A second-order-accurate fluctuation splitting scheme for unsteady hyperbolic problems

This paper attempts to extend the Fluctuation Splitting (FS) methodology developed by the authors for the steady state compressible Euler (and Navier—Stokes) equations, to the case of unsteady flows. Two slightly different approaches are proposed for the one- and two-dimensional flow-cases, respectively. For the one-dimensional Euler equations, a predictor-corrector scheme is proposed, which combines a first-order-accurate FS scheme at the predictor level with a standard LaxWendroff (LW) correction step, suitably limited to mantain monotone initial solutions. Such scheme is shown to be equivalent to Le Veque’s high-resolution scheme, while retaining the compact nature of FS schemes. For the case of two-dimensional flows, the linear advection equation is considered for simplicity. Again, a predictor-corrector scheme is proposed, which combines a first-orderaccurate FS predictor step with a flux-corrected-transport LW corrector one. Standard test problems are used to verify the accuracy of the proposed schemes.