Navier-Stokes Solvers for Incompressible Single- and Two-Phase Flows (Communications in Computational Physics, 2021)
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. Their accuracy and robustness arecompared to identify their respective strengths and weaknesses. Exact (also referredto as monolythic) solvers such as the Augmented Lagrangian and the Fully Coupledmethods address the saddle-point structure on the pressure-velocity couple of the discretized system by means of a penalization term or even directly, whereas approximate(segregated) solvers such as the Standard Projection method rely on operator splittingto break the problem down to decoupled systems. The objective is to compare all approaches in the context of two-phase flows at high viscosity and density ratios. Tocharacterize the interface location, a volume-of-fluid (VOF) approach is used basedon a Piecewise Linear Interface Construction (PLIC). Various 2D simulations are performed on single- and two-phase flows to characterize the behavior and performancesof the various solvers.
Keywords: Monolythic solvers; Augmented Lagrangian; two-phase flows; saddle point; projection method.