h-Adaptive FV Subcell Shock-Capturing for DGSEM on Heterogeneous Curvilinear Meshes

TL;DR

This paper introduces a robust shock-capturing method for high-order DGSEM on complex mixed meshes, combining h-adaptive subcell schemes with coordinate transformations for diverse element types.

Contribution

It develops an h-adaptive finite volume subcell shock-capturing scheme applicable to mixed curvilinear meshes with non-hexahedral elements, enhancing stability and resolution.

Findings

The method preserves conservation and convergence properties.

It effectively captures shocks in complex geometries.

Application demonstrated on flow around a NACA 0012 airfoil.

Abstract

High-order methods offer superior dispersion and dissipation properties compared to low-order schemes but require robust stabilization for discontinuities. To ensure stability, local artificial viscosity is common, but often degrades sub-element resolution. Conversely, subcell resolution preserving limiting strategies such as the finite volume subcell method are typically restricted to uniform topologies, such as purely hexahedral, or simplex meshes. This leaves a significant gap in treating the hybrid-element topologies necessary for complex engineering geometries. This paper presents a robust shock-capturing approach for the discontinuous Galerkin spectral element method on mixed curvilinear meshes containing hexahedral, prismatic, tetrahedral, and pyramid elements. Non-hexahedral elements are handled via collapsed coordinate transformations. The proposed method utilizes an h-adaptive finite volume subcell scheme with arbitrary subcell resolution; 2N + 1 in this work. The schemes essential properties, including conservation, spatial convergence, and the shock capturing capabilities are verified. Finally, the method's applicability to complex configurations is demonstrated through a simulation of the flow around a NACA 0012 airfoil.