基于间断有限元方法的可压缩水高速冲击平板特性研究

摘要

Based on Arbitrary Lagrangian-Eulerian method, an inviscid model is established to inves-tigate high velocity water impact problems.In order to capture the pressure wave, the Arbitrary La-grangian-Eulerian Discontinuous Galerkin method is proposed to simulate the two-dimensional flow of water jet impact on rigid plates. Discontinuous Galerkin method can be able to achieve high order of spatial accuracy and stability. The physics of wave propagation can be obtained exactly by solving the Riemann problem. For fluid domain deformation, radial basis function method is employed to de-rive the velocities of the internal fluid nodes given the velocities of the boundary nodes, which needs no grid connectivity information. The water jets with flat or round head impact are investigated. For water jet with flat head, the pressure at the center of rigid plate is in good agreement with those by AutoDyn-2D solver. The results show that compressibility plays an important role during the high speed water impact process, as the pressure wave is generated upon impact and propagated into wa-ter domain. A larger pressure can also be observed during the water jet with round head impact pro-cess.%基于任意欧拉拉格朗日（ALE）方法，忽略流体的粘性，建立水射流冲击刚性平板的数值模型。为了更为精确地捕捉流场中压力波，该文推导了在ALE框架下的间断有限元方法。该方法易于提高数值离散的空间精度，数值稳定性较　　好，利于精确模拟高速水射流冲击过程。对于自由液面的变形，采用径向基函数方法确定网格单元的速度。该方法采用边界网格节点的信息去推导出内部网格节点的信息，不需要单元信息。平头水柱射流冲击的数值结果与Autodyn的数值结果吻合较好。在验证方法合理性的基础上，文中对平头及圆头水柱中压力波的分布特性进行了分析。数值结果表明：当冲击在平板表面时，会在产生一个压力波之后向水域内传播，且使得平板受到较大压力的作用。此外，圆头水柱的射流冲击将会产生一个更大的压力峰值。