  The capability to incorporate moving geometric features within models for
complex simulations is a common requirement in many fields. Fluid mechanics
within aeronautical applications, for example, routinely feature rotating (e.g.
turbines, wheels and fan blades) or sliding components (e.g. in compressor or
turbine cascade simulations). With an increasing trend towards the
high-fidelity modelling of these cases, in particular combined with the use of
high-order discontinuous Galerkin methods, there is therefore a requirement to
understand how different numerical treatments of the interfaces between the
static mesh and the sliding/rotating part impact on overall solution quality.
In this article, we compare two different approaches to handle this
non-conformal interface. The first is the so-called mortar approach, where flux
integrals along edges are split according to the positioning of the
non-conformal grid. The second is a less-documented point-to-point
interpolation method, where the interior and exterior quantities for flux
evaluations are interpolated from elements lying on the opposing side of the
interface. Although the mortar approach has significant advantages in terms of
its numerical properties, in that it preserves the local conservation
properties of DG methods, in the context of complex 3D meshes it poses notable
implementation difficulties which the point-to-point method handles more
readily. In this paper we examine the numerical properties of each method,
focusing not only on observing convergence orders for smooth solutions, but
also how each method performs in under-resolved simulations of linear and
nonlinear hyperbolic problems, to inform the use of these methods in implicit
large-eddy simulations.
