A 3D FV method for Alpine Glaciers

The problem of mass and thermal flow in Alpine Glaciers has been approached in the literature by adopting simplifying assumptions such as the Shallow Ice approximation. Most of the proposed models are 2D or quasi-3D; no full 3D models have been proposed to our knowledge; the problem, however, is fully 3D due to the complex geometry of the domain and to the free surface which evolves in time because of atmospheric as well as of internal motion reasons. In the presented work a fully 3D model is proposed. The Finite Volume (FV) method is used for the space discretization in order to guarantee both local and global conservation of mass. The time advancing scheme is based on the Fractional Step theory and is capable of dealing with the free surface evolution. The proposed method is similar to the method proposed by Casulli but a higher approximation order is used for convective and diffusive terms and for the discretization of boundary conditions.