具有完全非线性自由表面边界条件的水动力势流模拟的统一稳态与非稳态公式
A unified steady and unsteady formulation for hydrodynamic potential flow simulations with fully nonlinear free surface boundary conditions
AI总结：
本文提出统一的稳态与非稳态完全非线性势流公式，通过将半拉格朗日自由表面条件改写为非穿透条件，并结合BEM与隐式BDF离散，使同一求解器可准确处理瞬态和经典稳态水波问题。
摘要：
本工作讨论了在基于势流理论的水波流动模拟中需要给定的完全非线性自由表面边界条件的正确建模。这一讨论的主要目标是确定一种数学公式和数值处理方法，使其既能用于开展瞬态模拟，也能用于计算任何存在稳态解的流动的稳态解。事实上，在数值拖曳水池的文献中，稳态和非稳态完全非线性势流求解器具有不同的数学公式。本文讨论了运动学和动力学完全非线性自由表面边界条件，尤其证明了以半拉格朗日形式写出的运动学自由表面边界条件可以经过变换，推导出另一种非穿透边界条件，该条件在各方面都与浮体表面或水池底部所使用的条件相同。所得的简化数学问题分别通过边界元法（BEM）和隐式后向差分公式（BDF）格式在空间和时间上进行离散。结果证实，所实现的求解器仅通过消去非稳态公式中的零时间导数，便能够求解稳态势流问题。所得数值结果证实，所实现的求解器能够准确复现文献中现有经典稳态流动求解器的结果。
英文摘要：
This work discusses the correct modeling of the fully nonlinear free surface boundary conditions to be prescribed in water waves flow simulations based on potential flow theory. The main goal of such a discussion is that of identifying a mathematical formulation and a numerical treatment that can be used both to carry out transient simulations, and to compute steady solutions -- for any flow admitting them. In the literature on numerical towing tank in fact, steady and unsteady fully nonlinear potential flow solvers are characterized by different mathematical formulations. The kinematic and dynamic fully nonlinear free surface boundary conditions are discussed, and in particular it is proven that the kinematic free surface boundary condition, written in semi-Lagrangian form, can be manipulated to derive an alternative non penetration boundary condition by all means identical to the one used on the surface of floating bodies or on the basin bottom. The simplified mathematical problem obtained is discretized over space and time via Boundary Element Method (BEM) and Implicit Backward Difference Formula (BDF) scheme, respectively. The results confirm that the solver implemented is able to solve steady potential flow problems just by eliminating null time derivatives in the unsteady formulation. Numerical results obtained confirm that the solver implemented is able to accurately reproduce results of classical steady flow solvers available in the literature.
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