Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations
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DOI：
10.1007/s10444-022-09977-9
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发表时间：
2022-10
影响因子：
1.7
通讯作者：
N. Jiang;Huanhuan Yang
中科院分区：
文献类型：
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作者：
N. Jiang;Huanhuan Yang
在本报告中，我们提出了一种二阶稳定的基于SAV的Crank-Nicolson跳青蛙（CNLF）集合方法，并对其进行了全面的数值研究，以及Jiang和Yang （SIAM J. Sci.）提出的带有线性外推的Crank-Nicolson集合方法（CNLE）。Comput.43: A2869-A2896)。这两种方法都非常有效，因为每次只需要解决一个具有多个右手的线性系统，即可实现（潜在的大量）流问题。特别是，完全离散系统的系数矩阵是一个不随时间步长变化的常数矩阵。我们对这两种方法进行了广泛的测试，并展示了每种方法的优点。我们还给出了两种方法的长时间稳定性分析。
In this report we present a second-order, stabilized SAV based, Crank–Nicolson leap-frog (CNLF) ensemble method, and perform a comprehensive numerical study of it as well as the Crank–Nicolson ensemble method with a linear extrapolation (CNLE) presented in Jiang and Yang (SIAM J. Sci. Comput.43:A2869–A2896, ). Both methods are extremely efficient as only one linear system with multiple right hands needs to be solved at each time for a (potentially large) number of realizations of the flow problems. In particular the coefficient matrix of the fully discretized system is a constant matrix that does not change from one time step to another. We present extensive testing of these two methods and demonstrate the advantages of each. We also present long time stability analysis for both methods.