Achieving high-order fluctuation splitting schemes by extending the stencil

An extension to the fluctuation splitting approach for approximating hyperbolic conservation laws is described, which achieves higher than second-order accuracy in both space and time by extending the range of the distribution of the fluctuations. Initial results are presented for a simple linear scheme which is third-order accurate in both space and time on uniform triangular grids. Numerically induced oscillations are suppressed by applying the flux-corrected transport algorithm. These schemes are evaluated in the context of existing fluctuation splitting approaches to modelling time-dependent flows and some suggestions for their future development are made.