Sharif Digital Repository

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... 

Employing a biharmonic boundary integral method with linear elements, coarsening dynamics of nanodroplets on topographical step heterogeneity is investigated. It is shown that the step height and droplet configuration have an influential effect on the dynamics. Increasing the step height slows down the process while locating the droplets close to the step boosts the coarsening rate. Considering a slip boundary condition enhances the dynamics and reveals a transition in the droplet migration direction. Our results reveal that increasing the surface wettability weakens the dynamics. Various types of the disjoining pressure over the step are also considered and their effects on the coarsening... 

The most suitable and widely used numerical integration method for boundary integrals in the BEM method is Gauss-Legendre integration. But, this integration method is not appropriate for singular and nearly singular integrations in BEM. In this study, some criteria are introduced for recognizing nearly singular integrals in the integral form of the Laplace equation. At the first stage, a criterion is obtained for the constant element and, at the later stages, higher order elements are investigated. In the present research, the Romberg integration method is used for nearly singular integrals. The results of this numerical method have good agreement with analytical integration. The singular...