Numerical simulation of free surface flows interacting with flexible structures

Abstract

Efficient numerical methods to simulate free-surface flows interacting with flexible structures are of great interest for enhancing, for instance, the design of marine structures. However, numerical instabilities can occur due to the unsteady free surface flow domain that induces abruptly changing loading conditions on the structure. Common simulation methods also require very small time-steps to accurately capture the free surface flow dynamics, resulting in excessively long computational times. In order to overcome these issues, this work focuses on developing a new efficient and stable free surface flow formulation and its integration in a partitioned fluid-structure interaction (FSI) approach to allow for the simulation of this multiphysics phenomenon. The free surface flow dynamics are described with the one-fluid formulation of the Navier-Stokes equations and the Volume of Fluid (VoF) method formulated in the arbitrary Lagrangian-Eulerian (ALE) framework. The implementations are made within the in-house finite volume solver FASTEST. First, a more efficient pressure-velocity coupling algorithm is developed. It is an enhanced SIMPLE algorithm with extra correction steps that achieves a better convergence rate of the velocity and pressure fields. Second, the fluid flow interface is captured with an interface capturing scheme implemented through the new Modified Normalized Weighting Factor (MNWF) method. The MNWF method improves the convergence rate and stability of the schemes for medium to high Courant numbers. Thus, larger time-steps can be used, reducing the computational time. Finally, the free-surface flow formulation is integrated into a partitioned FSI approach. The preCICE coupling tool implicitly couples the free surface code of FASTEST with the structural finite element program CalculiX. The developed solution algorithm and its parts are validated and used to solve benchmark test cases. The obtained results are in perfect accordance with the literature references, and the approach shows a positive effect on accuracy, computational time, and stability.