Towards unification of the Vorticity Confinement and Shock Capturing (TVD and ENO/WENO) methods

New multidimensional extensions of the TVD and finite difference ENO/WENO methods for the compressible flow equations are proposed. The novelty of the approach is in the discretization schemes that acquire by means of a single mechanism both shock-capturing and vorticity confinement capabilities. Thus, the new method can be interpreted as a unification of the two methodologies, intended initially for different purposes.