Two-dimensional two-fluid two-phase analysis of underwater shock wave and cavitation using approximate jacobian matrix method

Abstract

A two-dimensional compressible two-fluid two-phase flow model, made of two sets of phase governing equations, is formulated. We devise a two-phase second-order Harten, Lax, and van Leer (HLL) scheme using analytic eigenvalues from an approximate system Jacobian matrix and a two-phase split-coefficient matrix (SCM) scheme using numerical eigenvalues computed each time step. We solve a variety of two-phase flow problems using the methods: water faucet problem, phase separation problem, two-phase shock wave problem, underwater explosion problem, and shape cavitation by accelerating flows around two-dimensional geometries. The analytic eigenvalues are obtained from the approximate Jacobian matrix, the terms simplified a little by dropping the much small interfacial transfer terms. The total sound speed in the two-phase flow as evaluated by these eigenvalues agrees very well with the existing experimental data. The HLL scheme based on these analytic eigenvalues is proved efficient, accurate as well as robust in comparison with other existing methods.