# Direct numerical simulations of type Ia supernovae flames I: The landau-darrieus instability

## Abstract

Planar flames are intrinsically unstable in open domains due to the thermal expansion across the burning front--the Landau-Darrieus instability. This instability leads to wrinkling and growth of the flame surface, and corresponding acceleration of the flame, until it is stabilized by cusp formation. We look at the Landau-Darrieus in stability for C/O thermonuclear flames at conditions relevant to the late stages of a Type Ia supernova explosion. Two-dimensional direct numerical simulations of both single-mode and multi-mode perturbations using a low Mach number hydrodynamics code are presented. We show the effect of the instability on the flame speed as a function of both the density and domain size, demonstrate the existence of the small scale cutoff to the growth of the instability, and look for the proposed breakdown of the non-linear stabilization at low densities. The effects of curvature on the flame as quantified through measurements of the growth rate and computation of the corresponding Markstein number. While accelerations of a few percent are observed, they are too small to have any direct outcome on the supernova explosion.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Director. Office of Science. Office of Advanced Scientific Computing Research. Mathmatical Information and Computational Sciences Division, Oak Ridge National Laboratory Contract DE-AC05-00OR22725, University of California Santa Cruz. Supernova Science Center Grant DE-FC02-01ER41176; National Science Foundation Grant AST-0079757

- OSTI Identifier:
- 842899

- Report Number(s):
- LBNL-54088

R&D Project: K11001; TRN: US200516%%1107

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Journal Article

- Resource Relation:
- Other Information: Journal Publication Date: 05/10/2004

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCELERATION; BREAKDOWN; CUSPED GEOMETRIES; FLAMES; HYDRODYNAMICS; INSTABILITY; MACH NUMBER; STABILITY; STABILIZATION; SUPERNOVAE; THERMAL EXPANSION; VELOCITY; Type Ia Supernova CFD Landau-Darrieus Instability

### Citation Formats

```
Bell, J B, Day, M S, Rendleman, C A, Woosley, S E, and Zingale, M.
```*Direct numerical simulations of type Ia supernovae flames I: The landau-darrieus instability*. United States: N. p., 2003.
Web.

```
Bell, J B, Day, M S, Rendleman, C A, Woosley, S E, & Zingale, M.
```*Direct numerical simulations of type Ia supernovae flames I: The landau-darrieus instability*. United States.

```
Bell, J B, Day, M S, Rendleman, C A, Woosley, S E, and Zingale, M. Mon .
"Direct numerical simulations of type Ia supernovae flames I: The landau-darrieus instability". United States. https://www.osti.gov/servlets/purl/842899.
```

```
@article{osti_842899,
```

title = {Direct numerical simulations of type Ia supernovae flames I: The landau-darrieus instability},

author = {Bell, J B and Day, M S and Rendleman, C A and Woosley, S E and Zingale, M},

abstractNote = {Planar flames are intrinsically unstable in open domains due to the thermal expansion across the burning front--the Landau-Darrieus instability. This instability leads to wrinkling and growth of the flame surface, and corresponding acceleration of the flame, until it is stabilized by cusp formation. We look at the Landau-Darrieus in stability for C/O thermonuclear flames at conditions relevant to the late stages of a Type Ia supernova explosion. Two-dimensional direct numerical simulations of both single-mode and multi-mode perturbations using a low Mach number hydrodynamics code are presented. We show the effect of the instability on the flame speed as a function of both the density and domain size, demonstrate the existence of the small scale cutoff to the growth of the instability, and look for the proposed breakdown of the non-linear stabilization at low densities. The effects of curvature on the flame as quantified through measurements of the growth rate and computation of the corresponding Markstein number. While accelerations of a few percent are observed, they are too small to have any direct outcome on the supernova explosion.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2003},

month = {11}

}