Year: 2018
Communications in Computational Physics, Vol. 24 (2018), Iss. 2 : pp. 309–331
Abstract
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.
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2017-0097
Communications in Computational Physics, Vol. 24 (2018), Iss. 2 : pp. 309–331
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Two-phase flow non-conservative form hyperbolic equations Riemann Solver path-conservative approach.