A fully coupled Pressure-Based method for compressible flows at all Mach numbers

When extending the fully coupled pressure-based method to resolve compressible flows, the effective treatment of the boundary conditions is crucial due to the inherent characteristics of compressible flows. Failure to properly account for this can result in numerical instability and divergence. In this article, a detailed treatment of boundary conditions for compressible flows has been formulated in terms of the boundary face's contribution to the discretization equation of the boundary element. These boundary conditions involve subsonic inlet, supersonic inlet, subsonic outlet, and supersonic outlet boundary conditions. The analysis has been focused on test cases of flow through a bumped arc channel and a converging–diverging nozzle including quasi-incompressible, subsonic, transonic, supersonic and hypersonic speed regimes, where the Mach number ranges from 0.1 to 10. The results indicate the robust performance of the fully coupled method in resolving compressible flows. The computational results obtained from the fully coupled algorithm exhibit a high degree of consistency with available literature cases and analytical solutions, with a maximum error of less than 5%. Moreover, the findings also suggest that the coupled solver presents promising potential in handling hypersonic flows.