A second-order-accurate monotone implicit fluctuation splitting scheme for unsteady problems
This paper provides an 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 of the remarkable accuracy of the new method, which is applied with success to both scalar advection problems and unsteady inviscid flows in two space dimensions.
monotone solutions residual distribution method unsteady hyperbolic equations consistent mass matrix dual-time-stepping technique