On the convergence of the weakly compressible sharp-interface method for two-phase flows

A weakly compressible sharp-interface framework for two-phase flows is presented. Special emphasis is on investigating its convergence properties. For this purpose a well-defined set of benchmark configurations is introduced. These may serve as future references for the verification of sharp-interface methods. Global mass and momentum conservation is ensured by the conservative sharp-interface method. Viscous and capillary stresses are considered directly at the interface. A low-dissipation weakly compressible Roe Riemann solver, in combination with a 5th-order WENO scheme, leads to high spatial accuracy. A wavelet-based adaptive multi-resolution approach permits to combine computational efficiency with physical consistency. The first test configuration is a Rayleigh-Taylor instability at moderate Reynolds number and infinite Eötvös number. A second group of benchmark cases are isolated air bubbles rising in water at high Eötvös numbers, and low to high Reynolds numbers. With these test cases, three distinct types of complex interface evolution, which are typical for a wide range of industrial applications, are realized.