Abstract

A finite element method for the solution of the up-to-second-order wave diffraction-radiation problem in the time-domain is proposed. The solver has been validated against experimental data available for the HiPRWind semisubmersible platform (designed for floating wind turbines). To perform the validation, the wave diffraction-radiation solver is coupled to a body dynamics and mooring solvers in the time-domain. The HiPRWind movements and mooring forces have been compared for a large number of test cases, including decay tests, bichromatic, and irregular waves. Good agreement has been found for both, body movements and mooring forces.

Abstract

This work presents a novel proposal of a second-order accurate (in time and space) particle-based method for solving transport equations including incompressible flows problems within a mixed Lagrangian–Eulerian formulation. This methodology consists of a symmetrical operator splitting, the use of high-order operators to transfer data between the particles and the background mesh, and an improved version of the eXplicit Integration Following the Streamlines (X–IVS) method. In the case of incompressible flows, a large time-step iterative solver is employed where the momentum equation is split to improve the numerical approximation of the convective term.

New interpolation and projection operators are evaluated and quadratically accurate solutions of scalar transport tests are presented. Then, incompressible flow problems are solved where the rate of convergence of the method is assessed using both structured and unstructured background grids. The method is implemented in the open source platform OpenFOAM®allowing employing arbitrary meshes and obtaining reliable computing time comparisons with standardized solvers. The results obtained reveal that the current method is able to obtain a lower level of error than a fast Eulerian alternative, without increasing the total computing time.

Abstract

In this paper, 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 accelerations from the mesh to the particles. Convergence analyses are carried out to assess the second order convergence.