Unstructured grid arbitrarily shaped element method for fluid flow simulation

A three-dimensional unstructured grid arbitrarily shaped element method is developed for solving the Navier-Stokes equations. The proposed method is g enerally applicable to arbitrarily shaped elements and, thus, offers the po tential to unify many of the different grid topologies into a single formul ation Examples of grid topologies include a structured hexahedral mesh; uns tructured tetrahedral mesh; hybrid mesh using a combination of hexahedra, t etrahedra, prisms, and pyramids; Cartesian mesh with elements (cubes) cut b y now boundaries; and mixed arbitrary multiblock meshes. The concept of suc h an arbitrary element method is developed and implemented into a pressure- based finite volume solver. It utilizes a collocated and cell-centered stor age scheme. Expressions for second-order discretizatious of the convection and diffusion terms are derived and presented for an arbitrarily shaped ele ment. The developed code, as a first step, is applied to two selected three dimensional viscous flows using a structured hexahedral mesh and an unstru ctured tetrahedral mesh. It is demonstrated that the concept of the arbitra rily shaped element method can be viable and efficient.