Semi-implicit methods based on inflow implicit and outflow explicit time discretization of advection - Frolkovič, Peter (Proceedings of the Conference Algoritmy, 2016)
We introduce several numerical methods for the solution of advection equation using semi-implicit time discretization in which the inflow fluxes are discretized implicitly and the outflow fluxes explicitly. We derive the so called $κ$-scheme and show it is $2^{nd}$ order accurate and uncon\-ditionally stable in 1D and 2D case for tensor grids with a special choice of $κ$ giving $3^{rd}$ order accurate scheme for constant speed in 1D. Moreover, we present a $2^{nd}$ order accurate and unconditionally stable Corner Transport scheme in 2D case for tensor grids that is $3^{rd}$ order accurate for constant velocity. We discuss several improved properties of these schemes when compared to analogous fully explicit and fully implicit schemes.