Reduced Order Modeling (ROM) based method for the two-dimensional water exit problem using snapshot Proper Orthogonal Decomposition (POD) and CFD simulations

In this paper, the concepts of snapshot Proper Orthogonal Decomposition (POD) and Reduced Order Modeling (ROM) are combined (referred to the POD-ROM method) to solve the two-dimensional (2D) water exit problem. Attention is paid to the pressure distribution along the wetted surface of the body. Computational Fluid Dynamics (CFD) simulations are employed to obtain high-fidelity data on pressure distribution. After applying snapshot POD, it is found that two POD basis modes for the wedge model and three modes for the ship section model are adequate to capture dynamic features of the pressure distribution without losing too much detail. It can also be observed that neither the body motion state nor the initial immersion condition influences all POD functions of the wedge model, but the temporal POD functions of the ship section model are significantly dependent on the initial immersion height. A group of empirical formulae is provided to deal with this issue. The validity and reliability of our POD-ROM method are assessed by investigating water exit cases with both constant and time-varying body accelerations. In this context, after deriving POD functions of any given 2D body from a single CFD simulation, predictions of the pressure distribution along the body can be facilitated for further water exit cases.