Boundary Element Analysis of Non-Linear Liquid Motion in Two-Dimensional Containers

Summary

The nonlinear behavior of an incompressible and frictionless liquid with a free surface in two-dimensional containers with various kinds of shapes is analyzed numerically by the boundary element method based on the mixed Eulerian-Lagrangian procedure. The boundary-value problem of Iaplace equation described with the Euler coordinates is solved by means of the direct boundary element method with use of the simplest element (i.e the constant element). On the other hand, the initial-value problem of the free surface conditions given as the evolutional form in terms of the Lagrangian coordinates of a fluid particle on the free surface is solved approximately by using the simples time integration scheme (i.e. Euler scheme). In order to keep on stably numerical performance some effective solution procedures, which are a smoothing technique, an adaptive refinement of mesh and a relocation, are introduced. Applicability and efficiency of the method are examined through sloshing problems in two-dimensional containers subjected to forced acceleration with large amplitude.