In this paper, a new strategy for a sub-element-based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to interpret a DG element as a collection of data and construct a hierarchy of low-to-high-order discretizations on this set of data, including a first-order finite volume scheme up to the full-order DG scheme. The different DG discretizations are then blended according to sub-element troubled cell indicators, resulting in a final discretization that adaptively blends from low to high order within a single DG element. The goal is to retain as much high-order accuracy as possible, even in simulations with very strong shocks, as, e.g., presented in the Sedov test. The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing. The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.

In this paper, we present a discontinuous Galerkin solver based on previous work by the authors for magneto-hydrodynamics in form of a new fluid solver module integrated into the established and well-known multi-physics simulation code FLASH. Our goal is to enable future research on the capabilities and potential advantages of discontinuous Galerkin methods for complex multi-physics simulations in astrophysical settings. We give specific details and adjustments of our implementation within the FLASH framework and present extensive validations and test cases, specifically its interaction with several other physics modules such as (self-)gravity and radiative transfer. We conclude that the new DG solver module in FLASH is ready for use in astrophysics simulations and thus ready for assessments and investigations.

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