Developing new approaches for the path tubes method

The path tubes (PT) method for advection equations is a semi-Lagrangian algorithm recently introduced in the literature. PT method is simple, physically intuitive, backward-in-time and mass-conserving algorithm, whose formulation is based on the fundaments of the mechanics of continuous media, in the light of Lagrangian methodology. In present work, we describe new approaches for PT methodology, including an absolutely accurate semi-Lagrangian scheme for 1D problems and a new and attractive discretization for multidimensional problems. In addition, we show that PT method is unconditionally stable.