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On vector field reconstructions for semi-Lagrangian transport methods on geodesic staggered grids. (English) Zbl 1351.86005
Summary: 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.

86-08 Computational methods for problems pertaining to geophysics
86A10 Meteorology and atmospheric physics
76M12 Finite volume methods applied to problems in fluid mechanics
52B99 Polytopes and polyhedra
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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