TY - JOUR
T1 - A Second-Order Path-Conservative Method for the Compressible Non-Conservative Two-Phase Flow
JO - Communications in Computational Physics
VL - 2
SP - 309
EP - 331
PY - 2018
DA - 2018/08
SN - 24
DO - http://doi.org/10.4208/cicp.OA-2017-0097
UR - https://global-sci.org/intro/article_detail/cicp/12242.html
KW - Two-phase flow, non-conservative form, hyperbolic equations, Riemann Solver, path-conservative approach.
AB - <p style="text-align: justify;">A theoretical solution of the Riemann problem to the two-phase flow model
in non-conservative form of Saurel and Abgrall is presented under the assumption that
all the nonlinear waves are shocks. The solution, called 4-shock Riemann solver, is then
utilized to construct a path-conservative scheme for numerical solution of a general
initial boundary value problem for the two-phase flow model in the non-conservative
form.<br/>Moreover, a high-order path-conservative scheme of Godunov type is given via the
MUSCL reconstruction and the Runge-Kutta technique first in one dimension, based
on the 4-shock Riemann solver, and then extended to the two-dimensional case by dimensional splitting. A number of numerical tests are carried out and numerical results
demonstrate the accuracy and robustness of our scheme in the numerical solution of
the five-equations model for two-phase flow.</p>