A stabilized Powell–Sabin finite-element method for the 2D Euler equations in supersonic regime

Abstract : In this paper a Powell–Sabin finite-element (PS-FEM) scheme is presented for the solution of the 2D Euler equations in supersonic regime. The spatial discretization is based on PS splines, that are piecewise quadratic polynomials with a global continuity, defined on conforming triangulations. Some geometrical issues related to the practical construction of the PS elements are discussed, in particular, the generation of the control triangles and the imposition of the boundary conditions. A stabilized formulation is considered, and a novel shock-capturing technique in the context of continuous finite-elements is proposed to reduce oscillations around the discontinuity, and compared with the classical technique proposed by Tezduyar and Senga (2006). The code is verified using manufactured solutions and validated using two challenging numerical examples, which allows to evaluate the performance of the PS discretization in capturing the shocks.
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Computer Methods in Applied Mechanics and Engineering, Elsevier, 2018, 340, pp.216-235. 〈10.1016/j.cma.2018.05.032〉
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https://hal.inria.fr/hal-01865708
Contributeur : Boniface Nkonga <>
Soumis le : samedi 1 septembre 2018 - 09:53:57
Dernière modification le : lundi 4 mars 2019 - 14:04:17

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Giorgio Giorgiani, Hervé Guillard, Boniface Nkonga, Eric Serre. A stabilized Powell–Sabin finite-element method for the 2D Euler equations in supersonic regime. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2018, 340, pp.216-235. 〈10.1016/j.cma.2018.05.032〉. 〈hal-01865708〉

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