A finite element framework based on bivariate simplex splines on triangle configurations

Juan Cao, Xiaodong Wei
ELSEVIER SCIENCE SA, 2019
Article

Résumé

Recently, triangle configuration based bivariate simplex splines (referred to as TCB-spline) have been introduced to the geometric computing community. TCB-splines retain many attractive theoretic properties of classical B-splines, such as partition of unity, local support, polynomial reproduction and automatic inbuilt high-order smoothness. In this paper, we propose a computational framework for isogeometric analysis using TCB-splines. The centroidal Voronoi tessellation method is used to generate a set of knots that are distributed evenly over the domain. Then, knot subsets are carefully selected by a so-called link triangulation procedure (LTP), on which shape functions are defined in a recursive manner. To achieve high-precision numerical integration, triangle faces served as background integration cells are obtained by triangulating the entire domain restricted to all knot lines, i.e., line segments defined by any two knots in a knot subset. Various numerical examples are carried out to demonstrate the efficiency, flexibility and optimal convergence rates of the proposed method. (C) 2019 Elsevier B.V. All rights reserved.

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https://infoscience.epfl.ch/record/271620?ln=fr

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Juan Cao, Xiaodong Wei
ELSEVIER SCIENCE SA, 2019
Article

Résumé

Official source

https://infoscience.epfl.ch/record/271620?ln=fr

À propos de ce résultat

Concepts associés (6)

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EPFL1999

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Jean-Luc Desbiolles, Jacques Rappaz, Michel Rappaz

Micro-macrosegregation calculations have been performed for a rectangular cavity containing either a Pb-48 wt pct Sn alloy or a Sn-5 wt pct Pb alloy. The numerical results calculated with a finite volume method (FVM) and a finite element method (FEM) are compared with experimental results previously obtained by Hebditch and Hunt.([1]) The two methods are based on the same average conservation equations governing heat and mass transfer and the same assumptions: lever rule, equal and constant density of the solid and liquid phases (except in the buoyancy term), permeability of the mushy zone given by the Carman-Kozeny relation, and no transport of the solid phase. Although the same parameters are used in both calculations, small differences are observed as a result of the different formulations. In particular, the instabilities appearing in the mushy zone (channels) of the Sn-5 wt pct Pb alloy are more pronounced with the FVM formulation as compared with FEM, whereas the opposite trend is observed for the Pb-48 wt pct Sn alloy. Nevertheless, the final segregation maps at the end of solidification compare fairly well with the experimental findings.

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