A natural extension of the conventional finite volume method into polygonal unstructured meshes for CFD application.

A new general cell-centered solution procedure based upon the conventional control or finite volume (CV or FV) approach has been developed for numerical heat transfer and fluid flow which encompasses both structured and unstructured meshes for any kind of mixed polygon cell. Unlike conventional FV methods for structured and block structured meshes and both FV and FE methods for unstructured meshes, the irregular control volume (ICV) method does not require the shape of the element or cell to be predefined because it simply exploits the concept of fluxes across cell faces. That is, the ICV method enables meshes employing mixtures of triangular, quadrilateral, and any other higher order polygonal cells to be exploited using a single solution procedure. The ICV approach otherwise preserves all the desirable features of conventional FV procedures for a structured mesh; in the current implementation, collocation of variables at cell centers is used with a Rhie and Chow interpolation (to suppress pressure oscillation in the flow field) in the context of the SIMPLE pressure correction solution procedure. In fact all other FV structured mesh-based methods may be perceived as a subset of the ICV formulation. The new ICV formulation is benchmarked using two standard computational fluid dynamics (CFD) problems i.e., the moving lid cavity and the natural convection driven cavity. Both cases were solved with a variety of structured and unstructured meshes, the latter exploiting mixed polygonal cell meshes. The polygonal mesh experiments show a higher degree of accuracy for equivalent meshes (in nodal density terms) using triangular or quadrilateral cells; these results may be interpreted in a manner similar to the CUPID scheme used in structured meshes for reducing numerical diffusion for flows with changing direction.

Molecular dynamics simulation of fractures using an N-body potential

Molecular dynamics has been employed to model the fracture of a twodimensional triangular atomic lattice. The N-body Sutton-Chen potential developed for fcc metals and its extended version (Rafii-Tabar and Sutton) for fcc random binary alloys were used for the interatomic interactions. It is shown that at low temperatures cleavage fractures can occur in both an elemental metal and an alloy. At elevated temperatures the nucleation of dislocations is shown to cause a brittle-to-ductile transition. For the brittle crack propagation in the elemental metal, crack propagation speeds have been computed for different stress rates, and a crack instability found to exist as the speed reaches a critical value of about 32% of the Rayleigh wave speed. For the random alloy, we find that the dislocation movement can be affected by the distorted lattice.

Molecular dynamics simulation of fractures using an N-body potential

Molecular dynamics has been employed to model the fracture of a two dimensional triangular atomic lattice. The N-body Sutton-Chen potential developed for fcc metals and its extended version (Rafii-Tabar and Sutton) for fcc random binary alloys were used for the interatomic interactions. It is shown that at low temperatures cleavage fractures can occur in both an elemental metal and an alloy. At elevated temperatures the nucleation of dislocations is shown to cause a brittle-to-ductile transition. For the brittle crack propagation in the elemental metal, crack propagation speeds have been computed for different stress rates, and a crack instability found to exist as the speed reaches a critical value of about 32% of the Rayleigh wave speed. For the random alloy, we find that the dislocation movement can be affected by the distorted lattice.