A Simple Inteface-Capturing Scheme for Simulating Compressible Two-Phase Flows

To simulate compressible multiphase flows, diffuse-interface capturing methods offer the advantage of not explicitly tracking the interface, which results in a simpler system. However, these methods face challenges in modeling the mixture produced by the artificially diffused interface and in avoiding spurious pressure oscillation at the interface.

Here, a simple interface capturing scheme for 2D compressible two-phase flows is devised. It is based on the Navier-Sokes-Fourier system for single-phase gas dynamics with only one additional conservation law for a phase indicator, whereas both phases are modeled as compressible fluids via the stiffened equation of state. To thermodynamically close the system, the internal energy of the mixture is defined as a simple weighted average of the two phases, but to avoid the build up of pressure oscillations, it is crucial to correct the total energy equation in the mixture region. Further, special attention has to be given to the convective numerical fluxes at the cell interfaces. Very large density ratios and abrupt changes of the equation of state (e.g. at air-water interfaces) pose severe challenges for approximate Riemann solvers. Here, the Harten-Lax-van Leer-Contact (HLLC) Riemann solver is adapted and employed, while a MUSCL scheme is used to achieve second order accuracy.

For various 1D and 2D test cases convergence to the exact weak solution and robustness are demonstrated. Further it is shown that the scheme is accurate and computationally efficient.