High-order Discontinuous Galerkin hydrodynamics with sub-cell shock capturing on GPUs

Understand

Hydrodynamical numerical methods that converge with high-order hold particular promise for astrophysical studies, as they can in principle reach prescribed accuracy goals with higher computational efficiency than standard second- or third-order approaches.

• Here we consider the performance and accuracy benefits of Discontinuous Galerkin (DG) methods, which offer a particularly straightforward approach to reach extremely high order.
• Also, their computational stencil maps well to modern GPU devices, further raising the attractiveness of this approach.
• However, a traditional weakness of this method lies in the treatment of physical discontinuities such as shocks.