Notes on the PCICE method: Simplification, generalization, and compressibility properties

The pressure-based PCICE numerical method [R.C. Martineau, R.A. Berry, The pressure-corrected ICE finite element method (PCICE-FEM) for compressible flows on unstructured meshes, J. Comput. Phys. 198 (2004) 659] for computing transient fluid flows of all speeds from nearly incompressible to high supersonic with strong shocks is simplified and generalized. Its behavior is examined in the nearly incompressible limit and in the fully compressible limit. In the nearly incompressible limit the PCICE algorithm is found to reduce to a generalization of the incompressible MAC method, which includes the density gradient as a driving function in the pressure Poisson equation. In the fully compressible regime, it is found to reduce to an expression equivalent to density-based methods for high-speed flow.