论文标题
浅水方程的高阶熵稳定的不连续的盖金方法：弯曲的三角形网格和GPU加速度
High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration
论文作者
论文摘要
我们为在弯曲的三角形网格上的二维浅水方程（SWE）提供了一个高阶熵稳定的不连续的盖尔金（ESDG）方法。所介绍的方案保留了半混凝土熵的不等式，并且在连续的测深谱均保持良好平衡。我们提供数值实验，以证实该方案的高阶精度和理论特性，并根据基于简单的逐个列表（SBP）有限差异操作员进行比较的方案与熵稳定方案进行比较。最后，我们报告了图形处理单元（GPU）实现的计算性能，并提供了与四边形网格上高阶DG方法现有的GPU加速实现的比较。
We present a high-order entropy stable discontinuous Galerkin (ESDG) method for the two dimensional shallow water equations (SWE) on curved triangular meshes. The presented scheme preserves a semi-discrete entropy inequality and remains well-balanced for continuous bathymetry profiles. We provide numerical experiments which confirm the high-order accuracy and theoretical properties of the scheme, and compare the presented scheme to an entropy stable scheme based on simplicial summation-by-parts (SBP) finite difference operators. Finally, we report the computational performance of an implementation on Graphics Processing Units (GPUs) and provide comparisons to existing GPU-accelerated implementations of high-order DG methods on quadrilateral meshes.
