Positive cell-centered finite volume discretization methods for hyperbolic equations on irregular meshes

The conditions sufficient to ensure positivity and linearity preservation for a cell-centered finite volume scheme for time-dependent hyperbolic equations using irregular one-dimensional and triangular two-dimensional meshes are derived. The conditions require standard flux limiters to be modified and also involve possible constraints on the meshes. The accuracy of this finite volume scheme is considered and is illustrated by two simple numerical examples.

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