Multimodal method in sloshing - Lukovsky, I.O.; Tymokha, O.M. (Нелінійні коливання, 2015)
The multimodal method reduces the free-surface sloshing problem to a (modal) system of nonlinear ordinary differential equations. The method was originally proposed for nonimpulsive hydrodynamic loads but, recently, it was successfully extended to the sloshing-induced slamming. In the 50 – 60’s, the method was employed in the Computational Fluid Dynamics (CFD) but has lost the contest the algorithms of the 90-00’s. Nowadays, the method plays the dual role: firstly, as a unique analytical tool for studying nonlinear sloshing regimes, their stability, and chaos as well as for simulations when traditional CFD fails (e.g., containers with a perforated screen) and, secondly, as a source of the modal systems which are analogies of the Kordeweg – de Vries, Boussinesq etc. equations but for the contained liquid. The paper surveys the state-of-the-art and existing modal systems, specifies open problems.