论文标题
不连续的Galerkin非静态大气模型的隐式解释公式
IMplicit-EXplicit Formulations for Discontinuous Galerkin Non-Hydrostatic Atmospheric Models
论文作者
论文摘要
这项工作介绍了对可压缩的欧拉（DG）离散化的不连续的欧拉（DG）的分离公式，该方程是管理非静态大气流的。特别是，我们展示了两种不同的IMEX公式，它们不仅可以治疗由于管理动力学而引起的刚度，还可以处理域离散化。我们为通常在大气建模中使用的两个不同方程组提供了这些公式。对于两个方程组，都会得出有效的Schur补充，并讨论了挑战和补救措施。在2D（框）和3D（球形）测试问题上研究了这些IMEX公式的性能，并显示出其对中尺度和全球应用的理论收敛速率及其相对于中尺度和全球应用的效率。
This work presents IMplicit-EXplicit (IMEX) formulations for discontinuous Galerkin (DG) discretizations of the compressible Euler equations governing non-hydrostatic atmospheric flows. In particular, we show two different IMEX formulations that not only treat the stiffness due to the governing dynamics but also the domain discretization. We present these formulations for two different equation sets typically employed in atmospheric modeling. For both equation sets, efficient Schur complements are derived and the challenges and remedies for deriving them are discussed. The performance of these IMEX formulations of different orders are investigated on both 2D (box) and 3D (sphere) test problems and shown to achieve their theoretical rates of convergence and their efficiency with respect to both mesoscale and global applications are presented.
