论文标题
为可压缩的Navier-Stokes方程的现代强大淋巴结不连续的Galerkin光谱元素方法的构建
Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations
论文作者
论文摘要
由于其高阶精度和几何柔韧性，不连续的Galerkin（DG）方法在计算物理和工程方面具有悠久的历史悠久，可近似偏微分方程的解决方案。但是，DG并不完美，还有一些问题。关于鲁棒性，DG在过去的七年中经历了广泛的转变，为现代形式进行了有关线性和非线性问题解决方案界限的陈述。 本章采用一种建设性的方法来在三维曲线环境中介绍可压缩的Navier-Stokes方程的DG光谱元素方法的现代化身。数值方案的基础是光谱方法的经典原理，包括多项式近似值和高斯型四倍。我们将混叠视为经典DG光谱方法鲁棒性问题的一个根本原因。删除上述混叠错误需要特定的分化矩阵，并仔细地离散了管理方程中的对流通量项。
Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations.
