Interpolation of hydrodynamic velocity data with the continuity equation

Article type: Research Article

Authors: Núñez, Marco A.^{a; *} | Flores, Ciro^b | Juárez, Héctor^a

Affiliations: [a] Departamento de Física y Matemáticas, Universidad Autónoma Metropolitana Iztapalapa, A. P. 55-534, C.P. 09340, D. F., México | [b] Instituto Tecnológico y de Estudios Superiores de Monterrey, C.P. 42080, Hidalgo, México

Correspondence: [*] Corresponding author. Tel.: +52 555 804 4610 ext. 323; Fax: +52 555 804 4611; E-mail: manp@xanum.uam.mx.

Abstract: Meteorologists have developed a way of obtaining a velocity field V that satisfies the incompressible-flow continuity equation ∇·V=0 in a bounded domain Ω , starting from a finite set of data Vtrue(xk)k=1N measured in Ω. In this work a mathematical framework of the scheme, is given. The approach can be extended to consider data provided by experimental methods such as the so-called particle image velocimetry technique. The viability of the scheme is tested with synthetic data from analytic solutions of the two-dimensional version of the equation ∇·V=0. Numerical examples show that the scheme can yield an accurate approximation V of the true velocity field Vtrue.

Keywords: Atmospheric data assimilation, interpolation of solenoidal or nondivergent fields, particle image velocimetry

DOI: 10.3233/JCM-2007-7102

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 7, no. 1, pp. 21-42, 2007