Effective filtering and interpolation of 2D discrete velocity fields with Navier–Stokes equations. (21st September 2016)

• Record Type: Journal Article
• Authors: Saumier, Louis-Philippe; Khouider, Boualem; Agueh, Martial
• Is Part Of: Inverse problems. Volume 32:Number 11(2016:Nov.)
• Publication Date: 2016-09-21
• Subjects: velocity field -- interpolation -- filtering -- Navier–Stokes equations -- numerical method; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/11/115006
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We introduce a new variational technique to interpolate and filter a two-dimensional velocity vector field which is discretely sampled in a region of R 2 and sampled only once at a time, on a small time-interval [ 0, Δ t ] . The main idea is to find a solution of the Navier–Stokes equations that is closest to a prescribed field in the sense that it minimizes the l 2 norm of the difference between this solution and the target field. The minimization is performed on the initial vorticity by expanding it into radial basis functions of Gaussian type, with a fixed size expressed by a parameter ϵ . In addition, a penalty term with parameter k e is added to the minimizing functional in order to select a solution with a small kinetic energy. This additional term makes the minimizing functional strongly convex, and therefore ensures that the minimization problem is well-posed. The interplay between the parameters k e and ϵ effectively contributes to smoothing the discrete velocity field, as demonstrated by the numerical experiments on synthetic and real data.