On the use of NURBS-based domains for Discontinuous Galerkin methods

  • Duvigneau, Régis (Inria)
  • Pezzano, Stefano (Inria)

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Iso-Geometric Analysis (IGA) methods, proposed some years ago by T. Hughes and co-authors, have defined an appealing framework to achieve simulations using NURBS (Non-Uniform Rational B-Spline) domains consistent with Computer-Aided Design (CAD) representations. However, the Finite-Element method used is not well suited to hyperbolic systems of conservation laws and the construction of NURBS grids remains tedious for realistic geometries. This has motivated the development of an alternate isogeometric approach, more flexible, based on a Discontinuous Galerkin (DG) formulation. The objective of this work is to examine the potential of the proposed NURBS-based framework, and the current issues, regarding a set of typical problems encountered in aerodynamics: grid generation and local adaption from CAD data, moving and deformable domains using an Arbitrary Lagrangian-Eulerian formulation, conservative sliding grid algorithm, fluid-structure interactions, etc. Numerical illustrations are provided in the context of compressible Euler and Navier-Stokes equations for different flow regimes, from subsonic to supersonic.