An incremental-stencil WENO reconstruction for simulation of compressible two-phase flows

An incremental-stencil WENO reconstruction method, which uses low-order candidate stencils with incrementally increasing width, is proposed for finite-volume simulation of compressible two-phase flow with the quasi-conservative interface model. While recovering the original 5th-order WENO reconstruction in smooth region of the solution, due to the presence of 2-point candidate stencils, the present method is able to handle closely located discontinuities, which is a typical scenario of shock-interface interaction. Furthermore, a MOOD-type positivity preserving approach is applied to ensure physical meaningful reconstruction. Compared with the hybrid method which switches between with the 5th-order WENO and 2nd-order reconstructions, the present method is free of problem-dependent tunable parameters. A number of numerical examples show that the present method achieves small numerical dissipation and good robustness for simulating two-phase flow problems with strong shock-interface interaction and large density ratio.