  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 second order 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 wide stencils at high order, and offers an improved data locality
and a focus on local computations, which is favourable 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.
