Simulation Strategies for Compressible Multiphase Flows Using a Conservative Discretization Scheme

A dissipation-free, sharp-interface discretization strategy is presented for the accurate simulation of complex compressible multiphase flows, such as shock-droplet interaction. The approach employs a hybrid scheme where either a centered or WENO3 discretization in the bulk phases, time-integrated with a fourth-order Runge–Kutta method, is coupled at phasic interfaces to a semi-Lagrangian geometric volume-of-fluid method that transports discontinuous phasic quantities with second-order accuracy. The hybridization is both spatial and temporal, and it preserves the dissipation-free property across interfaces. Localized dissipation is introduced only where temporal errors become significant, improving robustness in challenging configurations. By minimizing numerical dissipation, the solver reveals the need for subgrid-scale models for under-resolved turbulence, shocks, and breakup—providing a platform for their development and evaluation. Simulations of shock impact on a liquid droplet at high Reynolds and Weber numbers demonstrate accuracy and robustness in multiphase environments relevant to hypersonic flows.