A conservative scheme for 2D and 3D adaptive semi-Lagrangian advection

This article describes a 2D and 3D adaptive and mass conserving semi-Lagrangian advection scheme for atmospheric transport problems. From the integral form of the conservation law we derive a semi-Lagrangian scheme based on conservation of mass along trajectories. The mapping of mass from the old (adaptively refined and possibly different) grid to the upstream control volume is performed by a mass packet based scheme, essentially consisting of a sub-grid discretization. We validate the new adaptive and conservative semi-Lagrangian scheme with four different analytic test cases