In this work, we introduce new finite-difference shock-capturing central schemes on staggered grids. Staggered schemes may have better resolution of the corresponding unstaggered schemes of the same order. They are based on high-order nonoscillatory reconstruction (ENO or WENO), and a suitable ODE solver for the computation of the integral of the flux. Although they suffer from a more severe stability restriction, they do not require a numerical flux function. A comparison of the new schemes with high-order finite volume (on staggered and unstaggered grids) and high order unstaggered finite difference methods is reported.
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Puppo, G., Russo, G. Staggered Finite Difference Schemes for Conservation Laws. J Sci Comput 27, 403–418 (2006). https://doi.org/10.1007/s10915-005-9036-x
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DOI: https://doi.org/10.1007/s10915-005-9036-x