A robust high-resolution discrete-equations method for compressible multi-phase flow with accurate interface capturing

The discrete-equations method (DEM) [1] provides a universal approach to solve multi-phase-flow equations as it combines the solutions of pairwise Riemann problems. Although very robust, the original DEM with piecewise-constant volume fractions suffers from strong diffusion preventing accurate interface capturing. High-order interface reconstruction, however, introduces a restrictive time-step limit. This paper presents RDEMIC, a robust extension of DEM for accurate interface capturing on Cartesian meshes. By a modified partitioning of the Riemann solutions and a specific combination of fluxes and non-conservative terms, the time-step restriction is effectively prevented, which is critical for making the method practically applicable. Moreover, the accuracy of interface and shock-wave propagation is maintained. RDEMIC is not limited to two-phase flow but defined for an arbitrary number of phases. The method is combined with a THINC scheme [2] to reconstruct volume fractions. The reconstruction is enhanced by a positivity-preserving averaging procedure, which is consistent with the underlying multi-stage Runge–Kutta scheme of the flow solver. The resulting scheme consisting of RDEMIC and the positivity-preserving THINC reconstruction is very robust and captures the interface with high accuracy. We demonstrate its performance for various cases of shock-interface interactions, which show very good agreement with reference results from literature.