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We propose a simple modification of standard WENO finite volume methods forCartesian grids, which retains the full spatial order of accuracy of theone-dimensional discretization when applied to nonlinear multidimensionalsystems of conservation laws.  We derive formulas, which allow us to compute high-order accurate pointvalues of the conserved quantities at grid cell interfaces. Using those pointvalues, we can compute a high-order flux at the center of a grid cellinterface. Finally, we use those point values to compute high-order accurateaveraged fluxes at cell interfaces as needed by a finite volume method.  The method is described in detail for the two-dimensional Euler equations ofgas dynamics. An extension to the three-dimensional case as well as to othernonlinear systems of conservation laws in divergence form is straightforward.Furthermore, similar ideas can be used to improve the accuracy of WENO typemethods for hyperbolic systems which are not in divergence form.  Several test computations confirm the high-order accuracy for smoothnonlinear problems.

Improved Accuracy of High-Order WENO Finite Volume Methods on Cartesian Grids