Search

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. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

The paper proposes a numerical technique based on the finite volume method for solving the three-dimensional unsteady viscous over a backward facing step. The mathematical model is based on the momentum and continuity equations written for the uncompressible viscous flow. Closure to the turbulence is considered by employing the LES model. The convergence of the unsteady solution is realized through an iterative process within the limits of an error imposed apriori. The engineering application spectrum is represented by the several practical flow cases over sudden expanded domains. The study emphasizes the 3D vortical character of the flow that was observed during the experiments. The theoretical relevance of the work consists in the originality of the numerical method employed to solve the aforementioned equations. [ABSTRACT FROM AUTHOR]