We present a smooth particle hydrodynamics (SPH) formulation that captures the sloshing frequencies of tanks and accurately simulates long-duration violent sloshing in partially filled tanks of arbitrary shape. The SPH simulations are performed using a modified version of the open-source code DualSPHysics that incorporates a density-based stabilization (δ-SPH) and imposes wall boundary conditions via ghost particles in order to achieve pressure fields without spurious spatial oscillations and to reduce non-physical energy dissipation. We verify the SPH scheme by showing that calculated sloshing wave heights, forces and natural sloshing frequencies of tanks of simple shapes, namely rectangular, cylindrical upright and spherical, match the analytical values given by the potential theory in the linear regime. The scheme is then validated by predicting the sloshing frequencies obtained experimentally in a toroidal tank and in a pill-shaped tank. Finally, we present a study of a pill-shaped tank subject to a long period of external forcing comparing simulated sloshing forces to experimental values obtained by ESA/ESTAC. The simulation is shown to fairly accurately reproduce the sloshing forces and predict the transition to swirling wave motion. Analysis of the frequency range further showed good agreement of the dominant frequencies between the experimental and simulated forces.

我们提出了一种光滑的颗粒流体动力学（SPH）公式，该公式捕获了油箱的晃动频率，并准确模拟了任意形状的部分填充的油箱中的长时间剧烈晃动。SPH仿真使用开源代码DualSPHysics的修改版本执行，该版本结合了基于密度的稳定化（δ-SPH），并通过幻影粒子施加了壁边界条件，从而获得了压力场而没有虚假的空间振荡并减少了噪声。 -物理能量耗散。我们通过显示计算得出的简单波箱（矩形，圆柱直立和球形）的晃动波高，力和自然晃动频率与线性方案中的势能理论给出的分析值相符，从而验证了SPH方案。然后通过预测在环形水箱和药丸状水箱中实验获得的晃动频率来验证该方案。最后，我们提出了一种药丸形储罐的研究，该储罐受到长期的外力作用，将模拟晃动力与ESA / ESTAC获得的实验值进行比较。该仿真显示可以相当准确地再现晃动力并预测到旋涡运动的过渡。频率范围的分析进一步表明，实验力和模拟力之间的主频率有很好的一致性。该仿真显示可以相当准确地再现晃动力并预测到旋涡运动的过渡。频率范围的分析进一步表明，实验力和模拟力之间的主频率有很好的一致性。该仿真显示可以相当准确地再现晃动力并预测到旋涡运动的过渡。频率范围的分析进一步表明，实验力和模拟力之间的主频率有很好的一致性。