Interpolation of multidimensional random processes with application to fluid flow

Vector-valued multidimensional random process interpolation is investigated with application to interpolating the velocity fields of turbulent fluid flow. The authors first model and define the problem of interpolating velocity fields from PTV (particle tracking velocimetry) data as a random process problem, and then derive the minimum mean squares error filters, which are the optimum interpolants, for the case of homogeneous turbulence. A windowed interpolation algorithm was applied to synthesized flow fields. The velocity field is modeled as a random field and the particle positions are approximated by a Poisson point process. The interpolation of this random field from these Poisson points can be solved as a minimum mean squares error problem. The minimum mean squares errors of the interpolation algorithm are analyzed as a function of data density.<>