A natural element updated Lagrangian strategy for free-surface fluid dynamics

We present a novel algorithm to simulate free-surface fluid dynamics phenomena at low Reynolds numbers in an updated Lagrangian framework. It is based on the use of one of the most recent meshless methods, the so-called natural element method. Free-surface tracking is performed by employing a particular instance of “shape constructors” called α-shapes. This means that at each time step the geometry of the domain is extracted by employing a particular member of the finite set of shapes described by the nodal cloud. The Lagrangian framework allows us to integrate the inertial terms of the Navier–Stokes equations by employing the method of characteristics which are, precisely, the nodal pathlines. A theoretical description of the method is included together with some examples showing its performance.