Abstract

Wave-structure interaction is a topic of great interest in naval and offshore engineering. This interest is growing in the last years due to the boost given by the development of the marine renewable energy field. In this context the development of an efficient time-domain coupled waves-structure solver is a main request from the industry.

Up to date the numerical seakeeping simulation has been mostly carried out using the frequency domain. The reason might be that the computational cost of time domain simulations were too high and computational time was too large. Moreover assumptions like linear waves and the harmonic nature of water waves made the frequency domain to be the right choice. However nowadays computing capabilities make possible to carry out numerical simulations in the time domain in a reasonable time, with the advantage of making easier the introduction of non-linearities into the algorithm and therefore coupling with other phenomena.

This presentation shows the work of the authors in developing a time-domain unstructured Finite Element Method (FEM) algorithm for analysis of coupled wave-structure interaction. For this purpose, a new diffraction-radiation solver using the FEM was developed. The solver has been implemented in GPU, using CUDA architecture. The speed-up obtained ranges from 5 to 10 times compare to the implementation in a standard CPU with a conjugate gradient and ILU preconditioner.

The seakeeping analysis tool has been integrated within a coupled waves-structure analysis tool. The coupling algorithm is based on a partitioned iterative algorithm, using an interpolation library able to communicate pressure forces and displacements of the structure at memory level. Furthermore, an innovative wetting and drying scheme able to improve the evaluation of the water action on the structure.

The accuracy of the new seakeeping formulation for analysis of waves and floating structures interaction has been verified in different validation cases and practical applications. 

Abstract

This paper presents advances in recent work of the authors to derive a fractional step scheme based on the stabilized finite element method that allows overcoming the above mentioned problem, resulting in a efficient time accurate scheme.

The starting point is the modified governing differential equations for the incompressible turbulent viscous flow and the free surface condition incorporating the necessary stabilization terms via a finite calculus (FIC) procedure developed by the authors .  This technique is based on writting the different balance equations over a domain of finite size and retaining higher order terms. These terms incorporate the ingredients for the necessary stabilization of any transient and steady state numerical solution already at the differential equations level.

The resulting stabilized equations are integrated in space using the standard finite element method, and in time using an implicit and uncoupled second order fractional step method.

Abstract

The Semi-Lagrangian Particle Finite Element Method (SL-PFEM) is a numerical method tailored for solving the fluid dynamics equations. Despite of its excellent numerical properties, such as a minimum numerical erosion in the convective transport and that it exhibits great stability, it  has not yet received much attention in the scientific literature. In this presentation, a second order SL-PFEM scheme for solving the incompressible Navier-Stokes equations is presented. This scheme is based on the second order velocity Verlet algorithm, which uses an explicit integration for the particle’s trajectory and an implicit integration for the velocity. The algorithm is completed with a predictor-multicorrector scheme for the integration of the velocity correction using the Finite Element Method. A second order projector based on least squares is used to transfer the intrinsic variables information from the particles onto the background mesh, while a second order interpolation scheme is used to transfer the pressure gradient and viscous accelerations from the mesh to the particles.