Blended numerical schemes for the advection equation

In this paper we propose a method to couple two or more explicit numerical schemes approximating the same equation, in order to create new schemes which inherit advantages (and drawbacks) of the original ones. The coupling can be either active everywhere and at any time, or can be localized following the philosophy of filtered schemes. For illustrative purposes, we focus on the coupling of two schemes only. We couple either macroscopic (Eulerian) schemes or a microscopic (Lagrangian) scheme with a macroscopic scheme. In the latter case we get a new kind of multiscale numerical method. As a test problem, we consider the advection equation.