Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations
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DOI：
10.1007/s11075-022-01382-z
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发表时间：
2022-08
影响因子：
2.1
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
本文提出了两种基于人工可压缩性(AC)的标量辅助变量(SAV)集合算法，用于不可压缩流动集合的快速计算。我们结合并利用了三种数值技术：集合时间推进、SAV、AC，以设计非常高效和快速的算法来计算(可能是大的)Navier-Stokes流动集合。所提出的数值算法的特点是：(1)所有系综成员共享一个公共常系数矩阵，允许使用有效的块求解器来显著减少所需的计算量；(2)速度和压力的计算是解耦的，并且压力可以直接更新，而不需要求解泊松方程，从而进一步降低了总的计算量。我们证明了这两种算法在参数波动条件下都是长时间稳定的，没有任何时间步长限制。通过大量的数值试验，验证了集成算法的有效性和有效性。
This report presents two scalar auxiliary variable (SAV) ensemble algorithms based on artificial compressibility (AC) for fast computation of incompressible flow ensembles. We combine and exploit three numerical techniques: ensemble timestepping, SAV, AC, to design extremely efficient and fast algorithms for the computation of a (possibly large) Navier-Stokes flow ensemble. The proposed numerical algorithms feature that (1) all ensemble members share a commonconstantcoefficient matrix allowing the use of efficient block solvers to significantly reduce required computational cost and (2) the computation of the velocity and the pressure is decoupled, and the pressure can be updated directly without solving a Poisson equation, further reducing the overall computational cost. We prove both algorithms are long time stable under a parameter fluctuation condition, without any timestep constraints. Extensive numerical tests are also presented to demonstrate the efficiency and effectiveness of the ensemble algorithms.