A high order projection method for low Mach number flows

The high order projection hybrid finite volume/finite element method presented in BFSV14 and BFTVC17 is extended to solve compressible low Mach number flows. The main differences with the incompressible method are highlighted. Detailed analysis of the flux term is presented aiming at correcting the spurious oscillations originated by changes in density. As a result a new upwind term is added to the numerical flux function. Moreover, LADER methodology is applied so a second order in space and time scheme is obtained. The mass conservation equation is used in order to compute the extrapolated and half-step in time evolved values of density. The proposed modifications on the methodology are endorsed by the study of the scalar advection-diffusion-reaction equation with time and space dependent coefficients. The formal order of accuracy of the schemes is assessed for various test problems.