The M.A.C. scheme (called FDV in Trio_U) has been proposed by Harlow & Welch in 1965. This scheme is very robust and has been successfully generalized to many physical models (single-phase, two-phase, compressible, incompressible, turbulent, laminar, …). The reasons of the high performances of this method are still mysterious. Its main known flaws are that (i) it does not accurately treat flows at high Mach number (for which hyperbolic solvers are preferred) and (ii) it is restricted cartesian structured grids, which makes it difficult to use in complex geometries and with adaptive mesh refinement. The Immersed Boundary Methods, Fictitious Domain Methods, etc. have been developed with some success to overcome the issue of the treatment of complex geometries.
Within the Trio_U project, we are interested in identifying the properties of the M.A.C. scheme that makes so robust and to develop a numerical method that satisfies these properties and that can handle unstructured meshes. We are also interested in fictitious boundary methods, in particular to treat moving boundaries.