The
finite-volume method (FVM) is a method for representing and evaluating
partial differential equations in the form of algebraic equations [LeVeque, 2002; Toro, 1999]. Similar to the
finite difference method or
finite element method, values are calculated at discrete places on a meshed geometry. "Finite volume" refers to the small volume surrounding each node point on a mesh. In the finite volume method, volume integrals in a partial differential equation that contain a
divergence term are converted to
surface integrals, using the
divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are
conservative. Another advantage of the finite volume method is that it is easily formulated to allow for unstructured meshes. The method is used in many
computational fluid dynamics packages.