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

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.

Cited by in corpus (3)

• HORSES3D: a high-order discontinuous Galerkin solver for flow simulations and multi-physics applications
• Provably Stable Flux Reconstruction High-Order Methods on Curvilinear Elements
• A Conservative High-Order Method Utilizing Dynamic Transfinite Mortar Elements for Flow Simulation on Curved Sliding Meshes