Convergence of Parareal for the Navier-Stokes equations depending on the Reynolds number
Convergence of Parareal for the Navier-Stokes equations depending on the Reynolds number
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DOI：
10.1007/978-3-319-10705-9__19
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发表时间：
2013-11
期刊：
影响因子：
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通讯作者：
Johannes Steiner;D. Ruprecht;R. Speck;R. Krause
中科院分区：
文献类型：
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作者：
Johannes Steiner;D. Ruprecht;R. Speck;R. Krause
本文首先给出了时间并行Parareal方法的线性稳定性分析，使用IMEX Euler作为粗传播子，Runge-Kutta-3方法作为细传播子，证实了主虚特征值对Parareal的收敛性有负面影响。这表明当Parareal应用于非线性Navier-Stokes方程时，可能会出现小粘度的问题。驱动腔基准的数值结果，证实Parareal的收敛确实可以恶化的粘度降低和流动变得越来越占主导地位的对流。这种效果强烈依赖于空间分辨率。
The paper presents first a linear stability analysis for the time-parallel Parareal method, using an IMEX Euler as coarse and a Runge-Kutta-3 method as fine propagator, confirming that dominant imaginary eigenvalues negatively affect Parareal’s convergence. This suggests that when Parareal is applied to the nonlinear Navier-Stokes equations, problems for small viscosities could arise. Numerical results for a driven cavity benchmark are presented, confirming that Parareal’s convergence can indeed deteriorate as viscosity decreases and the flow becomes increasingly dominated by convection. The effect is found to strongly depend on the spatial resolution.