Abstract
Solving the Euler equations of ideal hydrodynamics as accurately and
efficiently as possible is a key requirement in many astrophysical simulations.
It is therefore important to continuously advance the numerical methods
implemented in current astrophysical codes, especially also in light of
evolving computer technology, which favours certain computational approaches
over others. Here we introduce the new adaptive mesh refinement (AMR) code
TENET, which employs a high-order Discontinuous Galerkin (DG) scheme for
hydrodynamics. The Euler equations in this method are solved in a weak
formulation with a polynomial basis by means of explicit Runge-Kutta time
integration and Gauss-Legendre quadrature. This approach offers significant
advantages over commonly employed finite volume (FV) solvers. In particular,
the higher order capability renders it computationally more efficient, in the
sense that the same precision can be obtained at significantly less
computational cost. Also, the DG scheme inherently conserves angular momentum
in regions where no limiting takes place, and it typically produces much
smaller numerical diffusion and advection errors than a FV approach. A further
advantage lies in a more natural handling of AMR refinement boundaries, where a
fall back to first order can be avoided. Finally, DG requires no deep stencils
at high order, and offers an improved compute to memory access ratio compared
with FV schemes, which is favorable for current and upcoming highly parallel
supercomputers. We describe the formulation and implementation details of our
new code, and demonstrate its performance and accuracy with a set of two- and
three-dimensional test problems. The results confirm that DG schemes have a
high potential for astrophysical applications.
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