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.
翻译:这项工作讨论了根据潜在流理论在水浪流模拟中规定的完全非线性自由地表边界条件的正确建模问题。这种讨论的主要目的是确定数学配方和数字处理方法,既可用于进行瞬态模拟,又可用于计算稳定的解决办法 -- -- 对任何流动都予以接受。在关于数字拖车罐的文献中,稳定且不固定的完全非线性潜在流量溶解器的特征是不同的数学配方。讨论了动态和非线性完全非线性地表边界条件,特别是证明以半Lagrangian形式编写的运动自由地表边界条件可以被操纵,通过所有与漂浮体表面或盆地底部使用的相同的方式获得替代的非渗透边界条件。通过边界EEM方法(BEM)和隐含性的后向差异公式(BDF)方案,获得的简化的数学问题在空间和时间上是分解的。结果证实,所实施的解算器能够解决稳定的潜在流动问题,只要消除不固定时间衍生物,就可以稳定地稳定地稳定地稳定地稳定地稳定地复制流。