A non-linear finite element method on unstructured meshes for added resistance in waves

Abstract

In this work a finite element method (FEM) is proposed to solve the problem of estimating the added resistance of a ship in waves in the time domain and using unstructured meshes. Two different schemes are used to integrate the corresponding free surface kinematic and dynamic boundary conditions: the first one based on streamlines integration (SLI); and the second one based on the Streamline-Upwind Petrov-Galerking (SUPG) stabilization. The proposed numerical schemes have been validated in different test cases, including towing tank tests with monochromatic waves. The results obtained in this work show the suitability of the present method to estimate added resistance in waves in a computationally affordable manner.

Fully 3D ship hydroelasticity: Monolithic versus partitioned strategies for tight coupling

“…In this work the numerical solution using FEM of the above system reported in [22,23,24] will be used. It requires to solve the following system of equations:…”

“…Where 𝐋 ̿ is the Laplacian Matrix, and the right hand side is obtained summing up the vectors 𝐛 𝐵 , 𝐛 𝑍 0 , and 𝐛 𝑆 . The right hand side are obtained from discretizing the boundary conditions using FEM as in [23,24,25]. The above system can be written clustering the nodes lying on the body surface as:…”

“…In the case of having forward speed, the free surface boundary condition is integrated using the FEM SUPG scheme with the double body lineariazation, and the numerical details can be found in [22,23]. For the zero forward speed, a fourth order compact Padé scheme is used for the free surface, and the numerical details can be found in [22,24].…”

“…It has the advantage of solving the seakeeping and structural dynamics independently using the most efficient algorithms for each one. For instance, a deflated preconditioned iterative solver could be used for the seakeeping problem [24], while a direct solver could be used for the structural solver. The main drawbacks of the partitioned strategy are that it requires a robust iterative algorithm to guarantee the convergence of the solver within every time step and that the exchange of information between the two solvers might introduce large computational overheads.…”

“…On the one hand, the hydrodynamics model is based on a first-order linear potential flow and takes into account the forward speed effect using the double body linearization. The velocity potential is solved using the FEM along with the SUPG for the free surface boundary condition [23,24,25]. On the other hand, the structural dynamics is solved using a co-rotational shell FEM model that takes into account the geometric non-linearity.…”