A second-order curvilinear to Cartesian transformation of immersed interfaces and boundaries. Application to fictitious domains and multiphase flows

Arthur Sarthou (1) , Stéphane Vincent (1) , Jean-Paul Caltagirone (1)

1 TREFLE - Transferts, écoulements, fluides, énergétique

A global methodology dealing with fictitious domains of all kinds on orthogonal curvilinear grids is presented. The main idea is to transform the curvilinear workframe and its associated elements (velocity, immersed interfaces...) into a Cartesian grid. On such a grid, many operations can be performed much faster than on curvilinear grids. The method is coupled with a Thread Ray-casting algorithm which work on Cartesian grids only. This algorithm computes quickly the Heaviside function related to the interior of an object on an Eulerian grid. The approach is also coupled with an immersed boundary method ($L^2$-penalty method) or with phase advection with VOF-PLIC, VOF-TVD, Front-tracking or Level-set methods. Applications, convergence and speed tests are performed for shape initializations, immersed boundary methods, and interface tracking.

Mots clés: Curvilinear grids; structured Cartesian grids; fictitious domains; grid transformation; Front Tracking; VOF; Level-Set; multiphase flows

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

Arthur Sarthou, Stéphane Vincent, Jean-Paul Caltagirone. A second-order curvilinear to Cartesian transformation of immersed interfaces and boundaries. Application to fictitious domains and multiphase flows. Computers and Fluids, 2010, 46 (1), pp.422-428. ⟨10.1016/j.compfluid.2010.11.008⟩. ⟨hal-00479705⟩