General pressure-correction strategy to include density variation in incompressible algorithms

This work deals with the popular topic of extending incompressible numerical formulations to the compressible or variable density regime. Based on an analogy between the incompressible and compressible governing equations, a general strategy is suitably developed to facilitate the compressible flow solution through using incompressible algorithms. It is shown that the implementation of the extended strategy to an arbitrarily incompressible algorithm requires two minor modifications in the original algorithm. In fact, two on/off switches suffice to implement the two required modifications. Switch one includes the compressible source terms to the momentum governing equations. Switch two decides how to calculate the unknown density field as a secondary dependent variable of the algorithm. In this work the two modifications are employed in a popular incompressible algorithm, which utilizes semi-implicit method with pressure-linked equation. However, one important advantage of the extended strategy is its robust applicability to the other constant density algorithms as well. The strategy is examined by testing a number of test cases at various Mach and Reynolds numbers. Results are presented for driven-cavity flow, flow over a backward-facing step, flow through a channel, and inviscid flow through a converging-diverging nozzle. The study shows that the modified algorithm exhibits similar performance for both constant and variable density regimes.