- Donescu, P. and Virgin, L.N., An implicit boundary element solution with consistent linearization for free surface flows and non-linear fluid-structure interaction of floating bodies,
International Journal for Numerical Methods in Engineering, vol. 51 no. 4
pp. 379 - 412  .
(last updated on 2007/03/23)
In this work, a new comprehensive method has been developed which enables the solution of large, non-linear motions of rigid bodies in a fluid with a free surface. The application of the modern Eulerian-Lagrangian approach has been translated into an implicit time-integration formulation, a development which enables the use of larger time steps (where accuracy requirements allow it). Novel features of this project include: (1) an implicit formulation of the rigid-body motion in a fluid with a free surface valid for both two or three dimensions and several moving bodies; (2) a complete formulation and solution of the initial conditions; (3) a fully consistent (exact) linearization for free surface flows valid for any boundary elements such that optimal convergence properties are obtained when using a Newton-Raphson solver. The proposed framework has been completed with details on implementation issues referring mainly to the computation of the complete initial conditions and the consistent linearization of the formulation for free surface flows. The second part of the paper demonstrates the mathematical and numerical formulation through numerical results simulating large free surface flows and non-linear fluid structure interaction. The implicit formulation using a fully consistent linearization based on the boundary element method and the generalized trapezoidal rule has been applied to the solution of free surface flows for the evolution of a triangular wave, the generation of tsunamis and the propagation of a wave up to overturning. Fluid-structure interaction examples include the free and forced motion of a circular cylinder and the sway, heave and roll motion of a U-shaped body in a tank with a flap wave generator. The presented examples demonstrate the applicability and performance of the implicit scheme with consistent linearization. Copyright © 2001 John Wiley and Sons. Ltd.
Boundary element method;Integration;Linearization;Theorem proving;