A comparison of interpolation techniques for non-conformal high-order discontinuous Galerkin methods

TL;DR

This paper compares mortar and point-to-point interpolation techniques for non-conformal high-order discontinuous Galerkin methods, analyzing their numerical properties and performance in complex 3D simulations involving moving interfaces.

Contribution

It provides a detailed comparison of mortar and point-to-point interpolation methods, highlighting their advantages and challenges in high-fidelity, complex 3D simulations with moving interfaces.

Findings

Mortar approach preserves local conservation but is complex to implement in 3D.

Point-to-point interpolation is easier to implement but may have different numerical properties.

Both methods' convergence and performance are evaluated in hyperbolic problems.

Abstract

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.