Eur. Phys. J. Plus (2012) 127: 40
https://doi.org/10.1140/epjp/i2012-12040-0

Regular Article

Improving variational mass-consistent models of hydrodynamic flows via boundary conditions

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

Variational mass-consistent models for the velocity field v have been used by mesoscale meteorological community to modeling the wind field from an observed field v ⁰ in a bounded region Ω with boundary Γ. Variational calculus reduces the problem to the solution of an elliptic equation for a Lagrange multiplier λ subject to Dirichlet Boundary Condition (DBC) on flow-through boundaries. In this work, it is shown that DBC decreases the regularity of λ and this in turn decreases the accuracy with which the velocity field satisfies the mass-balance. The boundary condition (BC) v · n = v _T · ngiven by the true field v _T on the whole boundary Γ, leads only to a Neumann boundary condition (NBC) for λ. Approximations of this BC are studied. Analytic and numerical results show that the velocity field U ⁰ obtained from v ⁰ by direct integration of the continuity equation, yields a NBC that improves significantly the fields obtained with DBC’s.