Time in hyperbolic partial differential equations is no different from space variables. This allows one to interpret any of the spatial variables as time, and time as a spatial variable. With this inversion, the explicit CABARET scheme, which is unstable at Courant-Friedrichs-Levy (CFL) numbers greater than one, becomes stable. Implicit unconditionally stable difference schemes with CFL>2 have depressingly poor dispersion characteristics. This becomes critical for convection dominated transport equations. Space-time inversion eliminates this problem. The resulting hybrid scheme remains explicit, although a point-to-point computation must be used to find the solution on the next time layer. The new method is verified on scalar advection equation and shallow water equations over a flat bottom.

This is a joint work with A. Solovjev and N. Afanasiev