A NURBS-based Discontinuous Galerkin method for CAD compliant flow simulations

Régis Duvigneau (1) , Stefano Pezzano (1) , Maxime Stauffert (1)

1 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences

In this work, we explain how a classical nodal Discontinuous Galerkin (DG) method for conservation laws can be modified to be geometrically exact with respect to CAD (Computer-Aided Design) data. The proposed approach relies on the use of rational Bézier elements, that can exactly match geometries defined by NURBS (Non-Uniform Rational B-Splines) after some basic transformations. It has been found convenient to use the same basis to describe the solution, yielding a so-called isogeometric formulation. The resulting method exhibits optimal convergence rates and facilitates couplings with geometry, e.g. for local refinement, shape sensitivity analysis, or moving computational domains. Illustrations are provided for two-dimensional compressible Euler and Navier-Stokes equations.

Domaines: Mécanique des fluides [physics.class-ph]; Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Analyse numérique [cs.NA]

Régis Duvigneau, Stefano Pezzano, Maxime Stauffert. A NURBS-based Discontinuous Galerkin method for CAD compliant flow simulations. SHARK-VF 2019 - Conference on Sharing Higher-order Advanced Research Know-how on Finite Volume, May 2019, Minho, Portugal. ⟨hal-02303621⟩