KEEP scheme with strict entropy conservation for compressible two-phase seven-equation model

Compressible two-phase flows play a crucial role in a wide range of engineering applications, such as bubble acoustics, cavitation, and combustion. However, numerical simulations of compressible two-phase flows often suffer from numerical instabilities due to the high density ratio and the sharp gradients at the interfaces. Although these instabilities can be alleviated by introducing numerical dissipation, such dissipation nonphysically smears small-scale vortices, degrading the quality of high-fidelity two-phase turbulent flow simulations. Therefore, the development of a robust and non-dissipative scheme is essential for accurately simulating turbulent multiphase flows. In this study, we propose the kinetic energy and entropy preserving (KEEP) scheme for the compressible two-phase seven-equation model, extending an approach originally developed for single-component gas flows. The proposed scheme achieves stable and non-dissipative simulations by satisfying secondary conservation (kinetic energy and entropy) at the discrete level. Based on an entropy conservation error analysis, exact entropy-conservative numerical fluxes are derived, and the robustness of the proposed scheme is demonstrated through numerical experiments.