A Novel 2D BEM with Composed Elements to Study Sloshing Phenomenon


School of mechanical engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran.


In the Boundary Element Method (BEM), the corner elements make some difficulties in the numerical method. It means that, the results of BEM solution with linear elements are more accurate than constant elements inherently, but the difference between boundary conditions of one corner node from two adjacent boundaries causes to increase errors in linear element in comparison of constant element. In this article, a new approach of BEM discretizing has been introduced for simulating water sloshing in a 2D rectangular container which augments the accuracy. The time history of free surface shape has been obtained by applying Finite Difference Method (FDM) for free surface boundary conditions and BEM direct method with constant, linear and a novel element which has been named composed element in this study. Composed elements have been proposed for solving corner nodes problem. It means that all of the elements are linear except common nodes in two adjacent boundaries which are selected constant. This solution causes to decrease the number of elements for an acceptable precision and hence the time considerably saves potential flow and small amplitude water wave assumptions were applied in the present research. The results of this analysis illustrated acceptable agreement with other articles results with large dimension and small amplitude water wave assumptions. As a final point, the accuracy of results increased respect to linear, constant and composed elements.