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Volume 24, Issue 2
A Second-Order Path-Conservative Method for the Compressible Non-Conservative Two-Phase Flow

Yueling Jia, Song Jiang, Baolin Tian & Eleuterio F. Toro

DOI: 10.4208/cicp.OA-2017-0097

Commun. Comput. Phys., 24 (2018), pp. 309-331.

Published online: 2018-08

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  • 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.

  • Keywords

Two-phase flow, non-conservative form, hyperbolic equations, Riemann Solver, path-conservative approach.

  • AMS Subject Headings

35Q53, 35E15, 74C05, 74F10, 74M20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-309, author = {}, title = {A Second-Order Path-Conservative Method for the Compressible Non-Conservative Two-Phase Flow}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0097}, url = {http://global-sci.org/intro/article_detail/cicp/12242.html} }
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 -

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.

Yueling Jia, Song Jiang, Baolin Tian & Eleuterio F. Toro. (2020). A Second-Order Path-Conservative Method for the Compressible Non-Conservative Two-Phase Flow. Communications in Computational Physics. 24 (2). 309-331. doi:10.4208/cicp.OA-2017-0097
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