Section: New Results

Isogeometric analysis

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

We develop high-order isogeometric solvers, based on CAD representations for both geometry and solution space, for applications targeted by the team, in particular convection-dominated problems. Specifically, we investigate a Discontinuous Galerkin method for compressible Euler / Navier-Stokes 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 [34].

Recent extensions concern the capability to capture discontinuities in the solution, local refinement strategies by splitting algorithms [25] and high-order sensitivity analysis [24].

This topic is partially studied in A. Azaouzi's PhD work [21], [27], supervised by R. Duvigneau and M. Moakher.