Numerical simulation of an array of heaving floating point absorber wave energy converters using OpenFOAM

In this paper we use the CFD toolbox OpenFOAM to perform numerical simulations of multiple floating point absorber Wave Energy Converters (WECs) in a numerical wave basin. The two-phase Navier-Stokes fluid solver is coupled with a motion solver to simulate the wave-induced rigid body heave motion. The key of this paper is to extend numerical simulations of a single WEC unit to multiple WECs and to tackle the issues of modelling individual floating objects close to each other in an array lay-out. The developed numerical model is validated with laboratory experiments for free decay tests and for a regular wave train using two or five WECs in the array. For all the simulations presented, a good agreement is found between the numerical and experimental results for the WECs’ heave motions, the surge forces on the WECs and the perturbed wave field. As a result, our coupled CFD–motion solver proofs to be a suitable and accurate toolbox for the study of wave-structure interaction problems of multiple floating bodies in an array configuration

Precessional switching of thin nanomagnets: analytical study

We study analytically the precessional switching of the magnetization of a thin macrospin. We analyze its response when subjected to an external field along its in-plane hard axis. We derive the exact trajectories of the magnetization. The switching versus non switching behavior is delimited by a bifurcation trajectory, for applied fields equal to half of the effective anisotropy field. A magnetization going through this bifurcation trajectory passes exactly along the hard axis and exhibits a vanishing characteristic frequency at that unstable point, which makes the trajectory noise sensitive. Attempting to approach the related minimal cost in applied field makes the magnetization final state unpredictable. We add finite damping in the model as a perturbative, energy dissipation factor. For a large applied field, the system switches several times back and forth. Several trajectories can be gone through before the system has dissipated enough energy to converge to one attracting equilibrium state. For some moderate fields, the system switches only once by a relaxation dominated precessional switching. We show that the associated switching field increases linearly with the damping parameter. The slope scales with the square root of the effective anisotropy. Our simple concluding expressions are useful to assess the potential application of precessional switching in magnetic random access memories

Double smoothing technique for infinite-dimensional optimization problems with applications to optimal control

In this paper, we propose an efficient technique for solving some infinite-dimensional problems over the sets of functions of time. In our problem, besides the convex point-wise constraints on state variables, we have convex coupling constraints with finite-dimensional image. Hence, we can formulate a finite-dimensional dual problem, which can be solved by efficient gradient methods. We show that it is possible to reconstruct an approximate primal solution. In order to accelerate our schemes, we apply double-smoothing technique. As a result, our method has complexity O (1/[epsilon] ln 1/[epsilon]) gradient iterations, where [epsilon] is the desired accuracy of the solution of the primal-dual problem. Our approach covers, in particular, the optimal control problems with trajectory governed by a system of ordinary differential equations. The additional requirement could be that the trajectory crosses in certain moments of time some convex sets.convex optimization, optimal control, fast gradient methods, complexity bounds, smoothing technique