A cell-centered ICE method for multiphase flow simulations

The Implicit Continuous-fluid Eulerian (ICE) method is a finite-volume scheme that is stable for any value of the Courant number based on the sound speed. In the incompressible limit, the ICE method becomes essentially identical to the Marker and Cell (MAC) method, so the two schemes are closely related. In this article, the classical ICE method is extended to multiple interpenetrating phases, and employed with a single control volume (nonstaggered) mesh framework. The incompressible limit is preserved, so that problems involving equations of state, or those exhibiting constant material densities, can be addressed with the same computer code. The scheme reduces properly to a single-fluid method, enabling benchmarking using well-known test cases. Thus, the numerical issues focus only on those aspects unique to problems having multiple density, velocity and temperature fields. The discussion begins with a derivation of the exact, ensemble-averaged equations. Examples of the most basic closures axe given, and the well-posedness of the equations is demonstrated. The numerical method is described in operator notation, and the discretization is sketched. The flow patterns in a bubble column are computed as an incompressible flow example. For a compressible flow example, the expansion and compression of a bubble formed by high-explosive gases under water is shown. In each case, comparison to experimental data is made.