A multilevel local mesh refinement projection method for low Mach number flows

This paper addresses a sub-problem of low Mach number reactive flows modelling: the solution of the mass and momentum balance equations for a pressure-independent variable density flow. For this objective, we develop a novel numerical scheme: the time discretisation is performed by an incremental projection method, using the original form of the mass balance equation for the projection step; the resulting two semi-discrete problems are then discretised in space by finite volumes on a MAC staggered mesh, with a multilevel local mesh refinement algorithm based on the Flux Interface Correction (FIC) method. The efficiency of this numerical scheme, which offers the opportunity to avoid computing with non-uniform grids or unstructured meshes, is assessed against a practical test case, specifically produced for this purpose.