A 3D conservative sharp interface method for simulation of compressible two-phase flows

Abstract

A three-dimensional (3D) conservative sharp interface (CSI) method, which combines 3D cut-cell methods and finite volume methods in the arbitrary Lagrangian-Eulerian framework, is proposed to simulate compressible inviscid two-phase flows. The 3D cut-cell method allows to reconstruct interfaces on a Cartesian mesh and update unstructured interface cells in the vicinity of the interface, making the reconstructed interface always coinciding with the cell faces of the interface cells. The complexity in generating 3D interface cells is significantly reduced by exploiting the symmetry and rotational symmetry of fluid positions in a cut cell. Compared to our previous two-dimensional work (Lin et al. (2017) [17]), the occurrence of large interface cells is also avoided by using the new strategy of cell assembly. With the help of the 3D cut-cell method, a second-order finite volume method in the arbitrary Lagrangian-Eulerian framework can be used nearly in the whole domain, except for the interface cells with under-resolved interfaces or topology changes, at which a first-order finite volume method is used instead. The convergence of the 3D CSI method is examined by studying the Rayleigh collapse of a gas bubble in water, and second-order accuracy has been obtained for the interface evolution. Simulation of shock-induced bubble collapse demonstrates that the axisymmetricity of the interface is well preserved in the 3D computation. Moreover, the 3D CSI methods are also given experimental validation, including the interaction of a shock with 3D curved gas-gas interface and droplet deformation after shock impact. In all cases, a good agreement has been achieved with the experimental data, with respect to the interface evolution and flow features.