An incremental-stencil WENO reconstruction for simulation of compressible two-phase flows. (July 2018) - Wang, Bing; Xiang, Gaoming; Hu, Xiangyu Y.
Highlights: A simple solution to the long-standing problem of numerical instability in computing the two-phase flow. An incremental-stencil WENO reconstruction with minimum 2-point stencil. A simple method free of problem-dependent tuning parameters. Abstract: For simulation of compressible two-phase flows, especially those with high density ratio and strong shock wave, achieving good numerical stability is challenging. In this paper, a 5th-order incremental-stencil WENO (WENO-IS) reconstruction, which uses low-order candidate stencils with incrementally increasing width, is proposed for finite-volume simulation of compressible two-phase flows with a five-equation model. While recovering the original 5th-order WENO reconstruction, due to the presence of 2-point candidate stencils, the present reconstruction is able to handle closely located discontinuities, which is a typical scenario of shock-interface interaction. Several one-dimensional and two-dimensional problems are tested. The results shows that the present WENO-IS reconstruction has an advantage over the classical WENO and hybrid reconstructions for better numerical stability and less dissipation near the discontinuities.