In this paper a Lagrangian formulation of the Natural Element Method (NEM) is proposed to solve shallow water inviscid flows. NEM is a particle‐based method which revealed its capabilities in handling large distortion problems. Its main advantage is the interpolant character of its shape function and consequently the easiness of imposing Dirichlet boundary conditions.
In this paper we use the NEM method in a collocation form and in a Lagrangian kinematic description. This formulation is found to be a finite volume methodology with flux computation on the Voronoï diagram of the standard triangular or quadrilateral meshes. The Shallow‐Water equations are used as the mathematical model. Besides the Lagrangian behavior of the flow which is difficult to capture, these equations have discontinuous solutions. Thus, stabilization issues have been considered. Some inviscid bidimensional flows are used as preliminary benchmark tests. This kind of flows is similar to that of metal casting. Good results were found which promise an interesting future for this method in more complicated applications.
