Two-step mfs-based numerical approaches for 3D linear sloshing

This article is devoted to the numerical solution of the linear sloshing problem in a 3D tank filled with an inviscid incompressible liquid. The problem is reformulated as a linear evolution problem on a free surface with the operator coefficient. First, using either the Laguerre transformation or the Houbolt scheme with respect to time, we reduce the non-stationary problem to a recurrent sequence of operator equations. Then the method of fundamental solutions is used. As a result, a sequence of systems of linear equations with the same matrix and recurrent right-hand sides is obtained. The conditional convergence and stability properties of the proposed two-step methods are discussed. At the end numerical experiments are presented to confirm the effectiveness of the proposed approach.