Semi-Lagrangian methods receive wide acceptance for their favorable properties, namely stability, efficiency, parallelization. Even adaptivity with unstructured, locally refined meshes is easily achieved with this method of discretization.

However, semi-Lagrangian methods in their simple form lack conservation properties. In many fields of application, e.g. climate modelling, or modelling of nonlinear phenomena with shocks, conservation of mass (and other physical constituents) is essential.

We propose several modifications which add mass conservation to the advection case of the semi-Lagrangian method. A comparison highlights properties of the proposed schemes in different situations. Applications in planar and spherical geometries are given. The effectiveness of mass conservation is shown in test cases with diverging and converging wind fields.