Free-Stream Preservation for Curved Geometrically Non-Conforming Discontinuous Galerkin Spectral Elements

TL;DR

This paper addresses free-stream preservation errors in curved geometrically non-conforming discontinuous Galerkin spectral elements by deriving geometric conditions and proposing geometric approximation strategies.

Contribution

It introduces geometric conditions and specific approximation strategies that ensure free-stream preservation in non-conforming DG spectral elements with curved geometries.

Findings

Six geometric cases that preserve constant states.

Sub-parametric geometry approximation at half the solution order.

Numerical examples confirming theoretical results.

Abstract

The under integration of the volume terms in the discontinuous Galerkin spectral element approximation introduces errors at non-conforming element faces that do not cancel and lead to free-stream preservation errors. We derive volume and face conditions on the geometry under which a constant state is preserved. From those, we catalog six special cases on the geometry that preserve a constant state, the most general being to approximate the geometry sub-parametrically to one half the order of the solution. Numerical examples are presented to illustrate the results.