%0 Generic %1 schaal2015astrophysical %A Schaal, Kevin %A Bauer, Andreas %A Chandrashekar, Praveen %A Pakmor, Rüdiger %A Klingenberg, Christian %A Springel, Volker %D 2015 %K amr code hydrodynamics %T Astrophysical hydrodynamics with a high-order discontinuous Galerkin scheme and adaptive mesh refinement %U http://arxiv.org/abs/1506.06140 %X 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.

@misc{schaal2015astrophysical, 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.}, added-at = {2015-06-23T09:33:21.000+0200}, author = {Schaal, Kevin and Bauer, Andreas and Chandrashekar, Praveen and Pakmor, Rüdiger and Klingenberg, Christian and Springel, Volker}, biburl = {https://www.bibsonomy.org/bibtex/2c66228ffaee1685536cc321c9188d71c/miki}, description = {[1506.06140] Astrophysical hydrodynamics with a high-order discontinuous Galerkin scheme and adaptive mesh refinement}, interhash = {5f90c0d7b841a1462c3b322f55d96b9b}, intrahash = {c66228ffaee1685536cc321c9188d71c}, keywords = {amr code hydrodynamics}, note = {cite arxiv:1506.06140Comment: 23 pages, 12 figures, a movie may be accessed online: https://youtu.be/cTRQP6DSaqA, comments are welcome}, timestamp = {2015-06-23T09:33:21.000+0200}, title = {Astrophysical hydrodynamics with a high-order discontinuous Galerkin scheme and adaptive mesh refinement}, url = {http://arxiv.org/abs/1506.06140}, year = 2015 }