一种用于具有两个无界方向和一个均匀方向的外部流动的自适应晶格格林函数方法
An adaptive lattice Green's function method for external flows with two unbounded and one homogeneous directions
AI总结：
本文提出一种自适应晶格格林函数方法，通过Fourier伪谱与AMR交错网格有限体积格式混合，求解具有一个均匀方向的外部不可压缩流动，并在圆柱绕流转捩和湍流中验证了其有效性。
摘要：
我们使用晶格格林函数（LGF）方法求解不可压缩Navier-Stokes方程，该方法包含浸入边界（IB）和自适应网格细化（AMR），用于具有一个均匀方向的外部流动（例如任意截面的无限长圆柱体）。我们将用于均匀方向的Fourier配点（伪谱）方法与在AMR网格上专门设计的交错网格有限体积格式进行混合。Fourier级数还根据其他方向的细化级别进行可变截断。我们推导了新的算法来制表屏蔽Poisson算子的LGF和粘性积分因子。在调整了完全非均匀情况下的其他算法细节之后，我们分别以$Re=300$和$Re=12,000$的圆形圆柱体上的转捩流和湍流来验证和展示了新方法。
英文摘要：
We solve the incompressible Navier-Stokes equations using a lattice Green's function (LGF) approach, including immersed boundaries (IB) and adaptive mesh refinement (AMR), for external flows with one homogeneous direction (e.g. infinite cylinders of arbitrary cross-section). We hybridize a Fourier collocation (pseudo-spectral) method for the homogeneous direction with a specially designed, staggered-grid finite-volume scheme on an AMR grid. The Fourier series is also truncated variably according to the refinement level in the other directions. We derive new algorithms to tabulate the LGF of the screened Poisson operator and viscous integrating factor. After adapting other algorithmic details from the fully inhomogeneous case, we validate and demonstrate the new method with transitional and turbulent flows over a circular cylinder at $Re=300$ and $Re=12,000$, respectively.
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