Section: New Results

Isogeometric analysis for hyperbolic systems

Participants : Régis Duvigneau, Asma Azaouzi [ENIT] , Maher Moakher [ENIT] .

The use of high-order numerical schemes is necessary to reduce numerical diffusion/dispersion in simulations, maintain a reasonable computational time for 3D problems, estimate accurately uncertainties or sensitivities, etc. Moreover, the capability to handle exactly CAD data in physical solvers is desirable to foster design optimization or multidisciplinary couplings.

Consequently, we develop high-order isogeometric schemes for the applications targeted by the team, in particular for convection-dominated problems. Specifically, we investigate a Discontinuous Galerkin method for compressible Euler equations, based on an isogeometric formulation: the partial differential equations governing the flow are solved on rational parametric elements, that preserve exactly the geometry of boundaries defined by Non-Uniform Rational B-Splines (NURBS), while the same rational approximation space is adopted for the solution. This topic is partially studied in A. Azaouzi's PhD work.