A second-order-accurate monotone implicit fluctuation splitting scheme for unsteady problems

This paper provides a novel implicit fluctuation splitting scheme which achieves second-order accuracy in both space and time, while guaranteeing monotone solutions. The method is based on a dual-time stepping approach which allows to separate the spatial and temporal discretizations. A novel distribution scheme of the unsteady-fluctuation term, coupled with a new limiting procedure for hampering spurious extrema. are the key-ingredients leading to the remarkable accuracy of the new I method. This is applied with success to both scalar advection problems and unsteady inviscid flows in two space dimensions. In both applications the scheme is markedly superior to current state-of-the-art explicit fluctuation splitting schemes.