On vector field reconstructions for semi-Lagrangian transport methods on geodesic staggered grids

We analyse several vector reconstruction methods, based on the knowledge of only specific pointwise vector components, and extend their use to non-structured polygonal C-grids on the sphere. The emphasis is on the reconstruction of the vector field at arbitrary locations on the sphere, as required by semi-Lagrangian transport schemes. This is done by first reconstructing the vector field to fixed locations, followed by interpolations with generalized barycentric coordinates. We derive a hybrid scheme, combining the efficiency of Perot's method with the accuracy of a least square scheme. This method is second order accurate, and has shown to be competitive and computationally efficient. We analysed the vector reconstruction methods within a semi-Lagrangian transport method, and demonstrated that second order accurate reconstructions are enough to fulfil the requirements for second order accurate semi-Lagrangian methods on icosahedral C-grids.