Using mesh-free natural element numerical method in simulation of free surface flow in sudden expansion

The present paper is aimed to study performance of mesh-free natural element method in solving free surface shallow water equations. Natural element method is based on natural neighbor interpolation. In this research Sibson interpolation has been used. Due to inappropriateness of Gaussian integration, Nodal integration has been applied in present research. In order to validate the method, two-dimensional problem of subcritical shallow water flows in expansion has been analyzed and results were compared with experimental interpretations. In addition, in order to evaluate performance of the presented method, results were compared with those of finite volume method. Findings suggest that natural element method is relatively superior to finite volume method.

Keywords:

shallow water equations , mesh-free natural element method , Sibson interpolation , nodal integration