with the requirement that the space,time finite element discretization for the velocity and the pressure satisfy the inf,sup stability condition of Brezzi and Babu,ka. The finite element discretization for the pressure consists of piecewise linear functions, while piecewise linear functions enriched with a bubble function are used for the velocity. The stability proof and numerical results for some two-dimensional problems are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] Analysis of shear locking in Timoshenko beam elements using the function space approachINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2001Somenath Mukherjee Abstract Elements based purely on completeness and continuity requirements perform erroneously in a certain class of problems. These are called the locking situations, and a variety of phenomena like shear locking, membrane locking, volumetric locking, etc., have been identified. Locking has been eliminated by many techniques, e.g. reduced integration, addition of bubble functions, use of assumed strain approaches, mixed and hybrid approaches, etc. In this paper, we review the field consistency paradigm using a function space model, and propose a method to identify field-inconsistent spaces for projections that show locking behaviour. The case of the Timoshenko beam serves as an illustrative example. Copyright © 2001 John Wiley & Sons, Ltd. [source] Shape functions for polygonal domains with interior nodesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2004Elisabeth Anna Malsch Abstract The presented formulation follows in a series of publications which outline a method for constructing test functions which satisfy essential edge conditions exactly. The method promises a complete solution, satisfying all of the requirements of a Ritz coordinate function. The influence of interior points on the domain solution is included in this construction. Similar to conformal bubble functions, the test functions are zero along the boundary and single valued only at the points they describe. Unlike the bubble function construction, the interior points can be located at any desired point in the domain. The resulting set of trial functions can satisfy the required global conditions including the exact reproduction of constant and linear fields. Copyright © 2004 John Wiley & Sons, Ltd. [source] On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009D. 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] A new class of stabilized mesh-free finite elements for the approximation of the Stokes problemNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2004V. V. K. Srinivas Kumar Abstract Previously, we solved the Stokes problem using a new linear - constant stabilized mesh-free finite element based on linear Weighted Extended B - splines (WEB-splines) as shape functions for the velocity approximation and constant extended B-splines for the pressure (Kumar et al., 2002). In this article we derive another linear-constant element that uses the Haar wavelets for the pressure approximation and a quadratic - linear element that uses quadrilateral bubble functions for the enrichment of the velocity approximation space. The inf-sup condition or Ladyshenskaya-Babus,ka-Brezzi (LBB) condition is verified for both the elements. The main advantage of these new elements over standard finite elements is that they use regular grids instead of irregular partitions of domain, thus eliminating the difficult and time consuming pre-processing step. Convergence and condition number estimates are derived. Numerical experiments in two space dimensions confirm the theoretical predictions. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. [source] | ||||||||||