An efficient quasi‐Newton method for 2D steady free surface flow,International Journal for Numerical Methods in Fluids

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An efficient quasi‐Newton method for 2D steady free surface flow
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-01-17 , DOI: 10.1002/fld.4806
Toon Demeester ₁ , E. Harald Brummelen ₂ , Joris Degroote _{1,

3}

Affiliation

Steady free surface flows are of interest in the fields of marine and hydraulic engineering. Fitting methods are generally used to represent the free surface position with a deforming grid. Existing fitting methods tend to use time-stepping schemes, which is inefficient for steady flows. There also exists a steady iterative method, but that one needs to be implemented with a dedicated solver. Therefore a new method is proposed to efficiently simulate two-dimensional (2D) steady free surface flows, suitable for use in conjunction with black-box flow solvers. The free surface position is calculated with a quasi-Newton method, where the approximate Jacobian is constructed in a novel way by combining data from past iterations with an analytical model based on a perturbation analysis of a potential flow. The method is tested on two 2D cases: the flow over a bottom topography and the flow over a hydrofoil. For all simulations the new method converges exponentially and in few iterations. Furthermore, convergence is independent of the free surface mesh size for all tests.

中文翻译：

二维稳态自由表面流的有效拟牛顿法

稳定的自由表面流动在海洋和水利工程领域很受关注。拟合方法通常用于用变形网格表示自由表面位置。现有的拟合方法倾向于使用时间步长方案，这对于稳定流来说效率低下。还有一种稳定的迭代方法，但需要使用专用求解器来实现。因此，提出了一种新方法来有效模拟二维 (2D) 稳定自由表面流，适合与黑盒流求解器结合使用。自由表面位置是使用拟牛顿法计算的，其中近似雅可比行列式是通过将过去迭代的数据与基于势流扰动分析的分析模型相结合以一种新颖的方式构建的。该方法在两个 2D 案例上进行了测试：流过底部地形和流过水翼。对于所有模拟，新方法以指数方式收敛，并且迭代次数很少。此外，收敛与所有测试的自由表面网格大小无关。

更新日期：2020-01-17

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