## A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows [A robust and efficient finite volume method for compressible viscous two-phase flows]

## Abstract

A robust and efficient density-based finite volume method is developed for solving the six-equation single pressure system of two-phase flows at all speeds on hybrid unstructured grids. Unlike conventional approaches where an expensive exact Riemann solver is normally required for computing numerical fluxes at the two-phase interfaces in addition to AUSM-type fluxes for single-phase interfaces in order to maintain stability and robustness in cases involving interactions of strong pressure and void-fraction discontinuities, a volume-fraction coupling term for the AUSM ^{+}-up fluxes is introduced in this work to impart the required robustness without the need of the exact Riemann solver. The resulting method is significantly less expensive in regions where otherwise the Riemann solver would be invoked. A transformation from conservative variables to primitive variables is presented and the primitive variables are then solved in the implicit method in order for the current finite volume method to be able to solve, effectively and efficiently, low Mach number flows in traditional multiphase applications, which otherwise is a great challenge for the standard density-based algorithms. Here, a number of benchmark test cases are presented to assess the performance and robustness of the developed finite volume method for both inviscid and viscous two-phase flowmore »

- Authors:

- North Carolina State Univ., Raleigh, NC (United States)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); UT-Battelle LLC/ORNL, Oak Ridge, TN (Unted States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1543562

- Alternate Identifier(s):
- OSTI ID: 1532775

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 371; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Computer Science; Physics; Two-fluid model; Six equation; All-speed methods

### Citation Formats

```
Pandare, Aditya K., and Luo, Hong. A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows [A robust and efficient finite volume method for compressible viscous two-phase flows]. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2018.05.018.
```

```
Pandare, Aditya K., & Luo, Hong. A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows [A robust and efficient finite volume method for compressible viscous two-phase flows]. United States. doi:10.1016/j.jcp.2018.05.018.
```

```
Pandare, Aditya K., and Luo, Hong. Fri .
"A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows [A robust and efficient finite volume method for compressible viscous two-phase flows]". United States. doi:10.1016/j.jcp.2018.05.018. https://www.osti.gov/servlets/purl/1543562.
```

```
@article{osti_1543562,
```

title = {A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows [A robust and efficient finite volume method for compressible viscous two-phase flows]},

author = {Pandare, Aditya K. and Luo, Hong},

abstractNote = {A robust and efficient density-based finite volume method is developed for solving the six-equation single pressure system of two-phase flows at all speeds on hybrid unstructured grids. Unlike conventional approaches where an expensive exact Riemann solver is normally required for computing numerical fluxes at the two-phase interfaces in addition to AUSM-type fluxes for single-phase interfaces in order to maintain stability and robustness in cases involving interactions of strong pressure and void-fraction discontinuities, a volume-fraction coupling term for the AUSM+-up fluxes is introduced in this work to impart the required robustness without the need of the exact Riemann solver. The resulting method is significantly less expensive in regions where otherwise the Riemann solver would be invoked. A transformation from conservative variables to primitive variables is presented and the primitive variables are then solved in the implicit method in order for the current finite volume method to be able to solve, effectively and efficiently, low Mach number flows in traditional multiphase applications, which otherwise is a great challenge for the standard density-based algorithms. Here, a number of benchmark test cases are presented to assess the performance and robustness of the developed finite volume method for both inviscid and viscous two-phase flow problems. The numerical results indicate that the current density-based method provides an attractive and viable alternative to its pressure-based counterpart for compressible two-phase flows at all speeds.},

doi = {10.1016/j.jcp.2018.05.018},

journal = {Journal of Computational Physics},

number = C,

volume = 371,

place = {United States},

year = {2018},

month = {5}

}

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