# Numerical prediction of interfacial instabilities: Sharp interface method (SIM)

## Abstract

We introduce a sharp interface method (SIM) for the direct numerical simulation of unstable fluid-fluid interfaces. The method is based on the level set approach and the structured adaptive mesh refinement technology, endowed with a corridor of irregular, cut-cell grids that resolve the interfacial region to third-order spatial accuracy. Key in that regard are avoidance of numerical mixing, and a least-squares interpolation method that is supported by irregular datasets distinctly on each side of the interface. Results on test problems show our method to be free of the spurious current problem of the continuous surface force method and to converge, on grid refinement, at near-theoretical rates. Simulations of unstable Rayleigh-Taylor and viscous Kelvin-Helmholtz flows are found to converge at near-theoretical rates to the exact results over a wide range of conditions. Further, we show predictions of neutral-stability maps of the viscous Kelvin-Helmholtz flows (Yih instability), as well as self-selection of the most unstable wave-number in multimode simulations of Rayleigh-Taylor instability. All these results were obtained with a simple seeding of random infinitesimal disturbances of interface-shape, as opposed to seeding by a complete eigenmode. For other than elementary flows the latter would normally not be available, and extremely difficult to obtainmore »

- Authors:

- Center for Risk Studies and Safety, University of California, Santa Barbara (United States), E-mail: robert.nourgaliev@inl.gov
- NASA Glenn Research Center, Aeropropulsion Division, Cleveland (United States), E-mail: meng-sing.liou@grc.nasa.gov
- Center for Risk Studies and Safety, University of California, Santa Barbara (United States), E-mail: theo@engr.ucsb.edu

- Publication Date:

- OSTI Identifier:
- 21028320

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 227; Journal Issue: 8; Other Information: DOI: 10.1016/j.jcp.2007.12.008; PII: S0021-9991(07)00556-6; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; HELMHOLTZ INSTABILITY; INTERPOLATION; LEAST SQUARE FIT; RANDOMNESS; RAYLEIGH-TAYLOR INSTABILITY; SIMULATION; SURFACE FORCES

### Citation Formats

```
Nourgaliev, R.R., Liou, M.-S., and Theofanous, T.G.
```*Numerical prediction of interfacial instabilities: Sharp interface method (SIM)*. United States: N. p., 2008.
Web. doi:10.1016/j.jcp.2007.12.008.

```
Nourgaliev, R.R., Liou, M.-S., & Theofanous, T.G.
```*Numerical prediction of interfacial instabilities: Sharp interface method (SIM)*. United States. https://doi.org/10.1016/j.jcp.2007.12.008

```
Nourgaliev, R.R., Liou, M.-S., and Theofanous, T.G. Tue .
"Numerical prediction of interfacial instabilities: Sharp interface method (SIM)". United States. https://doi.org/10.1016/j.jcp.2007.12.008.
```

```
@article{osti_21028320,
```

title = {Numerical prediction of interfacial instabilities: Sharp interface method (SIM)},

author = {Nourgaliev, R.R. and Liou, M.-S. and Theofanous, T.G.},

abstractNote = {We introduce a sharp interface method (SIM) for the direct numerical simulation of unstable fluid-fluid interfaces. The method is based on the level set approach and the structured adaptive mesh refinement technology, endowed with a corridor of irregular, cut-cell grids that resolve the interfacial region to third-order spatial accuracy. Key in that regard are avoidance of numerical mixing, and a least-squares interpolation method that is supported by irregular datasets distinctly on each side of the interface. Results on test problems show our method to be free of the spurious current problem of the continuous surface force method and to converge, on grid refinement, at near-theoretical rates. Simulations of unstable Rayleigh-Taylor and viscous Kelvin-Helmholtz flows are found to converge at near-theoretical rates to the exact results over a wide range of conditions. Further, we show predictions of neutral-stability maps of the viscous Kelvin-Helmholtz flows (Yih instability), as well as self-selection of the most unstable wave-number in multimode simulations of Rayleigh-Taylor instability. All these results were obtained with a simple seeding of random infinitesimal disturbances of interface-shape, as opposed to seeding by a complete eigenmode. For other than elementary flows the latter would normally not be available, and extremely difficult to obtain if at all. Sample comparisons with our code adapted to mimic typical diffuse interface treatments were not satisfactory for shear-dominated flows. On the other hand the sharp dynamics of our method would appear to be compatible and possibly advantageous to any interfacial flow algorithm in which the interface is represented as a discrete Heaviside function.},

doi = {10.1016/j.jcp.2007.12.008},

url = {https://www.osti.gov/biblio/21028320},
journal = {Journal of Computational Physics},

issn = {0021-9991},

number = 8,

volume = 227,

place = {United States},

year = {2008},

month = {4}

}