Investigation of the Accuracy of Finite Volume Methods for 2- and 3-Dimensional Flows

Abstract

The accuracy of finite volume methods for the discretization of the unsteady Euler equations in the cartesian coordinate frame is investigated. For finite volume methods, general requirements are derived for a spatial discretization which yields first order accuracy on arbitrary meshes. An error analysis shows that in two dimensions methods based on a cell vertex scheme meet these requirements whereas methods based on a cell centered scheme do not. Numerical results on different two-dimensional meshes confirm the theoretical statement that only cell vertex schemes perform accurately on grids with slope discontinuities. Using structured coordinate grids for complex three-dimensional flow problems, even cell vertex schemes require additional effort to ensure first order accuracy on arbitrary meshes. The applicability of the cell vertex scheme is demonstrated by the calculation of the flow field in a nozzle and the flow around a powered nacelle.