TWO-DIMENSIONAL TWO-FLUID TWO-PHASE FLOW SIMULATION USING AN APPROXIMATE JACOBIAN MATRIX FOR HLL SCHEME

Abstract

In this article, a numerical method to solve the two-set, eight-equation, compressible, two-fluid, two-phase flow model is developed in two dimensions as an extension of the earlier one-dimensional version. The multidimensional two-fluid model can be effectively solved by a finite-volume method in a rotated reference frame. In order to estimate the fastest wave speeds in the hyperbolic equation system for the Harten-Lax-van Leer (HLL) scheme, we first regard the liquid phase as compressible by taking the stiffened-gas equation of state. Then we derive the two-dimensional approximate Jacobian matrix and obtain the associated eight analytic eigenvalues. Using the HLL scheme, we solve a few two-phase flow problems including shape cavitation and underwater explosion, demonstrating application of the present numerical method to meaningful problems.