Astrophysical hydrodynamics with a high-order discontinuous Galerkin scheme and adaptive mesh refinement
Astrophysical hydrodynamics with a high-order discontinuous Galerkin scheme and adaptive mesh refinement
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采用高阶不连续伽辽金方案和自适应网格细化的天体物理流体动力学
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
V. Springel
中科院分区：
文献类型：
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作者：
K. Schaal;A. Bauer;P. Chandrashekar;R. Pakmor;C. Klingenberg;V. Springel
尽可能准确有效地求解理想流体力学欧拉方程是许多天体物理模拟的关键要求。因此，重要的是不断推进在当前天体物理代码中实施的数值方法，特别是考虑到不断发展的计算机技术，它更倾向于某些计算方法。本文介绍了采用高阶不连续伽辽金（DG）格式的自适应网格细化（AMR）代码TENET。该方法利用显式龙格-库塔时间积分和高斯-勒让德正交，在多项式基的弱形式下求解欧拉方程。与常用的二阶有限体积（FV）求解方法相比，该方法具有显著的优势。特别是，高阶能力使其计算效率更高，即可以以更少的计算成本获得相同的精度。此外，DG方案固有地在没有限制的区域保留角动量，并且它通常比FV方法产生更小的数值扩散和平流误差。进一步的优势在于更自然地处理AMR细化边界，从而可以避免退回到一阶。最后，DG不需要高阶的宽模板，并且提供了改进的数据局域性和对局部计算的关注，这对当前和即将到来的高度并行超级计算机是有利的。我们描述了我们的新代码的制定和实现细节，并通过一组二维和三维测试问题证明了它的性能和准确性。结果证实了DG格式在天体物理应用方面具有很高的潜力。
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.
在 DUNE 框架中实现可压缩无粘性欧拉方程的不连续伽辽金方法
DOI：
10.1002/pamm.201410457
发表时间：
2014
期刊：
PAMM
影响因子：
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作者：
J. P. Gallego-Valencia;J. Löbbert;S. Müthing;P. Bastian;C. Klingenberg;Y. Xia
通讯作者：
Y. Xia