Development and Application of Finite Volume Method for the Computation of Flows Around Moving Bodies on Unstructured, Overlapping Grids
Development and Application of Finite Volume Method for the Computation of Flows Around Moving Bodies on Unstructured, Overlapping Grids
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DOI：
10.15480/882.231
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发表时间：
2006
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影响因子：
--
通讯作者：
Hidajet Hadžić
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作者：
Hidajet Hadžić
本文介绍了一种用于运动物体周围粘性不可压缩流动数值计算的重叠网格技术的发展和应用。采用全隐式二阶有限体积法对任意形状单元组成的非结构化网格上的非定常流体流动方程进行离散求解。计算域由许多网格覆盖，这些网格彼此重叠，并且可以以任意方式相互相对移动。对于网格运动的处理，除了基于控制方程的任意拉格朗日-欧拉形式的标准方法外，还提出了一种基于控制方程的欧拉形式解的新方法。因此，网格的运动可以通过控制方程的非定常项中局部时间导数的适当近似以及在近壁区域中加入运动壁面产生的质量源/汇来考虑，而不是网格的计算。新方法允许改变网格拓扑结构，并且可以方便地与重网格技术结合使用。提出了一种求解重叠网格解耦合的特殊隐式方法。用于计算沿网格界面分布的插值单元上的变量值的插值方程是由离散化引起的线性化方程组的整体系统。在所有网格同时得到解的条件下，对该修正线性方程组进行全域求解。这种方法实现了网格间的强耦合，具有整个重叠区域解光滑唯一、收敛速度快的特点。通过调整界面质量通量，实现了被插值所违背的质量守恒。为了成功地处理身体运动，计算单元可以是主动的或被动的，这取决于它们相对于计算域的位置。在当前时间步处于计算域之外的网格单元（例如被物体覆盖）被暂时停用。当这些细胞重新进入计算域时，它们被重新激活。用这种方法可以实现任意大尺度网格分量的运动。通过将本研究中开发的方法应用于一些已知数值解或实验数据或可以使用商业软件中可用的另一种数值技术获得解的流，验证了该方法。通过系统的网格校正，对该方法的精度进行了评价。在涉及复杂和大规模身体运动的许多流中，证明了所提出的重叠网格方法的潜力及其相对于其他可用技术处理运动物体的优势。
In this thesis the development and application of an overlapping grid technique for the numerical computation of viscous incompressible f ows around moving bodies is presented. A fully-implicit second-order f nite volume method is used to discretize and solve the unsteady f uid-f ow equations on unstructured grids composed of cells of arbitrary shape. The computational domain is covered by a number of grids which overlap with each other and can move relative to each other in an arbitrary fashion. For the treatment of grid movement, besides the standard method which is based on the arbitrary Lagrangian-Eulerian formulation of the governing equations, a novel method based on the solution of the governing equations in their Eulerian formulation was developed. Thus, instead the computation of grid f uxes, the grid motion is taken into account by appropriate approximation of the local time derivative in the unsteady term of the governing equations and by adding mass sources/sinks produced by moving walls in the near-wall region. The new method allows the change in grid topology and can be conveniently used with a re-meshing technique. A special implicit procedure for coupling of the solution on overlapping grids is developed. The interpolation equations used to compute the variable values at interpolation cells distributed along grid interfaces are involved in the global system of linearized equations that arise from discretization. Such a modif ed linear equation system is solved for the whole domain providing that the solution is obtained on all grids simultaneously. In this way a strong inter-grid coupling characterized by smooth and unique solution in the whole overlapping region and a good convergence rate is achieved. The mass conservation, which is violated by interpolation, is enforced by adjusting the interface mass f uxes. For a successful handling of body motion, the computational cells are allowed to be active or passive, depending on their position relative to the computational domain. The grid cells which are at the current time step outside the computational domain (e.g. covered by a body) are temporarily deactivated. These cells are reactivated when they reenter the computational domain. In this way a motion of grid components of arbitrary large scales can be achieved. The method developed in the present study was verif ed by applying it to some f ows for which either the numerical solution or experimental data were known or the solution could be obtained using another numerical technique available in the commercial software. The accuracy of the method was assessed through the systematical grid ref nement. The potential of the proposed overlapping grid method and its advantages over other available techniques for handling moving bodies was demonstrated on a number of f ows which involve complex and large-scale body motion.