Accurate solutions to unsteady problems by monotone implicit fluctuation splitting schemes

This paper aims at providing multi-dimensional upwind schemes for two-dimensional unsteady flow problems with second- and third-order accuracy on unstructured cell-vertex triangular grids. The methods are based on a residual distribution spatial discretization and a dual-time stepping approach. A recently developed distribution scheme of the unsteady-fluctuation term, coupled with a new limiting procedure for hampering spurious extrema, provides second-order accuracy for both scalar advection problems and inviscid flows with discontinuities. For the case of scalar ad-vection problems the method is improved to achieve third-order accuracy by employing a parabolic reconstruction of the solution over each triangle together with a third-order backward time discretization