Eur. Phys. J. Plus (2012) 127: 39
https://doi.org/10.1140/epjp/i2012-12039-5

Regular Article

A formulation to compute mass-consistent models of hydrodynamic flows

Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, A. P. 55-534, C.P. 09340, D. F., Mexico

^* e-mail: manp@xanum.uam.mx

Received: 19 December 2011
Revised: 6 March 2012
Accepted: 7 March 2012
Published online: 10 April 2012

Abstract

Standard interpolation methods of measured data of an incompressible fluid yield a non-solenoidal field v ⁰. A formulation to estimate a solenoidal field from v ⁰, is proposed. Variational calculus reduces the problem to the solution of an elliptic equation for a Lagrange multiplier. Examples illustrate how boundary conditions improve the mass-balance of velocity fields obtained in meteorology with similar approaches. The elliptic equation is separable in meteorological problems over a complex orography. This allows the use of fast-Poisson solvers. It is shown how the flow-rate can be used to define a low-pass filter which improves the results given by the Fast Fourier Algorithm.