C∞-Interpolation of Discrete Fields on Regular and Irregular Grids

The article proposes a simple C∞ interpolation of discretized lattice fields on regular and irregular grids. The method is based on localized C∞ but not analytic basis functions, which vanish outside an open set (region of influence). As a result, the interpolating fields at a point depend exclusively on the nodal values within the region of influence. The method can be applied to generic fields whose support is a limited set of n-dimensional space, starting from discretized values given on regular or irregular grids. Particular attention is focused on the interpolation of CFD-computed velocity fields that give rise to Lagrangian chaos.