Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations ✩

Giorgio Giorgiani (1) , Sonia Fernández-Méndez (2) , Antonio Huerta (2)

1 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres
2 LaCàN - Laboratori de Càlcul Numèric (LACAN)

A degree adaptive Hybridizable Discontinuous Galerkin (HDG) method for the solution of the incompressible Navier-Stokes equations is presented. The key ingredient is an accurate and computationally inexpensive a posteriori error estimator based on the super-convergence properties of HDG. The error estimator drives the local modification of approximation degree in the elements and faces of the mesh, aimed at obtaining a uniform error distribution below a user-given tolerance in a given are of interest. Three 2D numerical examples are presented. High efficiency of the proposed error estimator is found, and an important reduction of the computational effort is shown with respect to non-adaptive computations, both for steady state and transient simulations.

Mots clés: Hybrid methods; Discontinuous Galerkin; Navier-Stokes; equations; CFD; p-adaptivity; high-order; Hybridizable Discontinuous Galerkin

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Giorgio Giorgiani, Sonia Fernández-Méndez, Antonio Huerta. Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations ✩. Computers and Fluids, 2014. ⟨hal-01717504⟩