On the Necessity of Superparametric Geometry Representation for Discontinuous Galerkin Methods on Domains with Curved Boundaries
It clarifies geometry representation requirements for high-order methods in computational fluid dynamics, but the findings are incremental and limited to specific equations and 2D domains.
This paper shows that superparametric geometry representation is necessary for optimal convergence of Discontinuous Galerkin methods on curved domains for the Euler equations, but isoparametric representation suffices for the Navier-Stokes equations in the tested case.
We provide numerical evidence demonstrating the necessity of employing a superparametric geometry representation in order to obtain optimal convergence orders on two-dimensional domains with curved boundaries when solving the Euler equations using Discontinuous Galerkin methods. However, concerning the obtention of optimal convergence orders for the Navier-Stokes equations, we demonstrate numerically that the use of isoparametric geometry representation is sufficient for the case considered here.