An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model
Institut de Radioprotection et de Sûreté Nucléaire (IRSN), France. firstname.lastname@example.org; email@example.com
2 Université de Provence, France. firstname.lastname@example.org
Revised: 24 July 2009
We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the system decreases; in addition, when using for the drift velocity a closure law which takes the form of a Darcy-like relation, the drift term becomes dissipative. Finally, the present algorithm preserves a constant pressure and a constant velocity through moving interfaces between phases. To ensure the stability as well as to obtain this latter property, a key ingredient is to couple the mass balance and the transport equation for the dispersed phase in an original pressure correction step. The existence of a solution to each step of the algorithm is proven; in particular, the existence of a solution to the pressure correction step is derived as a consequence of a more general existence result for discrete problems associated to the drift-flux model. Numerical tests show a near-first-order convergence rate for the scheme, both in time and space, and confirm its stability.
Mathematics Subject Classification: 65N12 / 65N30 / 76N10 / 76T05 / 76M25
Key words: Drift-flux model / pressure correction schemes / finite volumes / finite elements
© EDP Sciences, SMAI, 2010