TITLE:
A Gas-Kinetic Scheme for Six-Equation Two-Phase Flow Model
AUTHORS:
Saqib Zia, Munshoor Ahmed, Shamsul Qamar
KEYWORDS:
Six-Equation Model; Kinetic Flux-Vector Splitting Scheme; Central Upwind Scheme; Non-Conservative System; Shock Solution
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.3,
February
12,
2014
ABSTRACT: A kinetic
flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation
two-phase flow model of Saurel et al.
[1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh
equation, describing the total mixture energy, is added to the model to
guarantee the correct treatment
of shocks in the single phase limit. Some salient features of the model are that it is hyperbolic with only three wave
propagation speeds and the volume fraction remains positive. The proposed
numerical scheme is based on the direct splitting of macroscopic flux functions of the system of
equations. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction
and Runge-Kutta time stepping method. Moreover, a pressure relaxation procedure is used to fulfill the
interface conditions. For validation, the results of suggested scheme are compared with those from the high resolution
central upwind and HLLC schemes. The central upwind scheme is also applied for the
first time to this model. The accuracy, efficiency and simplicity of the KFVS scheme
demonstrate its potential for
modeling two-phase flows.