Path tubes method: A semi-Lagrangian approach for linear advection equations

The present work proposes the path tubes (PT) method, a simple, physically intuitive, backward-in-time, semi-Lagrangian and mass-conserving algorithm for the linear advection equations, whose development is based on the fundaments of the mechanics of continuous media, in the light of Lagrangian methodology. The path tubes method is an explicit scheme capable of advecting step-functions, even if large time steps are used in the resolution of the convection equation. Here, PT method is illustrated on a classical numerical benchmark with bi-dimensional examples.