论文标题
高阶重量调整后的不连续的盖尔金方法用于移动弯曲网格的波传播
High order weight-adjusted discontinuous Galerkin methods for wave propagation on moving curved meshes
论文作者
论文摘要
本文介绍了高阶准确的不连续的盖尔金（DG）方法，用于以一般的基础和正交选择弯曲网眼时进行波浪问题。所提出的方法采用任意的拉格朗日 - 欧拉（ALE）公式，以将声波方程从依赖时间依赖的移动物理结构域映射到固定的参考域上。对于移动的弯曲网格，使用显式时间步进方法时，必须在每个时间步长组装加权质量矩阵。我们通过利用易于可逆的重量调整后的近似来避免此步骤。所得的半分化权重调整的DG方案可证明能量稳定至一个术语，该术语以与最佳$ l^2 $误差估算相同的速率收敛到零。使用多项式和B-Spline碱基的数值实验验证了提出方法的高阶精度和能量稳定性。
This paper presents high order accurate discontinuous Galerkin (DG) methods for wave problems on moving curved meshes with general choices of basis and quadrature. The proposed method adopts an arbitrary Lagrangian-Eulerian (ALE) formulation to map the acoustic wave equation from the time-dependent moving physical domain onto a fixed reference domain. For moving curved meshes, weighted mass matrices must be assembled and inverted at each time step when using explicit time stepping methods. We avoid this step by utilizing an easily invertible weight-adjusted approximation. The resulting semi-discrete weight-adjusted DG scheme is provably energy stable up to a term which converges to zero with the same rate as the optimal $L^2$ error estimate. Numerical experiments using both polynomial and B-spline bases verify the high order accuracy and energy stability of proposed methods.
