POSITIVE CELL-CENTERED FINITE-VOLUME DISCRETIZATION METHODS FOR HYPERBOLIC-EQUATIONS ON IRREGULAR MESHES

The conditions sufficient to ensure positivity and linearity preservat ion for a cell-centered finite volume scheme for time-dependent hyperb olic equations using irregular one-dimensional and triangular two-dime nsional meshes are derived. The conditions require standard flux limit ers to be modified and also involve possible constraints on the meshes . The accuracy of this finite volume scheme is considered and is illus trated by two simple numerical examples.