# An enhanced AUSM ^{+}-up scheme for high-speed compressible two-phase flows on hybrid grids

## Abstract

Here in this work, an enhanced AUSM ^{+}-up scheme is presented for high-speed compressible two-phase flows using a six-equation two-fluid single-pressure model. Based on the observation that the AUSM ^{+}-up flux function does not take into account relative velocity between the two phases and thus is not stable and robust for computation of two-phase flows involving interaction of strong shock waves and material interfaces, the enhancement is in the form of a volume fraction coupling term and a modification of the velocity diffusion term, both proportional to the relative velocity between the two phases. These modifications in the flux function obviate the need to employ the exact Riemann solver, leading to a significantly less expensive yet robust flux scheme. Furthermore, the Tangent of Hyperbola for INterface Capturing (THINC) scheme is used in order to provide a sharp resolution for material interfaces. A number of benchmark test cases are presented to assess the performance and robustness of the enhanced AUSM ^{+}-up scheme for compressible two-phase flows on hybrid unstructured grids. Lastly, the numerical experiments demonstrate that the enhanced AUSM ^{+}-up scheme along with THINC scheme can efficiently compute high-speed two-fluid flows such as shock–bubble interactions, while accurately capturing material interfaces.

- Authors:

- North Carolina State Univ., Raleigh, NC (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1482001

- Report Number(s):
- LA-UR-18-24062

Journal ID: ISSN 0938-1287

- Grant/Contract Number:
- AC52-06NA25396; AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Shock Waves

- Additional Journal Information:
- Journal Name: Shock Waves; Journal ID: ISSN 0938-1287

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; Two-fluid model; shock waves; material interfaces; AUSM

### Citation Formats

```
Pandare, Aditya Kiran, Luo, Hong, and Bakosi, Jozsef. An enhanced AUSM+-up scheme for high-speed compressible two-phase flows on hybrid grids. United States: N. p., 2018.
Web. doi:10.1007/s00193-018-0861-x.
```

```
Pandare, Aditya Kiran, Luo, Hong, & Bakosi, Jozsef. An enhanced AUSM+-up scheme for high-speed compressible two-phase flows on hybrid grids. United States. doi:10.1007/s00193-018-0861-x.
```

```
Pandare, Aditya Kiran, Luo, Hong, and Bakosi, Jozsef. Tue .
"An enhanced AUSM+-up scheme for high-speed compressible two-phase flows on hybrid grids". United States. doi:10.1007/s00193-018-0861-x. https://www.osti.gov/servlets/purl/1482001.
```

```
@article{osti_1482001,
```

title = {An enhanced AUSM+-up scheme for high-speed compressible two-phase flows on hybrid grids},

author = {Pandare, Aditya Kiran and Luo, Hong and Bakosi, Jozsef},

abstractNote = {Here in this work, an enhanced AUSM+-up scheme is presented for high-speed compressible two-phase flows using a six-equation two-fluid single-pressure model. Based on the observation that the AUSM+-up flux function does not take into account relative velocity between the two phases and thus is not stable and robust for computation of two-phase flows involving interaction of strong shock waves and material interfaces, the enhancement is in the form of a volume fraction coupling term and a modification of the velocity diffusion term, both proportional to the relative velocity between the two phases. These modifications in the flux function obviate the need to employ the exact Riemann solver, leading to a significantly less expensive yet robust flux scheme. Furthermore, the Tangent of Hyperbola for INterface Capturing (THINC) scheme is used in order to provide a sharp resolution for material interfaces. A number of benchmark test cases are presented to assess the performance and robustness of the enhanced AUSM+-up scheme for compressible two-phase flows on hybrid unstructured grids. Lastly, the numerical experiments demonstrate that the enhanced AUSM+-up scheme along with THINC scheme can efficiently compute high-speed two-fluid flows such as shock–bubble interactions, while accurately capturing material interfaces.},

doi = {10.1007/s00193-018-0861-x},

journal = {Shock Waves},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {9}

}

#### Figures / Tables:

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*