A mixed particle-mode function method for nonlinear marine fluid-structure interaction problems with free surface

Abstract

In this study, a computational model which couples particle method for fluid part and modal superposition for structure part is developed to investigate the Fluid Structure Interaction problems with free surface.

As a Lagrangian mesh-free method, the MPS (Moving Particle Semi-implicit) method is very suitable for simulating violent flows such as breaking waves on free surface. However, despite its wide range of applicability, the original MPS algorithm suffers from some inherent difficulties in obtaining an accurate fluid pressure in both spatial and time domain. Different modifications to improve the method have been proposed in the literature. In this study, the following modifications are proposed to improve the accuracy of pressure calculations and the stability of the method: i) A density error compensation source term in the pressure Poisson equation with no artificial term in the formulation, ii) New solid and free surface boundary handling methods, iii) Particle position shifting and collision handling, and iv) A new version of “cell-link” neighbour particle searching strategy, which reduces about 6.5/9 ( 72%) of the searching area compared with traditional “cell-link” algorithm. For problems where violent free surface deformation only occur in a constrained area, the efficiency of MPS is further improved by weakly coupling with BEM (Boundary Element Method).

For the structure that undergoes very large rigid motions and relatively small elastic deformation, an efficient computational model that couples the rigid-body and flexible modes in the same set of formulation. Unlike the traditional modal analysis, this model takes into account the mutual effect between rigid-body motion and flexible deformation. It is more efficient compared with FE(Finite Element) method, regardless of the size of the structure. For 2D cases,if only the first three modes are chosen to represent the flexible deformation of the structure, it only results in a 6 x 6 equation system to be solved.

For the fluid structure interaction coupling, the Gauss-Seidel iteration with Aitken relaxation scheme is used.

The effectiveness of the proposed modifications for MPS method is validated by a 2D Dam-break flow. Furthermore, various typical impact flow problems in marine engineering are simulated to test the applicability of the modified MPS method. It includes 2D/3D Dam-break with different boundary conditions (such as obstacle in the middle of the tank, spring supported rigidwall and flexible cantilever beam), liquid sloshing, wedge-shape and ship-section-shape dropping problems. The weak coupling scheme between MPS and BEM are also tested by the 2D breaking solitary wave impacting a flexible wall problem. The coupling of fluid and structure solver is also tested by various problems including 2D flexible wedge dropping and 2D/3D floating beam/ship slamming problems. The numerical results obtained are found to be in good agreement with the available numerical or experimental results. With the proposed modifications, the stability and accuracy of the pressure field are improved in spatial and time domains. The proposed structure model also proves to be effective.

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