《pp187-203》.pdf

Electronic Transactions on Numerical Analysis. ETNA Volume 34, pp. 187-203, 2009. Kent State University Copyright  2009, Kent State University. ISSN 1068-9613. COMPARISON BETWEEN DIFFERENT NUMERICAL DISCRETIZATIONS FOR A DARCY-FORCHHEIMER MODEL∗ ´ † † ´ ‡ HILDA LOPEZ , BR´ıGIDA MOLINA , AND JOSE J. SALAS Dedicated to Vıctor Pereyra on the occasion of his 70th birthday ´ Abstract. This paper is a numerical study of different discretizations for a mixed formulation of the Darcy- Forchheimer equation. Different finite elements are used: constant functions, conformal linear functions and Crouzeix- Raviart non-conformal finite elements. The behavior of the discretizations is analyzed through a comparative study of some test problems. The numerical results suggest that one of the proposed discretizations has better convergence properties for the velocity. Key words. Darcy-Forchheimer’s model, mixed formulation, numerical discretizations, finite elements, algo- rithm of alternating directions. AMS subject classifications. 35Q35, 74S05, 58C15, 65F10 1. Introduction. The following model describes the steady Darcy-Forchheimer flow of a single phase fluid in a porous medium in a bounded domain Ω in two or three dimensions: µ −1 β K u + |u|u + ∇p = 0 in Ω, (1.1) ρ ρ with the divergence constraint div u = b in Ω,