Navier-Stokes solvers for incompressible single-and two-phase flows

Mohamed El Ouafa , Vincent Stéphane (1) , Vincent Le Chenadec (2)

1 TREFLE - Transferts, écoulements, fluides, énergétique
2 EM2C - Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion

The presented work is dedicated to the mathematical and numerical modeling of unsteady single-and two-phase flows using finite volume and penalty methods. Two classes of Navier-Stokes solvers are considered in order to compare their accuracy and robustness, as well as to highlight their limitations. Exact (or monolythic) solvers such as the Augmented Lagrangian and the Fully Coupled methods address the saddle-point structure on the pressure-velocity couple of the discretized system by means of a penalization term or even directly, whereas the approximate (or segregated) solvers such as the Standard Projection method rely on operator splitting to break the problem down into decoupled systems. The objective is to compare all approaches in the context of two-phase flows at high viscosity and density ratios. To characterize the interface location, a volume of fluid (VOF) approach is used based on a Piecewise Linear Interface Construction (PLIC). Various 2D simulations are performed on single-and two-phase flows to characterize the behavior and performances of the various solvers.

Mots clés: Monolythic solvers; Augmented Lagrangian; two-phase flows; saddle point; projection method

Domaines: Mécanique des fluides [physics.class-ph]

Mohamed El Ouafa, Vincent Stéphane, Vincent Le Chenadec. Navier-Stokes solvers for incompressible single-and two-phase flows. 2020. ⟨hal-02892344⟩