NEFEM for EULER equations
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Inclou dades d'ús des de 2022
Cita com:
hdl:2099/7195
Tipus de documentText en actes de congrés
Data publicació2009-02-16
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
An improvement of the classical finite element method is proposed in [1], the NURBS-Enhanced Finite Element Method (NEFEM). It considers an exact representation of the geometry by means of the usual CAD description of the boundary with Non-Uniform Rational B-Splines (NURBS). For elements not intersecting the boundary, a standard finite element interpolation and numerical integration is used. Specifically designed piecewise polynomial interpolation and numerical integration are proposed for those finite elements intersecting the NURBS boundary.
In [2] a numerical example involving an electromagnetic scattering application, is used
in order to demonstrate the applicability and behavior of the proposed methodology. The
results are encouraging and show that the NEFEM is more accurate than the corresponding
isoparametric finite elements, using a Discontinuous Galerkin (DG) formulation. Recent
studies also demonstrate that, for a desired precision, the NEFEM is also more efficient
in terms of number of degrees of freedom, and in terms of CPU time.
In the present work the NEFEM is reviewed and applied to the solution of the Euler
equations of a compressible inviscid fluid. This set of hyperbolic equations represents a
more challenging application for the NEFEM because the nonlinearity of the hyperbolic
system and the sensitivity of DG formulations to the imposition of the wall boundary
condition in curved domains.
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