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

A global methodology dealing with fictitious domains of all kinds on curvilinear grids is presented. The main idea is to transform the curvilinear framework and its associated elements (velocity, immersed interfaces…) into a Cartesian grid. On such grids, many operations can be performed much faster than on curvilinear grids. The method is coupled with a Thread Ray-casting algorithm which works 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 (L2-penalty) or with phase advection methods such as VOF–PLIC, VOF–TVD, Front-tracking or Level-set approaches. Applications, convergence and speed tests are performed for shape initializations, immersed boundary methods, and interface tracking.