论文标题
高阶不连续的Galerkin流体动力学，并在GPU上捕获子细胞冲击
High-order Discontinuous Galerkin hydrodynamics with sub-cell shock capturing on GPUs
论文作者
论文摘要
与标准的二阶或三阶方法相比，与高阶有关的流体动力学方法对天体物理研究具有特殊的诺言，其计算效率具有更高的计算效率。在这里，我们考虑了不连续的Galerkin（DG）方法的性能和准确性优势，该方法提供了一种特别直接的方法来达到极高的高度。此外，他们的计算模具映射到现代的GPU设备，进一步提高了这种方法的吸引力。但是，这种方法的传统弱点在于治疗诸如冲击之类的身体不连续性。我们通过调用人造粘度场来解决此问题，以在需要的情况下提供所需的耗散，并在需要的情况下以物理粘度和热导率来增加，从而对可压缩流体的Navier-Stokes方程进行高阶处理。我们表明，我们的方法会导致子细胞冲击捕获能力，这与传统的限制方案不同，这些方案往往会在以许多冲击为特征的问题中击败DG进入高级阶段的好处。我们证明，将求解器的指数收敛呈指数融合，因为将其应用于平滑流量时，例如kelvin-helmholtz参考问题ARXIV：1509.03630。我们还证明了在不同计算节点上分布的数百个GPU的GPU实现的出色可扩展性。在第一个用于驱动的，亚音湍流的应用中，我们强调了高阶DG的准确性优势与传统的二阶准确方法相比，我们强调了物理粘度对于获得准确速度功率光谱的重要性。
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. We address this by invoking an artificial viscosity field to supply required dissipation where needed, and which can be augmented, if desired, with physical viscosity and thermal conductivity, yielding a high-order treatment of the Navier-Stokes equations for compressible fluids. We show that our approach results in sub-cell shock capturing ability, unlike traditional limiting schemes that tend to defeat the benefits of going to high order in DG in problems featuring many shocks. We demonstrate exponential convergence of our solver as a function of order when applied to smooth flows, such as the Kelvin-Helmholtz reference problem of arXiv:1509.03630. We also demonstrate excellent scalability of our GPU implementation up to hundreds of GPUs distributed on different compute nodes. In a first application to driven, sub-sonic turbulence, we highlight the accuracy advantages of high-order DG compared to traditional second-order accurate methods, and we stress the importance of physical viscosity for obtaining accurate velocity power spectra.
