Consistent and conservative Phase-Field method with bound-preserving WENO scheme and adaptive mesh refinement for compressible multiphase flows

The consistent and conservative Phase-Field method couples the Phase-Field mechanism with compressible multiphase flows, resulting in an interface thickness that is uniform in space and constant over time on the order of the mesh size. The present study further improves the method by incorporating high-order WENO schemes and adaptive mesh refinement (AMR), enabling a sharp representation of discontinuities, like shocks and material interfaces, on the order of the finest AMR mesh size via dynamical mesh refinement and coarsening. However, direct implementation of these techniques to compressible multiphase flows may produce numerical oscillations along material interfaces. The mechanisms of these spurious oscillations are illustrated and analyzed, which results in a novel time integration procedure and a consistent and bound-preserving WENO scheme. The proposed approach is demonstrated in various compressible two-/N-phase flows.