High-Order ADER-DG Hydrodynamics with ExaHyPE: Implementation, Validation, and Astrophysical Benchmarking

TL;DR

This paper presents a high-order ADER-DG solver integrated into the ExaHyPE framework, capable of accurately simulating complex hydrodynamic phenomena with adaptive refinement and shock capturing.

Contribution

The work introduces a novel high-order ADER-DG implementation within ExaHyPE, combining advanced numerical techniques for improved accuracy and stability in hydrodynamics simulations.

Findings

The solver accurately reproduces expected wave patterns in 1D tests.

High-order methods improve resolution in smooth regions and near discontinuities.

The subcell limiter ensures stability near shocks and steep interfaces.

Abstract

We describe a high-order ADER-DG solver for the compressible Euler equations within the ExaHyPE framework. The implementation combines a high-order ADER-DG polynomial representation, a local space-time DG predictor, adaptive mesh refinement, and an a posteriori subcell finite-volume limiter. We test the code on a deliberately mixed set of one- and two-dimensional problems: a strong-shock Sod-type problem, the Shu-Osher shock-entropy interaction, the Woodward-Colella blast wave, a contact-driven vortex sheet, and a shock-interface interaction. The one-dimensional cases recover the expected Euler wave patterns and show clear order-dependent gains in smooth and oscillatory regions. The two-dimensional cases probe a different part of the method, namely contact preservation, shear-driven roll-up, baroclinic vorticity deposition, and Richtmyer-Meshkov-type growth. In these tests the high-order update gives the expected resolution away from discontinuities, whereas the subcell limiter keeps the calculation stable near shocks and steep interfaces. The resulting code provides a reproducible ExaHyPE implementation for idealised inviscid, non-relativistic flows in which shocks, contacts, and multidimensional interfaces are the dominant features.