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首页> 外文期刊>Journal of Computational Physics >Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows
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Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

机译:3D非定常不可压缩流的非结构笛卡尔精细化与尖锐的界面浸入边界方法

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摘要

A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggeredon-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates the potential of the method to simulate turbulent flows past geometrically complex bodies on locally refined meshes. In all the cases, the results are found to be in very good agreement with published data and savings in computational resources are achieved. (C) 2016 Elsevier Inc. All rights reserved.
机译:开发了一种新颖的数值方法,用于在具有任意复杂的沉浸边界的区域中求解局部细化的完全非结构化笛卡尔网格上的3D,不稳定,不可压缩的Navier-Stokes方程。由于在非结构化笛卡尔混合交错/非交错网格布局上使用分数步长方法,避免了通量失配和压力不连续性问题,并且零散约束固有地满足了机器零。辅助/悬挂节点用于简化控制方程的离散化。通过使用多维Lagrange插值算子和具有不同细化级别的区域的界面处的适当微分方案,可以确保求解器的二阶精度。尖锐的界面浸入边界方法通过局部近边界精化得到增强,以处理任意复杂的边界。离散动量方程采用无矩阵牛顿-克雷洛夫方法求解,而克雷洛夫子空间方法用于求解泊松方程。通过用已知的解析解求解泊松方程,证明了该方法在非结构化笛卡尔网格上的二阶精度。越来越复杂的许多三维层流模拟说明了该方法处理一系列雷诺数和流态的流量的能力。层流的稳态和非稳态流过一个球体,安装在两个端壁之间的圆柱体产生的倾斜涡旋流证明了精度和效率以及鳞片和连贯结构在整个精炼水平上的平稳过渡。经过微型风力涡轮机转子的大涡流模拟(LES),使用执行器线法进行了参数化,表明完全非结构化求解器能够模拟复杂的湍流。最后,通过完整的流体动力学涡轮机解决湍流的LES的几何形状说明了该方法在局部精制网格上模拟通过几何复杂体的湍流的潜力。在所有情况下,发现结果与已发布的数据非常吻合,并且节省了计算资源。 (C)2016 Elsevier Inc.保留所有权利。

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