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波浪-复杂外形刚性浮体相互作用的多分辨率MPS数值模拟

MULTI-RESOLUTION MPS MODELING OF WAVE-COMPLEX SHAPED RIGID FLOATING BODY INTERACTIONS

  • 摘要: 波浪作用下复杂几何形状浮体的运动响应涉及自由液面演化、浮体大幅运动以及不规则壁面边界处理等问题. 采用单一分辨率移动粒子半隐式法(Moving Particle Semi-implicit, MPS)进行数值模拟时, 为保证计算精度, 通常需要在整个计算域内布置高分辨率粒子, 因而导致较高的计算成本. 针对上述问题, 本文开发了一种基于虚拟格子边界模型(Ghost Cell Boundary, GCB)的多分辨率MPS与刚体耦合算法, 用于模拟规则波作用下复杂几何形状刚性浮体的运动响应. 该方法采用拉格朗日形式的MPS方法描述流体运动, 并将浮体视为不发生弹性变形的刚体. 针对复杂几何形状浮体表面壁面边界处理困难的问题, 引入GCB模型, 实现复杂边界的简便、准确处理. 同时, 在波浪与浮体相互作用区域采用高分辨率粒子, 在远场区域采用低分辨率粒子, 以兼顾计算精度与计算效率. 不同分辨率粒子之间的有效相互作用范围根据粒子间距确定: 粒子间距较大时, 有效作用半径相应增大; 粒子间距较小时, 有效作用半径相应减小. 流体粒子的运动状态由核函数作用范围内的相邻粒子共同确定. 本研究基于Fortran语言自主开发数值计算程序, 实现了上述算法及相关功能. 首先, 在程序中引入数值造波功能, 并通过典型算例验证其准确性. 其次, 分别开展规则波与自由浮体及系泊浮体相互作用的数值模拟, 并将计算结果与参考文献及商业软件结果进行对比, 验证了所开发耦合算法的有效性. 最后, 对规则波作用下复杂几何浮体的运动响应进行分析, 进一步验证了所提出数值算法在海洋工程问题中的适用性.

     

    Abstract: The motion responses of complex-shaped floating bodies under wave action involve several challenging issues, including free-surface evolution, large-amplitude body motions, and the treatment of irregular wall boundaries. When the single-resolution Moving Particle Semi-implicit (MPS) method is employed, high-resolution particles generally need to be distributed throughout the entire computational domain to ensure numerical accuracy, resulting in substantial computational cost. To address this issue, a multi-resolution MPS-rigid body coupling algorithm based on the Ghost Cell Boundary (GCB) model is developed to simulate the motion responses of complex-shaped rigid floating bodies subjected to regular waves. In the proposed method, fluid motion is described using the Lagrangian MPS formulation, while the floating body is treated as a rigid body without elastic deformation. To overcome the difficulty in imposing wall boundary conditions on complex-shaped body surfaces, the GCB model is introduced to enable convenient and accurate treatment of complex boundaries. Meanwhile, high-resolution particles are employed in the wave-body interaction region, whereas low-resolution particles are used in the far-field region, thereby achieving a balance between computational accuracy and efficiency. The effective interaction range between particles of different resolutions is determined according to the particle spacing. A larger particle spacing corresponds to a larger effective interaction radius, whereas a smaller particle spacing leads to a smaller interaction radius. The motion state of each fluid particle is determined collectively by its neighboring particles within the support domain of the kernel function. A numerical program was independently developed in Fortran to implement the proposed algorithm and associated computational capabilities. First, a numerical wave-generation function was incorporated into the program and validated through representative benchmark cases. Subsequently, numerical simulations of regular-wave interactions with both freely floating and moored bodies were conducted. Comparisons with results reported in the literature and those obtained using commercial software demonstrate the validity of the developed coupling algorithm. Finally, the motion responses of complex-shaped floating bodies subjected to regular waves were investigated, further confirming the applicability of the proposed numerical method to marine engineering problems.

     

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