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An interpolation-free ALE scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids

机译:三维自适应网格上具有大边界位移的非定常无粘性流计算的无插值ALE方案

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摘要

A novel strategy to solve the finite volume discretization of the unsteady Euler equations within the Arbitrary Lagrangian–Eulerian framework over tetrahedral adaptive grids is proposed. The volume changes due to local mesh adaptation are treated as continuous deformations of the finite volumes and they are taken into account by adding fictitious numerical fluxes to the governing equation. This peculiar interpretation enables to avoid any explicit interpolation of the solution between different grids and to compute grid velocities so that the Geometric Conservation Law is automatically fulfilled also for connectivity changes. The solution on the new grid is obtained through standard ALE techniques, thus preserving the underlying scheme properties, such as conservativeness, stability and monotonicity. The adaptation procedure includes node insertion, node deletion, edge swapping and points relocation and it is exploited both to enhance grid quality after the boundary movement and to modify the grid spacing to increase solution accuracy. The presented approach is assessed by three-dimensional simulations of steady and unsteady flow fields. The capability of dealing with large boundary displacements is demonstrated by computing the flow around the translating infinite- and finite-span NACA 0012 wing moving through the domain at the flight speed. The proposed adaptive scheme is applied also to the simulation of a pitching infinite-span wing, where the bi-dimensional character of the flow is well reproduced despite the three-dimensional unstructured grid. Finally, the scheme is exploited in a piston-induced shock-tube problem to take into account simultaneously the large deformation of the domain and the shock wave. In all tests, mesh adaptation plays a crucial role.
机译:提出了一种新颖的策略来解决四面体自适应网格上任意Lagrangian-Eulerian框架内非定常Euler方程的有限体积离散化。由于局部网格自适应而引起的体积变化被视为有限体积的连续变形,并通过在控制方程式中添加虚拟数值通量来考虑它们。这种特殊的解释可以避免对不同网格之间的解决方案进行任何显式内插,并可以计算网格速度,从而对于连通性变化也自动满足几何守恒定律。新网格上的解决方案是通过标准ALE技术获得的,因此保留了基本的方案属性,例如保守性,稳定性和单调性。自适应过程包括节点插入,节点删除,边缘交换和点重定位,并且可以利用该过程既提高边界移动后的网格质量,又修改网格间距以提高求解精度。通过对稳态和非稳态流场进行三维模拟来评估所提出的方法。通过计算在飞行速度下通过平移的无限和有限跨NACA 0012机翼周围的气流,证明了处理大边界位移的能力。所提出的自适应方案也被应用到俯仰无限跨机翼的仿真中,尽管具有三维非结构化网格,该流的二维特性仍能很好地再现。最后,该方案在活塞引起的激波管问题中得到了利用,同时考虑了磁畴和激波的大变形。在所有测试中,网格自适应都起着至关重要的作用。

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