Skew-symmetric convection form and secondary conservative finite difference methods for moving grids
Skew-symmetric convection form and secondary conservative finite difference methods for moving grids
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DOI：
10.1016/j.jcp.2013.01.040
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Yohei Morinishi;K. Koga
中科院分区：
文献类型：
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作者：
Yohei Morinishi;K. Koga
对流项的二次守恒有限差分法被认为是非定常流动模拟的有用工具。然而，二次守恒对流格式和相关的斜对称形式尚未扩展到移动网格。本文提出了ALE型动网格模拟的斜对称格式和二次守恒对流格式。对于移动网格模拟，度量和雅可比矩阵的几何守恒律（GCL）被认为是捕获均匀流的数学约束。一个新的角色的GCL揭示关联的可扩展性和守恒性质的对流计划。然后分别对可压缩流和不可压缩流构造了移动网格下的二次守恒对流格式。对于可压缩流动，有必要引入激波捕捉方法来解决间断问题。然而，激波捕捉方法并不适用于湍流模拟，因为它们的过度数值耗散。另一方面，二次保守有限差分法对于具有不连续性的流动并不适用。在这项研究中，我们还提出了一种计算技术，结合激波捕捉和二次守恒有限差分方法。为了检验对流格式的收敛性和守恒性，在移动网格上对可压缩和不可压缩无粘周期性流动进行了数值试验。通过活塞问题、俯仰翼型绕流和振荡方柱绕流的数值计算，验证了格式的可靠性。
The secondary conservative finite difference method for the convective term is recognized as a useful tool for unsteady flow simulations. However, the secondary conservative convection scheme and associated skew-symmetric form have not been extended to those for moving grids. In this study, the skew-symmetric form and the secondary conservative convection schemes for ALE type moving grid simulations are proposed. For the moving grid simulations, the geometric conservation law (GCL) for metrics and the Jacobian is known as a mathematical constraint for capturing a uniform flow. A new role of the GCL is revealed in association with the commutability and conservation properties of the convection schemes. The secondary conservative convection schemes for moving grids are then constructed for compressible and incompressible flows, respectively. For compressible flows, it is necessary to introduce a shock capturing method to resolve discontinuities. However, the shock capturing methods do not work well for turbulent flow simulations because of their excessive numerical dissipation. On the other hand, the secondary conservative finite difference method does not work well for flows with discontinuities. In this study, we also present a computational technique that combines the shock capturing and the secondary conservative finite difference methods. In order to check the commutability and conservation properties of the convection schemes, numerical tests are done for compressible and incompressible inviscid periodic flows on moving grids. Then, the reliabilities of the schemes are demonstrated on the piston problem, the flow around pitching airfoil, and the flow around an oscillating square cylinder.