Numerical computation of Navier-Stokes two-phase flows

Philippe Angot (1, 2)

1 I2M - Institut de Mathématiques de Marseille
2 AMU SCI - Aix-Marseille Université - Faculté des Sciences

This lecture presents recent advances for the efficient computation of Navier-Stokes multiphase flows. In particular, the vector penalty-projection splitting methods including the so-called kinematic version are detailed. The space discretization is made by finite volumes on the Cartesian MAC staggered grid or with edge-based generalized MAC-type unstructured meshes. Moreover, an accurate Lagrangian front-tracking method is proposed. Compared to the scalar projection methods of Chorin (1968) and Temam (1969), this family of numerical splitting methods is especially designed for the cases with large density/viscosity ratios, large surface tension and open boundary conditions expressed with the stress vector. Several sharp benchmark problems are solved such as the free fall of a heavy rigid ball in air (with a density ratio of $10^6$) or air-bubble dynamics in a melted steel with a density ratio of $10^4$ and strong capillary forces.

Mots clés: Navier-Stokes Equations; Multiphase flows; Large density/viscosity ratios; Large surface tension; Open boundary conditions with stress vector; Vector penalty-projection methods; Edge-based generalized MAC unstructured meshes; Accurate Lagrangian front-tracking method

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]; Modélisation et simulation

Philippe Angot. Numerical computation of Navier-Stokes two-phase flows: Recent advances for strong stresses and open boundary conditions. Mathematical Fluid Dynamics -- Advanced Summer School, Aug 2021, Cargèse (Institut d'Etudes Scientifiques), Corsica, France. ⟨hal-03356887⟩