Adaptive Two-Step Peer Methods for Incompressible Navier–Stokes Equations
Adaptive Two-Step Peer Methods for Incompressible Navier–Stokes Equations
复制标题
不可压缩纳维-斯托克斯方程的自适应两步同行方法
DOI：
10.1007/978-3-642-11795-4_41
复制
发表时间：
2010
影响因子：
1.7
通讯作者：
J. Lang
中科院分区：
文献类型：
--
作者：
Bettina Gottermeier;J. Lang
本文提出了六阶两步同行方法的数值研究，应用于非平稳不可压缩纳维-斯托克斯方程。这些线性隐式方法表现出良好的稳定性，但相对于一步法的主要优点在于，即使对于偏微分方程也没有观察到阶数降低。为了研究配备可变时间步长的两步对等方法的高阶收敛是否在实际相关的 CFD 计算中得到回报，我们考虑了典型的基准问题。与 Rosenbrock 类型的经典三阶一步方法相比，可以观察到两步同行方法具有更高的精度和更好的效率。
The paper presents a numerical study of two-step peer methods up to order six, applied to the non-stationary incompressible Navier–Stokes equations. These linearly implicit methods show good stability properties, but the main advantage over one-step methods lies in the fact that even for PDEs no order reduction is observed. To investigate whether the higher order of convergence of the two-step peer methods equipped with variable time steps pays off in practically relevant CFD computations, we consider typical benchmark problems. Higher accuracy and better efficiency of the two-step peer methods compared to classical third-order one-step methods of Rosenbrock-type can be observed.