A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented . The theory of the stability and feasibility of the hyperbolic grid generation method is presented . The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer . The grid , however , retains structure in the body - normal direction and has a computational cell shaped like a triangular prism . In order to take advantage of the structure in the normal direction , a finite - volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated .