In this paper we present a two-dimensional extension of the staggered Lax-Friedrichs scheme for the approximate solution of hyperbolic conservation laws on unstructured grids. By evolving the numerical solution on two staggered grids, the proposed scheme avoids the resolution of the Riemann problems arising at the cell interfaces. The control cells of the original grid are regular triangular cells of a finite element triangulation, while the staggered dual cells are quadrilaterals constructed on the triangular cells of the original grid. The accuracy and stability of the scheme are investigated and classical problems arising in gas dynamics are solved. The obtained results are in good agreement with corresponding ones appearing in the literature thus confirming the efficiency and potential of the proposed method.

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